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In: Statistics and Probability

Provide an example and explanation of how you would use Hypothesis Tests in the field of...

Provide an example and explanation of how you would use Hypothesis Tests in the field of psychology

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A statistical hypothesis test is a method of making statistical decisions from and about experimental data. Null-hypothesis testing just answers the question of "how well the findings fit the possibility that chance factors alone might be responsible." This is done by asking and answering a hypothetical question. One use is deciding whether experimental results contain enough information to cast doubt on conventional wisdom.

As an example, consider determining whether a suitcase contains some radioactive material. Placed under a Geiger counter, it produces 10 counts per minute. The null hypothesis is that no radioactive material is in the suitcase and that all measured counts are due to ambient radioactivity typical of the surrounding air and harmless objects in a suitcase. We can then calculate how likely it is that the null hypothesis produces 10 counts per minute. If it is likely, for example if the null hypothesis predicts on average 9 counts per minute and a standard deviation of 1 count per minute, we say that the suitcase is compatible with the null hypothesis (which does not imply that there is no radioactive material, we just can't determine!); on the other hand, if the null hypothesis predicts for example 1 count per minute and a standard deviation of 1 count per minute, then the suitcase is not compatible with the null hypothesis and there are likely other factors responsible to produce the measurements.

The test described here is more fully the null-hypothesis statistical significance test. The null hypothesis is a conjecture that exists solely to be falsified by the sample. Statistical significance is a possible finding of the test - that the sample is unlikely to have occurred by chance given the truth of the null hypothesis. The name of the test describes its formulation and its possible outcome. One characteristic of the test is its crisp decision: reject or do not reject (which is not the same as accept). A calculated value is compared to a threshold.

A statistical hypothesis test is a method of making statistical decisions from and about experimental data. Null-hypothesis testing just answers the question of "how well the findings fit the possibility that chance factors alone might be responsible." This is done by asking and answering a hypothetical question. One use is deciding whether experimental results contain enough information to cast doubt on conventional wisdom.

As an example, consider determining whether a suitcase contains some radioactive material. Placed under a Geiger counter, it produces 10 counts per minute. The null hypothesis is that no radioactive material is in the suitcase and that all measured counts are due to ambient radioactivity typical of the surrounding air and harmless objects in a suitcase. We can then calculate how likely it is that the null hypothesis produces 10 counts per minute. If it is likely, for example if the null hypothesis predicts on average 9 counts per minute and a standard deviation of 1 count per minute, we say that the suitcase is compatible with the null hypothesis (which does not imply that there is no radioactive material, we just can't determine!); on the other hand, if the null hypothesis predicts for example 1 count per minute and a standard deviation of 1 count per minute, then the suitcase is not compatible with the null hypothesis and there are likely other factors responsible to produce the measurements.

The test described here is more fully the null-hypothesis statistical significance test. The null hypothesis is a conjecture that exists solely to be falsified by the sample. Statistical significance is a possible finding of the test - that the sample is unlikely to have occurred by chance given the truth of the null hypothesis. The name of the test describes its formulation and its possible outcome. One characteristic of the test is its crisp decision: reject or do not reject (which is not the same as accept). A calculated value is compared to a threshold.

Details:

One may be faced with the problem of making a definite decision with respect to an uncertain hypothesis which is known only through its observable consequences. A statistical hypothesis test, or more briefly, hypothesis test, is an algorithm to choose between the alternatives (for or against the hypothesis) which minimizes certain risks.

This article describes the commonly used frequentist treatment of hypothesis testing. From the Bayesian point of view, it is appropriate to treat hypothesis testing as a special case of normative decision theory (specifically a model selection problem) and it is possible to accumulate evidence in favor of (or against) a hypothesis using concepts such as likelihood ratios known as Bayes factors.

There are several preparations we make before we observe the data.

1. The null hypothesis must be stated in mathematical/statistical terms that make it possible to calculate the probability of possible samples assuming the hypothesis is correct. For example: The mean response to treatment being tested is equal to the mean response to the placebo in the control group. Both responses have the normal distribution with this unknown mean and the same known standard deviation ... (value).
2. A test statistic must be chosen that will summarize the information in the sample that is relevant to the hypothesis. In the example given above, it might be the numerical difference between the two sample means, m1 − m2.
3. The distribution of the test statistic is used to calculate the probability sets of possible values (usually an interval or union of intervals). In this example, the difference between sample means would have a normal distribution with a standard deviation equal to the common standard deviation times the factor √1n1+1n21n1+1n2 where n1 and n2 are the sample sizes.
4. Among all the sets of possible values, we must choose one that we think represents the most extreme evidence against the hypothesis. That is called the critical region of the test statistic. The probability of the test statistic falling in the critical region when the null hypothesis is correct, is called the alpha value (or size) of the test.
5. The probability that a sample falls in the critical region when the parameter is θθ, where θθ is for the alternative hypothesis, is called the power of the test at θθ. The power function of a critical region is the function that maps θθ to the power of θθ.

After the data are available, the test statistic is calculated and we determine whether it is inside the critical region.

If the test statistic is inside the critical region, then our conclusion is one of the following:

1. Reject the null hypothesis. (Therefore the critical region is sometimes called the rejection region, while its complement is the acceptance region.)
2. An event of probability less than or equal to alpha has occurred.

The researcher has to choose between these logical alternatives. In the example we would say: the observed response to treatment is statistically significant.

If the test statistic is outside the critical region, the only conclusion is that there is not enough evidence to reject the null hypothesis. This is not the same as evidence in favor of the null hypothesis. That we cannot obtain using these arguments, since lack of evidence against a hypothesis is not evidence for it. On this basis, statistical research progresses by eliminating error, not by finding the truth.

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