Control system

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Control_system 

The centrifugal governor is an early proportional control mechanism.

A control system manages, commands, directs, or regulates the behavior of other devices or systems using control loops. It can range from a single home heating controller using a thermostat controlling a domestic boiler to large industrial control systems which are used for controlling processes or machines. The control systems are designed via control engineering process.

For continuously modulated control, a feedback controller is used to automatically control a process or operation. The control system compares the value or status of the process variable (PV) being controlled with the desired value or setpoint (SP), and applies the difference as a control signal to bring the process variable output of the plant to the same value as the setpoint.

For sequential and combinational logic, software logic, such as in a programmable logic controller, is used.

Open-loop and closed-loop control

There are two common classes of control action: open loop and closed loop. In an open-loop control system, the control action from the controller is independent of the process variable. An example of this is a central heating boiler controlled only by a timer. The control action is the switching on or off of the boiler. The process variable is the building temperature. This controller operates the heating system for a constant time regardless of the temperature of the building.

In a closed-loop control system, the control action from the controller is dependent on the desired and actual process variable. In the case of the boiler analogy, this would utilize a thermostat to monitor the building temperature, and feed back a signal to ensure the controller output maintains the building temperature close to that set on the thermostat. A closed-loop controller has a feedback loop which ensures the controller exerts a control action to control a process variable at the same value as the setpoint. For this reason, closed-loop controllers are also called feedback controllers.

Feedback control systems

Example of a single industrial control loop; showing continuously modulated control of process flow.

 

A basic feedback loop

In the case of linear feedback systems, a control loop including sensors, control algorithms, and actuators is arranged in an attempt to regulate a variable at a setpoint (SP). An everyday example is the cruise control on a road vehicle; where external influences such as hills would cause speed changes, and the driver has the ability to alter the desired set speed. The PID algorithm in the controller restores the actual speed to the desired speed in the optimum way, with minimal delay or overshoot, by controlling the power output of the vehicle's engine.

Control systems that include some sensing of the results they are trying to achieve are making use of feedback and can adapt to varying circumstances to some extent. Open-loop control systems do not make use of feedback, and run only in pre-arranged ways.

Logic control

Logic control systems for industrial and commercial machinery were historically implemented by interconnected electrical relays and cam timers using ladder logic. Today, most such systems are constructed with microcontrollers or more specialized programmable logic controllers (PLCs). The notation of ladder logic is still in use as a programming method for PLCs.

Logic controllers may respond to switches and sensors, and can cause the machinery to start and stop various operations through the use of actuators. Logic controllers are used to sequence mechanical operations in many applications. Examples include elevators, washing machines and other systems with interrelated operations. An automatic sequential control system may trigger a series of mechanical actuators in the correct sequence to perform a task. For example, various electric and pneumatic transducers may fold and glue a cardboard box, fill it with product and then seal it in an automatic packaging machine.

PLC software can be written in many different ways – ladder diagrams, SFC (sequential function charts) or statement lists.

On–off control

Main article: Bang–bang control

On–off control uses a feedback controller that switches abruptly between two states. A simple bi-metallic domestic thermostat can be described as an on-off controller. When the temperature in the room (PV) goes below the user setting (SP), the heater is switched on. Another example is a pressure switch on an air compressor. When the pressure (PV) drops below the setpoint (SP) the compressor is powered. Refrigerators and vacuum pumps contain similar mechanisms. Simple on–off control systems like these can be cheap and effective.

Linear control

Linear control systems use negative feedback to produce a control signal to maintain the controlled PV at the desired SP. There are several types of linear control systems with different capabilities.

Proportional control

Main article: Proportional control

 

Step responses for a second order system defined by the transfer function ${\displaystyle H(s)={\frac {\omega _{n}^{2}}{s^{2}+2\zeta \omega _{n}s+\omega _{n}^{2}}}}$, where ${\displaystyle \zeta }$ is the damping ratio and ${\displaystyle \omega _{n}}$ is the undamped natural frequency.

Proportional control is a type of linear feedback control system in which a correction is applied to the controlled variable which is proportional to the difference between the desired value (SP) and the measured value (PV). Two classic mechanical examples are the toilet bowl float proportioning valve and the fly-ball governor.

The proportional control system is more complex than an on–off control system, but simpler than a proportional-integral-derivative (PID) control system used, for instance, in an automobile cruise control. On–off control will work for systems that do not require high accuracy or responsiveness, but is not effective for rapid and timely corrections and responses. Proportional control overcomes this by modulating the manipulated variable (MV), such as a control valve, at a gain level that avoids instability, but applies correction as fast as practicable by applying the optimum quantity of proportional correction.

A drawback of proportional control is that it cannot eliminate the residual SP–PV error, as it requires an error to generate a proportional output. A PI controller can be used to overcome this. The PI controller uses a proportional term (P) to remove the gross error, and an integral term (I) to eliminate the residual offset error by integrating the error over time.

In some systems, there are practical limits to the range of the MV. For example, a heater has a limit to how much heat it can produce and a valve can open only so far. Adjustments to the gain simultaneously alter the range of error values over which the MV is between these limits. The width of this range, in units of the error variable and therefore of the PV, is called the proportional band (PB).

Furnace example

When controlling the temperature of an industrial furnace, it is usually better to control the opening of the fuel valve in proportion to the current needs of the furnace. This helps avoid thermal shocks and applies heat more effectively.

At low gains, only a small corrective action is applied when errors are detected. The system may be safe and stable, but may be sluggish in response to changing conditions. Errors will remain uncorrected for relatively long periods of time and the system is overdamped. If the proportional gain is increased, such systems become more responsive and errors are dealt with more quickly. There is an optimal value for the gain setting when the overall system is said to be critically damped. Increases in loop gain beyond this point lead to oscillations in the PV and such a system is underdamped. Adjusting gain to achieve critically damped behavior is known as tuning the control system.

In the underdamped case, the furnace heats quickly. Once the setpoint is reached, stored heat within the heater sub-system and in the walls of the furnace will keep the measured temperature rising beyond what is required. After rising above the setpoint, the temperature falls back and eventually heat is applied again. Any delay in reheating the heater sub-system allows the furnace temperature to fall further below setpoint and the cycle repeats. The temperature oscillations that an underdamped furnace control system produces are undesirable.

In a critically damped system, as the temperature approaches the setpoint, the heat input begins to be reduced, the rate of heating of the furnace has time to slow and the system avoids overshoot. Overshoot is also avoided in an overdamped system but an overdamped system is unnecessarily slow to initially reach setpoint respond to external changes to the system, e.g. opening the furnace door.

PID control

A block diagram of a PID controller

 

Effects of varying PID parameters (K_p,K_i,K_d) on the step response of a system.

 

Main article: PID controller

Pure proportional controllers must operate with residual error in the system. Though PI controllers eliminate this error they can still be sluggish or produce oscillations. The PID controller addresses these final shortcomings by introducing a derivative (D) action to retain stability while responsiveness is improved.

Derivative action

The derivative is concerned with the rate-of-change of the error with time: If the measured variable approaches the setpoint rapidly, then the actuator is backed off early to allow it to coast to the required level; conversely, if the measured value begins to move rapidly away from the setpoint, extra effort is applied—in proportion to that rapidity to help move it back.

On control systems involving motion control of a heavy item like a gun or camera on a moving vehicle, the derivative action of a well-tuned PID controller can allow it to reach and maintain a setpoint better than most skilled human operators. If derivative action is over-applied, it can, however, lead to oscillations.

Integral action

Change of response of a second-order system to a step input for varying Ki values.

The integral term magnifies the effect of long-term steady-state errors, applying an ever-increasing effort until the error is removed. In the example of the furnace above working at various temperatures, if the heat being applied does not bring the furnace up to setpoint, for whatever reason, integral action increasingly moves the proportional band relative to the setpoint until the PV error is reduced to zero and the setpoint is achieved.

Ramp up % per minute

Some controllers include the option to limit the "ramp up % per minute". This option can be very helpful in stabilizing small boilers (3 MBTUH), especially during the summer, during light loads. A utility boiler "unit may be required to change load at a rate of as much as 5% per minute (IEA Coal Online - 2, 2007)".

Other techniques

It is possible to filter the PV or error signal. Doing so can help reduce instability or oscillations by reducing the response of the system to undesirable frequencies. Many systems have a resonant frequency. By filtering out that frequency, stronger overall feedback can be applied before oscillation occurs, making the system more responsive without shaking itself apart.

Feedback systems can be combined. In cascade control, one control loop applies control algorithms to a measured variable against a setpoint but then provides a varying setpoint to another control loop rather than affecting process variables directly. If a system has several different measured variables to be controlled, separate control systems will be present for each of them.

Control engineering in many applications produces control systems that are more complex than PID control. Examples of such field applications include fly-by-wire aircraft control systems, chemical plants, and oil refineries. Model predictive control systems are designed using specialized computer-aided-design software and empirical mathematical models of the system to be controlled.

Fuzzy logic

Main article: Fuzzy logic

Fuzzy logic is an attempt to apply the easy design of logic controllers to the control of complex continuously varying systems. Basically, a measurement in a fuzzy logic system can be partly true.

The rules of the system are written in natural language and translated into fuzzy logic. For example, the design for a furnace would start with: "If the temperature is too high, reduce the fuel to the furnace. If the temperature is too low, increase the fuel to the furnace."

Measurements from the real world (such as the temperature of a furnace) are fuzzified and logic is calculated arithmetic, as opposed to Boolean logic, and the outputs are de-fuzzified to control equipment.

When a robust fuzzy design is reduced to a single, quick calculation, it begins to resemble a conventional feedback loop solution and it might appear that the fuzzy design was unnecessary. However, the fuzzy logic paradigm may provide scalability for large control systems where conventional methods become unwieldy or costly to derive.

Fuzzy electronics is an electronic technology that uses fuzzy logic instead of the two-value logic more commonly used in digital electronics.

Physical implementation

A DCS control room where large screens display plant information. The operators can view and control any part of the process from their computer screens, whilst retaining a plant overview on the larger screens.

 

A control panel of a hydraulic heat press machine

The range of control system implementation is from compact controllers often with dedicated software for a particular machine or device, to distributed control systems for industrial process control for a large physical plant.

Logic systems and feedback controllers are usually implemented with programmable logic controllers.

Null hypothesis

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Null_hypothesis 

In inferential statistics, the null hypothesis (often denoted H₀) is that two possibilities are the same. The null hypothesis is that the observed difference is due to chance alone. Using statistical tests, it is possible to calculate the likelihood that the null hypothesis is true.

Basic definitions

The null hypothesis and the alternative hypothesis are types of conjectures used in statistical tests, which are formal methods of reaching conclusions or making decisions on the basis of data. The hypotheses are conjectures about a statistical model of the population, which are based on a sample of the population. The tests are core elements of statistical inference, heavily used in the interpretation of scientific experimental data, to separate scientific claims from statistical noise.

"The statement being tested in a test of statistical significance is called the null hypothesis. The test of significance is designed to assess the strength of the evidence against the null hypothesis. Usually, the null hypothesis is a statement of 'no effect' or 'no difference'." It is often symbolized as H₀.

The statement that is being tested against the null hypothesis is the alternative hypothesis. Symbols include H₁ and H_a.

Statistical significance test: "Very roughly, the procedure for deciding goes like this: Take a random sample from the population. If the sample data are consistent with the null hypothesis, then do not reject the null hypothesis; if the sample data are inconsistent with the null hypothesis, then reject the null hypothesis and conclude that the alternative hypothesis is true."

The following adds context and nuance to the basic definitions.

Given the test scores of two random samples, one of men and one of women, does one group differ from the other? A possible null hypothesis is that the mean male score is the same as the mean female score:

H₀: μ₁ = μ₂

where

H₀ = the null hypothesis,

μ₁ = the mean of population 1, and

μ₂ = the mean of population 2.

A stronger null hypothesis is that the two samples are drawn from the same population, such that the variances and shapes of the distributions are also equal.

Terminology

Main article: Statistical hypothesis testing § Definition of terms

Simple hypothesis

Any hypothesis which specifies the population distribution completely. For such a hypothesis the sampling distribution of any statistic is a function of the sample size alone.

Composite hypothesis

Any hypothesis which does not specify the population distribution completely. Example: A hypothesis specifying a normal distribution with a specified mean and an unspecified variance.

The simple/composite distinction was made by Neyman and Pearson.

Exact hypothesis

Any hypothesis that specifies an exact parameter value. Example: μ = 100. Synonym: point hypothesis.

Inexact hypothesis

Those specifying a parameter range or interval. Examples: μ ≤ 100; 95 ≤ μ ≤ 105.

Fisher required an exact null hypothesis for testing (see the quotations below).

A one-tailed hypothesis (tested using a one-sided test) is an inexact hypothesis in which the value of a parameter is specified as being either:

• above or equal to a certain value, or
• below or equal to a certain value.

A one-tailed hypothesis is said to have directionality.

Fisher's original (lady tasting tea) example was a one-tailed test. The null hypothesis was asymmetric. The probability of guessing all cups correctly was the same as guessing all cups incorrectly, but Fisher noted that only guessing correctly was compatible with the lady's claim.

Examples

• Are boys taller than girls at age eight? The null hypothesis is "they are the same average height."
• Do teens use restaurant locator apps more than adults? The null hypothesis is "they use these apps the same average amount."
• Does eating an apple a day reduce visits to the doctor? The null hypothesis is "apples do not reduce doctor visits."
• Are small states more densely populated than large states? The null hypothesis is "small states have the same population density as large states."
• Are large states more densely populated than small states? The null hypothesis is "large states have the same population density as small states."
• Does the size of a state affect population density? The null hypothesis is "all states have the same population density."
• Do large dogs prefer large food kibbles? The null hypothesis is "large dogs have no preference for large kibble size."
• Do cats prefer fish or milk? The null hypothesis is "cats have no preference; they like them the same."

Technical description

The null hypothesis is a default hypothesis that a quantity to be measured is zero (null). Typically, the quantity to be measured is the difference between two situations. For instance, trying to determine if there is a positive proof that an effect has occurred or that samples derive from different batches.

The null hypothesis states that a quantity (of interest) is larger or equal to zero and smaller or equal to zero. If either requirement can be positively overturned, the null hypothesis is "excluded from the realm of possibilities".

The null hypothesis is generally assumed to remain possibly true. Multiple analyses can be performed to show how the hypothesis should either be rejected or excluded e.g. having a high confidence level, thus demonstrating a statistically significant difference. This is demonstrated by showing that zero is outside of the specified confidence interval of the measurement on either side, typically within the real numbers. Failure to exclude the null hypothesis (with any confidence) does not logically confirm or support the (unprovable) null hypothesis. (When it is proven that something is e.g. bigger than x, it does not necessarily imply it is plausible that it is smaller or equal than x; it may instead be a poor quality measurement with low accuracy. Confirming the null hypothesis two-sided would amount to positively proving it is bigger or equal than 0 and to positively proving it is smaller or equal than 0; this is something for which infinite accuracy is needed as well as exactly zero effect, neither of which normally are realistic. Also measurements will never indicate a non-zero probability of exactly zero difference.) So failure of an exclusion of a null hypothesis amounts to a "don't know" at the specified confidence level; it does not immediately imply null somehow, as the data may already show a (less strong) indication for a non-null. The used confidence level does absolutely certainly not correspond to the likelihood of null at failing to exclude; in fact in this case a high used confidence level expands the still plausible range.

A non-null hypothesis can have the following meanings, depending on the author a) a value other than zero is used, b) some margin other than zero is used and c) the "alternative" hypothesis.

Testing (excluding or failing to exclude) the null hypothesis provides evidence that there are (or are not) statistically sufficient grounds to believe there is a relationship between two phenomena (e.g., that a potential treatment has a non-zero effect, either way). Testing the null hypothesis is a central task in statistical hypothesis testing in the modern practice of science. There are precise criteria for excluding or not excluding a null hypothesis at a certain confidence level. The confidence level should indicate the likelihood that much more and better data would still be able to exclude the null hypothesis on the same side.

The concept of a null hypothesis is used differently in two approaches to statistical inference. In the significance testing approach of Ronald Fisher, a null hypothesis is rejected if the observed data are significantly unlikely to have occurred if the null hypothesis were true. In this case, the null hypothesis is rejected and an alternative hypothesis is accepted in its place. If the data are consistent with the null hypothesis statistically possibly true, then the null hypothesis is not rejected. In neither case is the null hypothesis or its alternative proven; with better or more data, the null may still be rejected. This is analogous to the legal principle of presumption of innocence, in which a suspect or defendant is assumed to be innocent (null is not rejected) until proven guilty (null is rejected) beyond a reasonable doubt (to a statistically significant degree).

In the hypothesis testing approach of Jerzy Neyman and Egon Pearson, a null hypothesis is contrasted with an alternative hypothesis, and the two hypotheses are distinguished on the basis of data, with certain error rates. It is used in formulating answers in research.

Statistical inference can be done without a null hypothesis, by specifying a statistical model corresponding to each candidate hypothesis, and by using model selection techniques to choose the most appropriate model. (The most common selection techniques are based on either Akaike information criterion or Bayes factor).

Principle

Hypothesis testing requires constructing a statistical model of what the data would look like if chance or random processes alone were responsible for the results. The hypothesis that chance alone is responsible for the results is called the null hypothesis. The model of the result of the random process is called the distribution under the null hypothesis. The obtained results are compared with the distribution under the null hypothesis, and the likelihood of finding the obtained results is thereby determined.

Hypothesis testing works by collecting data and measuring how likely the particular set of data is (assuming the null hypothesis is true), when the study is on a randomly selected representative sample. The null hypothesis assumes no relationship between variables in the population from which the sample is selected.

If the data-set of a randomly selected representative sample is very unlikely relative to the null hypothesis (defined as being part of a class of sets of data that only rarely will be observed), the experimenter rejects the null hypothesis, concluding it (probably) is false. This class of data-sets is usually specified via a test statistic, which is designed to measure the extent of apparent departure from the null hypothesis. The procedure works by assessing whether the observed departure, measured by the test statistic, is larger than a value defined, so that the probability of occurrence of a more extreme value is small under the null hypothesis (usually in less than either 5% or 1% of similar data-sets in which the null hypothesis does hold).

If the data do not contradict the null hypothesis, then only a weak conclusion can be made: namely, that the observed data set provides insufficient evidence against the null hypothesis. In this case, because the null hypothesis could be true or false, in some contexts this is interpreted as meaning that the data give insufficient evidence to make any conclusion, while in other contexts, it is interpreted as meaning that there is not sufficient evidence to support changing from a currently useful regime to a different one. Nevertheless, if at this point the effect appears likely and/or large enough, there may be an incentive to further investigate, such as running a bigger sample.

For instance, a certain drug may reduce the risk of having a heart attack. Possible null hypotheses are "this drug does not reduce the risk of having a heart attack" or "this drug has no effect on the risk of having a heart attack". The test of the hypothesis consists of administering the drug to half of the people in a study group as a controlled experiment. If the data show a statistically significant change in the people receiving the drug, the null hypothesis is rejected.

Goals of null hypothesis tests

There are many types of significance tests for one, two or more samples, for means, variances and proportions, paired or unpaired data, for different distributions, for large and small samples; all have null hypotheses. There are also at least four goals of null hypotheses for significance tests:

• Technical null hypotheses are used to verify statistical assumptions. For example, the residuals between the data and a statistical model cannot be distinguished from random noise. If true, there is no justification for complicating the model.
• Scientific null assumptions are used to directly advance a theory. For example, the angular momentum of the universe is zero. If not true, the theory of the early universe may need revision.
• Null hypotheses of homogeneity are used to verify that multiple experiments are producing consistent results. For example, the effect of a medication on the elderly is consistent with that of the general adult population. If true, this strengthens the general effectiveness conclusion and simplifies recommendations for use.
• Null hypotheses that assert the equality of effect of two or more alternative treatments, for example, a drug and a placebo, are used to reduce scientific claims based on statistical noise. This is the most popular null hypothesis; It is so popular that many statements about significant testing assume such null hypotheses.

Rejection of the null hypothesis is not necessarily the real goal of a significance tester. An adequate statistical model may be associated with a failure to reject the null; the model is adjusted until the null is not rejected. The numerous uses of significance testing were well known to Fisher who discussed many in his book written a decade before defining the null hypothesis.

A statistical significance test shares much mathematics with a confidence interval. They are mutually illuminating. A result is often significant when there is confidence in the sign of a relationship (the interval does not include 0). Whenever the sign of a relationship is important, statistical significance is a worthy goal. This also reveals weaknesses of significance testing: A result can be significant without a good estimate of the strength of a relationship; significance can be a modest goal. A weak relationship can also achieve significance with enough data. Reporting both significance and confidence intervals is commonly recommended.

The varied uses of significance tests reduce the number of generalizations that can be made about all applications.

Choice of the null hypothesis

The choice of the null hypothesis is associated with sparse and inconsistent advice. Fisher mentioned few constraints on the choice and stated that many null hypotheses should be considered and that many tests are possible for each. The variety of applications and the diversity of goals suggests that the choice can be complicated. In many applications the formulation of the test is traditional. A familiarity with the range of tests available may suggest a particular null hypothesis and test. Formulating the null hypothesis is not automated (though the calculations of significance testing usually are). Sir David Cox said, "How [the] translation from subject-matter problem to statistical model is done is often the most critical part of an analysis".

A statistical significance test is intended to test a hypothesis. If the hypothesis summarizes a set of data, there is no value in testing the hypothesis on that set of data. Example: If a study of last year's weather reports indicates that rain in a region falls primarily on weekends, it is only valid to test that null hypothesis on weather reports from any other year. Testing hypotheses suggested by the data is circular reasoning that proves nothing; It is a special limitation on the choice of the null hypothesis.

A routine procedure is as follows: Start from the scientific hypothesis. Translate this to a statistical alternative hypothesis and proceed: "Because H_a expresses the effect that we wish to find evidence for, we often begin with H_a and then set up H₀ as the statement that the hoped-for effect is not present." This advice is reversed for modeling applications where we hope not to find evidence against the null.

A complex case example is as follows: The gold standard in clinical research is the randomized placebo-controlled double-blind clinical trial. But testing a new drug against a (medically ineffective) placebo may be unethical for a serious illness. Testing a new drug against an older medically effective drug raises fundamental philosophical issues regarding the goal of the test and the motivation of the experimenters. The standard "no difference" null hypothesis may reward the pharmaceutical company for gathering inadequate data. "Difference" is a better null hypothesis in this case, but statistical significance is not an adequate criterion for reaching a nuanced conclusion which requires a good numeric estimate of the drug's effectiveness. A "minor" or "simple" proposed change in the null hypothesis ((new vs old) rather than (new vs placebo)) can have a dramatic effect on the utility of a test for complex non-statistical reasons.

Directionality

Main article: One- and two-tailed tests

The choice of null hypothesis (H₀) and consideration of directionality (see "one-tailed test") is critical.

Tailedness of the null-hypothesis test

Consider the question of whether a tossed coin is fair (i.e. that on average it lands heads up 50% of the time) and an experiment where you toss the coin 5 times. A possible result of the experiment that we consider here is 5 heads. Let outcomes be considered unlikely with respect to an assumed distribution if their probability is lower than a significance threshold of 0.05.

A potential null hypothesis implying a one-tail test is "this coin is not biased toward heads". Beware that, in this context, the word "tail" takes two meanings: either as outcome of a single toss, or as region of extremal values in a probability distribution.

Indeed, with a fair coin the probability of this experiment outcome is 1/2⁵ = 0.031, which would be even lower if the coin were biased in favour of tails. Therefore, the observations are not likely enough for the null hypothesis to hold, and the test refutes it. Since the coin is ostensibly neither fair nor biased toward tails, the conclusion of the experiment is that the coin is biased towards heads.

Alternatively, a null hypothesis implying a two-tailed test is "this coin is fair". This one null hypothesis could be examined by looking out for either too many tails or too many heads in the experiments. The outcomes that would tend to refuse this null hypothesis are those with a large number of heads or a large number of tails, and our experiment with 5 heads would seem to belong to this class.

However, the probability of 5 tosses of the same kind, irrespective of whether these are head or tails, is twice as much as that of the 5-head occurrence singly considered. Hence, under this two-tailed null hypothesis, the observation receives a probability value of 0.063. Hence again, with the same significance threshold used for the one-tailed test (0.05), the same outcome is not statistically significant. Therefore, the two-tailed null hypothesis will be preserved in this case, not supporting the conclusion reached with the single-tailed null hypothesis, that the coin is biased towards heads.

This example illustrates that the conclusion reached from a statistical test may depend on the precise formulation of the null and alternative hypotheses.

Discussion

Fisher said, "the null hypothesis must be exact, that is free of vagueness and ambiguity, because it must supply the basis of the 'problem of distribution,' of which the test of significance is the solution", implying a more restrictive domain for H₀. According to this view, the null hypothesis must be numerically exact—it must state that a particular quantity or difference is equal to a particular number. In classical science, it is most typically the statement that there is no effect of a particular treatment; in observations, it is typically that there is no difference between the value of a particular measured variable and that of a prediction.

Most statisticians believe that it is valid to state direction as a part of null hypothesis, or as part of a null hypothesis/alternative hypothesis pair. However, the results are not a full description of all the results of an experiment, merely a single result tailored to one particular purpose. For example, consider an H₀ that claims the population mean for a new treatment is an improvement on a well-established treatment with population mean = 10 (known from long experience), with the one-tailed alternative being that the new treatment's mean > 10. If the sample evidence obtained through x-bar equals −200 and the corresponding t-test statistic equals −50, the conclusion from the test would be that there is no evidence that the new treatment is better than the existing one: it would not report that it is markedly worse, but that is not what this particular test is looking for. To overcome any possible ambiguity in reporting the result of the test of a null hypothesis, it is best to indicate whether the test was two-sided and, if one-sided, to include the direction of the effect being tested.

The statistical theory required to deal with the simple cases of directionality dealt with here, and more complicated ones, makes use of the concept of an unbiased test.

The directionality of hypotheses is not always obvious. The explicit null hypothesis of Fisher's Lady tasting tea example was that the Lady had no such ability, which led to a symmetric probability distribution. The one-tailed nature of the test resulted from the one-tailed alternate hypothesis (a term not used by Fisher). The null hypothesis became implicitly one-tailed. The logical negation of the Lady's one-tailed claim was also one-tailed. (Claim: Ability > 0; Stated null: Ability = 0; Implicit null: Ability ≤ 0).

Pure arguments over the use of one-tailed tests are complicated by the variety of tests. Some tests (for instance the χ² goodness of fit test) are inherently one-tailed. Some probability distributions are asymmetric. The traditional tests of 3 or more groups are two-tailed.

Advice concerning the use of one-tailed hypotheses has been inconsistent and accepted practice varies among fields. The greatest objection to one-tailed hypotheses is their potential subjectivity. A non-significant result can sometimes be converted to a significant result by the use of a one-tailed hypothesis (as the fair coin test, at the whim of the analyst). The flip side of the argument: One-sided tests are less likely to ignore a real effect. One-tailed tests can suppress the publication of data that differs in sign from predictions. Objectivity was a goal of the developers of statistical tests.

It is a common practice to use a one-tailed hypothesis by default. However, "If you do not have a specific direction firmly in mind in advance, use a two-sided alternative. Moreover, some users of statistics argue that we should always work with the two-sided alternative."

One alternative to this advice is to use three-outcome tests. It eliminates the issues surrounding directionality of hypotheses by testing twice, once in each direction and combining the results to produce three possible outcomes. Variations on this approach have a history, being suggested perhaps 10 times since 1950.

Disagreements over one-tailed tests flow from the philosophy of science. While Fisher was willing to ignore the unlikely case of the Lady guessing all cups of tea incorrectly (which may have been appropriate for the circumstances), medicine believes that a proposed treatment that kills patients is significant in every sense and should be reported and perhaps explained. Poor statistical reporting practices have contributed to disagreements over one-tailed tests. Statistical significance resulting from two-tailed tests is insensitive to the sign of the relationship; Reporting significance alone is inadequate. "The treatment has an effect" is the uninformative result of a two-tailed test. "The treatment has a beneficial effect" is the more informative result of a one-tailed test. "The treatment has an effect, reducing the average length of hospitalization by 1.5 days" is the most informative report, combining a two-tailed significance test result with a numeric estimate of the relationship between treatment and effect. Explicitly reporting a numeric result eliminates a philosophical advantage of a one-tailed test. An underlying issue is the appropriate form of an experimental science without numeric predictive theories: A model of numeric results is more informative than a model of effect signs (positive, negative or unknown) which is more informative than a model of simple significance (non-zero or unknown); in the absence of numeric theory signs may suffice.

History of statistical tests

Main article: Statistical hypothesis testing § Origins and early controversy

The history of the null and alternative hypotheses is embedded in the history of statistical tests.

• Before 1925: There are occasional transient traces of statistical tests for centuries in the past, which provide early examples of null hypotheses. In the late 19th century statistical significance was defined. In the early 20th century important probability distributions were defined. Gossett and Pearson worked on specific cases of significance testing.
• 1925: Fisher published the first edition of Statistical Methods for Research Workers which defined the statistical significance test and made it a mainstream method of analysis for much of experimental science. The text was devoid of proofs and weak on explanations, but it was filled with real examples. It placed statistical practice in the sciences well in advance of published statistical theory.
• 1933: In a series of papers (published over a decade starting in 1928) Neyman & Pearson defined the statistical hypothesis test as a proposed improvement on Fisher's test. The papers provided much of the terminology for statistical tests including alternative hypothesis and H₀ as a hypothesis to be tested using observational data (with H₁, H₂... as alternatives). Neyman did not use the term null hypothesis in later writings about his method.
• 1935: Fisher published the first edition of the book The Design of Experiments which introduced the null hypothesis (by example rather than by definition) and carefully explained the rationale for significance tests in the context of the interpretation of experimental results; see quotations regarding the null hypothesis.
• Following: Fisher and Neyman quarreled over the relative merits of their competing formulations until Fisher's death in 1962. Career changes and World War II ended the partnership of Neyman and Pearson. The formulations were merged by relatively anonymous textbook writers, experimenters (journal editors) and mathematical statisticians without input from the principals. The subject today combines much of the terminology and explanatory power of Neyman & Pearson with the scientific philosophy and calculations provided by Fisher. Whether statistical testing is properly one subject or two remains a source of disagreement. Sample of two: One text refers to the subject as hypothesis testing (with no mention of significance testing in the index) while another says significance testing (with a section on inference as a decision). Fisher developed significance testing as a flexible tool for researchers to weigh their evidence. Instead testing has become institutionalized. Statistical significance has become a rigidly defined and enforced criterion for the publication of experimental results in many scientific journals. In some fields significance testing has become the dominant and nearly exclusive form of statistical analysis. As a consequence the limitations of the tests have been exhaustively studied. Books have been filled with the collected criticism of significance testing.

War on women

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/War_on_women

War on women is a slogan in United States politics used to describe certain Republican Party policies and legislation as a wide-scale effort to restrict women's rights, especially reproductive rights. Prominent Democrats such as Nancy Pelosi and Barbara Boxer, as well as feminists, have used the phrase to criticize proponents of these laws as trying to force their social views on women through legislation. The slogan has been used to describe Republican policies in areas such as access to reproductive health services, particularly birth control and abortion services; the definition of rape for the purpose of the public funding of abortion; the prosecution of criminal violence against women; and workplace discrimination against women.

While used in other contexts, and prior to 2010, it became a common slogan in American political discourse after the 2010 congressional elections. The term is often used to describe opposition to the contraceptive mandate in Obamacare and policies to defund women's health organizations that perform abortions, such as Planned Parenthood. The concept again gained attention in the 2016 U.S. presidential election, when Republican nominee Donald Trump drew notice for a history of inflammatory statements and actions toward women.

The phrase and the concept have been criticized by Republicans and some anti-abortion Democrats. Republican National Committee chairman Reince Priebus described it as an over-simplified fiction advanced by Democrats and the media while other Republicans contended that such rhetoric was used as a distraction from President Barack Obama and the Democrats' handling of the economy. In August 2012, Todd Akin's controversial comments regarding pregnancy and rape sparked renewed media focus on the concept. Republicans have tried to turn the phrase against Democrats by using it to argue hypocrisy for not critiquing sex scandals of members within their party who have cheated, sexted, and harassed women, and for not supporting bills to combat sex-selective abortion.

Development of the term

In 1989, radical feminist Andrea Dworkin wrote in a book introduction about "war on women" and, in 1997, she collected that and other writings in Life and Death, for which the subtitle was Unapologetic Writings on the Continuing War Against Women. Feminist Susan Faludi's 1991 book Backlash: The Undeclared War Against American Women, argued that throughout the 1980s the media created a "backlash" against the feminist advances of the 1970s. Former Republican political consultant Tanya Melich's 1996 memoir, The Republican War Against Women: An Insider's Report from Behind the Lines, describes the incorporation of the anti-abortion movement and opposition to the Equal Rights Amendment by Republicans as a divergence from feminist causes.

George W. Bush's administration met with resistance from feminists and women's rights activists throughout his Presidency. In 2004 The Feminist Press published Laura Flanders' collection of essays The W Effect: Bush's War On Women. The same year, Sylvia Federici's Caliban and the Witch used "war on women" as a framework for analysis of the restructuring of gender relations in early modern Europe. In 2006 economist Barbara Finlay's critique of the Bush administration's treatment of women was published by Zed Books under the title George W. Bush and the War on Women: Turning Back the Clock on Progress.

In the 2010 midterm elections, the Republican Party (GOP) won the majority in the House of Representatives. On January 4, 2011, the day after Congress convened, Kaili Joy Gray of the liberal Daily Kos wrote an opinion piece titled "The Coming War on Women". In the article, she outlined many of the measures that Republicans intended to push through the House of Representatives, including personhood laws, fetal pain laws, and the effort to defund Planned Parenthood. In February 2011, an AlterNet article by Sarah Seltzer and Lauren Kelley entitled "9 New laws in the GOP's War on Women" began to document state-level legislation restricting abortion access and rights. That same month, New York Representative Jerrold Nadler referred to the proposed No Taxpayer Funding for Abortion Act, one of the Congress's first actions and one that would have changed policy to allow only victims of "forcible rape" or child sex abuse to qualify for Medicaid funding for abortion, as "an entirely new front in the war on women and their families". Florida Representative and Chair of the Democratic National Committee Debbie Wasserman Schultz began using the term "war on women" in March 2011.

Reproductive rights

Zerlina Maxwell, in an editorial for U.S. News & World Report, cited these figures from the Guttmacher Institute as evidence of a "war on American women". The findings, according to the Guttmacher Institute, show that state restrictions on abortion greatly increased in 2011.

Main article: Reproductive rights

The "war on women" slogan was used often when describing the unprecedented rise in the passage of provisions related to women's health and reproductive rights in 2011 and 2012. In 2011, state legislatures across the United States introduced over 1100 provisions related to women's health and reproductive rights, and in the first quarter of 2012 an additional 944 provisions were introduced in state legislatures, half of which would restrict access to abortion. Legislation has focused on mandatory ultrasounds, narrowing the time when abortions may be performed and limiting insurance coverage of abortion.

Abortion restrictions

See also: Types of abortion restrictions in the United States

Democratic strategist Zerlina Maxwell wrote an editorial for U.S. News & World Report in which she cited a Guttmacher Institute analysis showing state legislatures enacted 135 pieces of legislation affecting women's reproductive rights as evidence that the "Republican 'War on Women' is no fiction." The analysis found that between 2000 and 2011, the number of states hostile to abortion rights have increased markedly, and that in 2011 there was an unprecedented rise in the number of provisions passed by state legislatures restricting abortion.

Many states have adopted model legislation written by Americans United for Life, an anti-abortion advocacy group. In June 2011, Charmaine Yoest and Denise M. Burke of Americans United, acknowledged the expression in an op-ed for The Wall Street Journal, writing that "Indiana is being threatened with the loss of federal funding for health care and being held up to scorn as having 'declared war on women.'"

Mandatory ultrasounds

Ultrasound of fetus at 14 weeks (profile)

In 2011 and 2012, "war on women" was used to describe the legislation passed by many states requiring that women seeking abortions first undergo government-mandated ultrasounds. Some states require that women view the image of the fetus and others require that women be offered the opportunity to listen to the fetal heartbeat. Since many women's pregnancies are not far enough along to get an image via a traditional ultrasound, transvaginal ultrasounds, which involve the physician inserting a probe into the woman's vagina, may be required, but these requirements vary state to state. Critics have questioned the value of having a medically unnecessary procedure, and characterized it as similar to some states' legal definition of rape. Writer Megan Carpentier underwent the procedure and indicated that although it was not comparable to being raped, the process was "uncomfortable to the point of being painful, emotionally triggering... and something that no government should force its citizens to undergo to make a political point." However, in an article critical of the assumptions of those on both sides of the issue, sociologist Tracy Weitz, who opposes mandatory ultrasound, notes that "the use of trans-vaginal ultrasounds is routine among abortion providers."

Virginia State legislators passed a bill in 2012 requiring women to have an ultrasound before having an abortion. The legislation, signed by Governor Bob McDonnell, would require that the provider of an abortion make a copy of the fetal image and include it in the file of the patient. In Louisiana, where pregnant women are already required to view ultrasounds of their fetuses before receiving an abortion, lawmakers proposed a bill that would require them to listen to the embryonic/fetal heartbeat as well. Pennsylvania Governor Tom Corbett drew criticism when he said of his state's new mandatory transvaginal ultrasound law that "You can't make anybody watch, okay? Because you just have to close your eyes. As long as it's on the exterior and not the interior."

Gestational limits on abortion

See also: Late termination of pregnancy § United States 2

In June 2013, Representative Trent Franks of Arizona, passed a national bill in the House Judiciary Committee that would ban abortions after the 20th week of pregnancy. The bill did not include exceptions for rape, incest or health of the mother. In responding to the bill's lack of exception for rape victims, Franks stated that "the incidence of rape resulting in pregnancy are very low," which was compared to the controversial statements made by Todd Akin; studies show that the incidence of pregnancy from rape is approximately equal to or higher than the rate from consensual sex. Afterwards, the House Rules Committee added exceptions for rape and incest. Georgia legislators passed HB 954, a "fetal pain bill" criminalizing abortions performed after the 20th week of pregnancy. The bill, which does not contain exemptions for rape or incest, has been referred to as the "women as livestock bill" by opponents after Representative Terry England made a comparison between women seeking abortions for stillborn fetuses to delivering calves and pigs on a farm.

In April 2012, Arizona passed legislation banning abortions occurring 20 weeks after a woman's last menstrual period. A judge from the District Court initially upheld this ban, but the Ninth Circuit Court of Appeals ruled in August 2012 that the ban could not be enforced until an appeal on the law had been decided. The Ninth Circuit then struck down the law as unconstitutional in May 2013. Eight other states, including Nebraska, Alabama, Georgia, Indiana, Idaho and Oklahoma, have passed such bills; unlike Arizona, the gestational age in these states is calculated from fertilization (20 weeks post-fertilization-which means 22 weeks LMP). In 2013, Idaho's ban was struck down as unconstitutional by a federal judge. States such as Ohio have proposed six-week abortion bans, the earliest time embryonic or fetal cardiac activity can usually be detected.

Defining the beginning of human personhood

Main article: Beginning of human personhood

In 2011, voters in Mississippi rejected Initiative 26, a measure that would have declared that human life begins at fertilization, which had drawn support from conservative Republicans and Democrats. Critics of the initiative indicated that the law would have made abortion illegal even in cases where the mother's life is in danger.

Targeted regulation of abortion providers

Since the mid-1990s, the regulatory burden on abortion providers has increased. TRAP laws (Targeted Regulation of Abortion Providers) have been passed in numerous states. In 2015, the United States Supreme Court agreed to an emergency appeal regarding a Texas law that would have shut down 10 of the remaining 19 abortion clinics within the state. Sometime in the fall of 2015, the Supreme Court will decide whether or not to hear the clinics' full appeal of the ruling, which, if held, would be the largest abortion case before the Supreme Court in nearly 25 years.

Other

In February 2011, South Dakota state legislators considered a bill that would expand that state's definition of justifiable homicide to include killings committed by a party other than a pregnant woman for the purpose of preventing harm to a fetus, a measure interpreted by critics as allowing the killing of abortion providers. Similar legislation was considered in Iowa.

Several state legislatures have passed or are considering legislation to prevent parents from suing doctors who fail to warn them of fetal problems, which are sometimes known as wrongful birth lawsuits. Some of the laws, such as one proposed in Arizona, make exceptions for "intentional or grossly negligent acts", while others do not.

A Kansas bill passed March 2012 requires doctors to warn women seeking abortions that they are linked to breast cancer, a claim that has been refuted by the medical community.

In April 2012, Wisconsin Governor Scott Walker signed into law a bill requiring doctors who prescribe the medical abortion pill to have three meetings with patients or be subject to felony charges. Planned Parenthood suspended non-surgical abortions in the state.

Birth control

On January 20, 2012, Health and Human Services' Secretary Kathleen Sebelius announced a mandate requiring that all health plans provide coverage for all contraceptives approved by the FDA as part of preventive health services for women. Following complaints from Catholic bishops, an exception was created for religious institutions whereby an employee of a religious institution that does not wish to provide reproductive health care can seek it directly from the insurance company at no additional cost. Missouri Senator Roy Blunt proposed an amendment (the Blunt Amendment) that would have "allowed employers to refuse to include contraception in health care coverage if it violated their religious or moral beliefs", but it was voted down 51-48 by the U.S. Senate on March 1, 2012. A bill passed by the Arizona House would allow employers to exclude medication used for contraceptive purposes from their health insurance plans.

In February 2012, Republican Congressman Darrell Issa convened an all-male panel addressing religious freedom and contraceptive mandates for health insurers. He did not allow Sandra Fluke, a Georgetown University Law Center student who was proposed as a witness by the Democrats, to participate in the hearing, arguing that Fluke was not a member of the clergy. Democratic Representatives then staged a separate panel where Fluke was allowed to speak. Later that month, American conservative talk-show host Rush Limbaugh controversially called Sandra Fluke a "slut" and "prostitute" and continued in similar fashion for the next two days. Foster Friess, the billionaire supporting the candidacy of Rick Santorum, suggested in February 2012 that women put aspirin between their knees as a form of contraception. Limbaugh echoed the sentiment, saying he would "buy all of the women at Georgetown University as much aspirin to put between their knees as they want." Nancy Pelosi circulated a petition and asked that Republicans in the House of Representatives disavow the comments by Friess and Limbaugh, which she called "vicious and inappropriate".

Defunding Planned Parenthood

Several Democrats used the phrase War on Women to criticize the Republican Party after House Republicans passed legislation to cut off funding for Planned Parenthood in February 2011. Texas, Indiana and Kansas have passed legislation in an effort to defund the organization. Arizona, Ohio and New Hampshire are considering similar legislation. In Texas, lawmakers reduced funds for family planning from $111M to $37M. The future of the Women's Health Program in Texas, which receives 90% of its funding from the federal government, is unclear. The Indiana legislature passed a bill restricting Medicaid funds for Planned Parenthood. Indiana Representative Bob Morris later referred to the Girl Scouts of the USA as a tactical arm of Planned Parenthood. A 2011 Kansas statute cut funding to Planned Parenthood.

On January 31, 2012, breast cancer organization Susan G. Komen for the Cure stopped funding Planned Parenthood, citing a congressional investigation by Rep. Cliff Stearns and a newly created internal rule about not funding organizations under any federal, state or local investigation. Four days later, Komen's Board of Directors reversed the decision and announced that it would amend the policy to "make clear that disqualifying investigations must be criminal and conclusive in nature and not political". Several top-level staff members resigned from Komen during the controversy.

Defunding international family planning

The National Organization for Women (NOW), in the U.S., in 2011, stated its opinion that "the 'war on women' isn't restricted to U.S. women", saying that the House of Representatives planned to "cut ... international family planning assistance.... [to] include the elimination of all U.S. funds designated for UNFPA" (now known as the United Nations Population Fund).

Violence against women

Rape

Main article: Rape and pregnancy statement controversies in the 2012 United States elections

See also: Pregnancy from rape

In January 2011, the No Taxpayer Funding for Abortion Act moved to change how rape is treated when used to determine whether abortions qualify for Medicaid funding. Under the language of the bill, only cases of "forcible rape" or child sexual abuse would have qualified. Political activist groups Moveon.org and Emily's List charged that this constituted a Republican attempt to "redefine rape".

In 2014, Michigan law prohibited all public and most private insurers from covering abortions including in cases of rape and incest. It requires women to buy separate insurance and has been called "rape insurance" by opponents because of the possibility that women will need to have separate insurance for an abortion resulting from rape.

Unsuccessful Missouri Republican candidate to the U.S. Senate Todd Akin made controversial comments in August 2012 asserting (falsely) that women who are victims of "legitimate rape" rarely experience pregnancy from rape. While he issued an apology for his comments, they were widely criticized, and they sparked a renewed focus on Republican attitudes towards women and "shift[ed] the national discussion to divisive social issues that could repel swing voters rather than economic issues that could attract them".

There were multiple calls from Republicans for Akin to step down as nominee. The Washington Post reported a "stampede" of Republicans dissociating from Akin. NRSC chairman John Cornyn said the Republican Party would no longer provide him Senate election funding. A campaign spokesman for Mitt Romney and Paul Ryan said both disagreed with Akin's position and would not oppose abortion in instances of rape. Ryan reportedly called Akin to advise him to step aside. RNC Chairman Reince Priebus warned Akin not to attend the upcoming 2012 Republican convention and said he should resign the nomination. He described Akin's comments as "biologically stupid" and "bizarre" and said that "This is not mainstream talk that he's referring to and his descriptions of whatever an illegitimate rape is."

Other Republican candidates in the 2012 election also created controversy with their comments on rape. Indiana Senate candidate Richard Mourdock, when discussing his opposition to exceptions on abortion bans in cases of rape, said, "I think even if life begins in that horrible situation of rape, that it is something that God intended to happen." Tom Smith, the Senate candidate in Pennsylvania, compared pregnancy from rape to pregnancy out of wedlock. Akin, Mourdock, and Smith all lost their races due to backlash from women voters.

Military sexual assault

See also: Sexual assault in the United States military

Columnist Margery Eagan has said that opposition to reforming the military in order to better prosecute sexual assaults constitutes a war on women. Senator Saxby Chambliss of Georgia was criticized for saying that part of the cause of the sexual assault was young officers' "hormone level created by nature".

Domestic violence

The renewal of the Violence Against Women Act, which provides for community violence prevention programs and battered women's shelters, was fiercely opposed by conservative Republicans in 2012. The Act was originally passed in 1994 and has been reauthorized by Congress twice. Senate Minority leader Mitch McConnell, who has previously voted against renewal of the Act, said the bill was a distraction from a small business bill. However, in 2013 a strengthened version of the act was passed by Congress with bipartisan support.

Financial assistance

In February 2011, Ms. magazine charged House Republicans with launching a new "war on women" for their proposal to cut the WIC budget by 10%. The WIC program, which President Barack Obama has called a spending priority, is a federal assistance program for low-income pregnant women, breastfeeding women, and infants and children under the age of five. The program had been running a surplus, primarily due to decreases in the cost of milk, which make up 20% of WIC expenditures, and lower participation than expected. WIC's budget was later cut by 5.2% as part of the bipartisan budget sequestration in 2013.

Workplace and pay discrimination

In April 2012, Governor Scott Walker's repeal of Wisconsin's Equal Pay Enforcement Act was described by opponents as furthering the "war on women", which became a big issue in his recall election. The Equal Pay Enforcement Act was passed in 2009 in response to the large gap between the wages of men and women in Wisconsin. Among other provisions, it allowed workplace discrimination victims redress in the less costly and more accessible state court system, rather than in federal court. Defending the repeal, Walker stated that the Act had essentially been nothing but a boon for trial lawyers, incentivizing them to sue job creators, including female business owners, and that the law was being used to clog up the legal system in his state. While it is still illegal in Wisconsin to pay women less on the basis of their sex, the repeal was criticized for reinforcing the gender pay gap, a recurrent theme in the struggle for women's rights. Republican State Senator Glenn Grothman said of the repeal, "You could argue that money is more important for men. I think a guy in their first job, maybe because they expect to be a breadwinner someday, may be a little more money-conscious." Law student Sandra Fluke, criticized Grothman's comment, highlighting legislation that supports equal pay for equal work, such as the federal Lilly Ledbetter Fair Pay Act of 2009.

Public opinion

A May 2012 Kaiser Family Foundation poll found that 31 percent of women and 28 percent of men believed there was an ongoing and wide-scale effort to "limit women's reproductive health choices and services". 45 percent of women and 44 percent of men responded that some groups would like to limit these choices and services, but it's not wide‐scale. Democrats were more likely than Republicans to say there is a movement, but the largest gap was between liberal and conservative ideologies. Among those women believing these efforts to be wide-scale, 75 percent saw this as "a bad thing" against 16 percent who saw this as "a good thing". In the same poll, 42 percent of women and men have said they have taken some action in response to what they heard regarding reproductive health issues.

Political campaigns

Mark Udall

In the Colorado race of the 2014 midterm elections, the Republican candidate Cory Gardner unseated the incumbent Democratic Senator Mark Udall. NARAL Pro-Choice America gives Udall a 100% rating for abortion rights, and Gardner earned a 0% rating. Udall ran a number of TV ads highlighting his abortion stance, which critics said was a negative campaign that overplayed the "war on women" issue.

Sandra Fluke stood as a candidate in California, losing by 61 to 39.

2016 presidential candidates

Political analysts have interpreted the 2016 Hillary Clinton presidential campaign as appealing to a female constituency, and have used the phrase "war on women" to describe Republican opposition. Republican presidential candidate Carly Fiorina said "If Hillary Clinton were to face a female nominee, there are a whole set of things that she won't be able to talk about. She won't be able to talk about being the first woman president. She won't be able to talk about a war on women without being challenged. She won't be able to play the gender card."

Donald Trump, a Republican candidate for the 2016 Presidency attended a Fox News debate in August 2015, where Megyn Kelly asked him about how he would respond to a Hillary Clinton campaign saying that he was waging a "war on women". In a later interview with Don Lemon on CNN Tonight, Trump said that Kelly is a "lightweight" and had "blood coming out of her eyes, blood coming out of her wherever". Trump tweeted that his remark referred to Kelly's "nose" but was interpreted by critics as a reference to menstruation. RedState editor Erick Erickson cancelled Trump's invitation to a RedState meeting, saying "there are just real lines of decency a person running for President should not cross".

Reaction

Response from Republicans

Critics of the term have denied that a war on women exists and some have suggested that it is a ploy to influence women voters. Reince Priebus, the Chairman of the RNC, referred to the War as a "fiction", saying: "If the Democrats said we had a war on caterpillars and every mainstream media outlet talked about the fact that Republicans have a war on caterpillars, then we'd have problems with caterpillars." Republican Representative Cathy McMorris Rodgers called the war a myth, saying "It's an effort to drive a political wedge in an election year." Referring to the 2010 elections and Nancy Pelosi, she said that "It could be argued that the women actually unelected the first woman Speaker of the House." South Carolina Governor Nikki Haley said in 2012 "There is no war on women. Women are doing well." Republican Representative Paul Ryan mocked the idea of a Republican War on Women, saying "Now it's a war on women; tomorrow it's going to be a war on left-handed Irishmen or something like that."

Republican Senator Lisa Murkowski countered the criticism from her fellow party members, challenging them to "go home and talk to your wife and your daughters" if they did not think there was a war on women, saying "It makes no sense to make this attack on women."

After the 2012 rape and pregnancy controversies, Republican strategists met with aides of Republican figures to advise them on how to run against female candidates.

Democratic sexual harassment scandals

Members of the Democratic Party, both prominent and local, have been accused of participating in the war on women. In a column for USA Today, Glenn Reynolds wrote in July 2013 that "most of the action in the war on women seems to be coming from the Democratic front," referring to the allegations of sexual harassment against San Diego mayor Bob Filner, the Anthony Weiner sexting scandal, and the Eliot Spitzer prostitution scandal. The Republican National Senatorial Committee has also used these scandals in press releases, tying Democratic Senators in Iowa and New Hampshire to the allegations.

The messaging from Republicans was described as unlikely to be effective by Garance Franke-Ruta in The Atlantic because "[the War on Women] was an argument about Republican policies on women ... rather than about reprehensible individual behavior." Noting that many of the targets are not on upcoming ballots, Franke-Ruta continued by saying the Republican Party "is going to need its own pro-active framework for thinking about what is happening in America and why women have been drawn to Democrats in numbers that matter in key elections."

Other reactions

Jonathan Alter characterized the phrase as an "alliteratve but unfair notion".

David Weigel called for "a moment of silence" in his article entitled "The 'War on Women' Is Over: The life cycle of a political talking point, from birth to adolescence to death." In it he explained his understanding of the stages in the "life cycle" of the Democratic "talking point".

Molly Redden wrote an article for Mother Jones entitled "The War on Women is Over -- and Women Lost". She described the difficulties faced by abortion providers: "Activists have been calling it the 'war on women.' But the onslaught of new abortion restrictions has been so successful, so strategically designed, and so well coordinated that the war in many places has essentially been lost."

Feminist Camille Paglia has called the term "war on women" a "tired cliché that is as substance-less as a druggy mirage but that the inept GOP has never been able to counter."