Post-traumatic stress of POWs. Psychological Assessment...

Post-traumatic stress of POWs. Psychological Assessment (Mar. 1995 ) published the results of a study of World War II aviators captured by German forces after having been shot down. Having located a total of 239 World War II aviator POW survivors, the researchers asked each veteran to participate in the study; 33 responded to the letter of invitation. Each of the 33 POW survivors was administered the Minnesota Multiphasic Personality Inventory, one component of which measures level of post-traumatic stress disorder (PTSD). [Note: The higher the score, the higher is the level of PTSD.] The aviators produced a mean PTSD score of $\bar{x}=9.00$ and a standard deviation of $s=9.32$. Conduct a test to determine if the true mean PTSD score for all World War II aviator POWS is less than 16. [Note: The value 16 represents the mean PTSD score established for Vietnam POWS.] Use $\alpha=.10$.

Post-traumatic stress of POWs. Psychological Assessment (Mar. 1995 ) published the results of a study of World War II aviators captured by German forces after having been shot down. Having located a total of 239 World War II aviator POW survivors, the researchers asked each veteran to participate in the study; 33 responded to the letter of invitation. Each of the 33 POW survivors was administered the Minnesota Multiphasic Personality Inventory, one component of which measures level of post-traumatic stress disorder (PTSD). [Note: The higher the score, the higher is the level of PTSD.] The aviators produced a mean PTSD score of $\bar{x}=9.00$ and a standard deviation of $s=9.32$. Conduct a test to determine if the true mean PTSD score for all World War II aviator POWS is less than 16. [Note:
The value 16 represents the mean PTSD score established for Vietnam POWS.] Use $\alpha=.10$.

Key Concepts

p-Value

The p-value is the probability of obtaining a t-statistic as extreme as, or more extreme than, the one observed in the data, assuming that the null hypothesis is true. It is used to determine whether the observed effect in the sample is statistically significant. If the p-value is less than the predetermined significance level, the evidence is considered strong enough to reject the null hypothesis in favor of the alternative hypothesis.

Significance Level

The significance level, denoted by alpha (?), is the threshold for rejecting the null hypothesis. It represents the probability of committing a Type I error, which is the error of rejecting a true null hypothesis. A significance level of 0.10, for example, indicates a 10% risk of such an error.

t-Distribution and Degrees of Freedom

The t-distribution is employed instead of the normal distribution when the sample size is small and the population standard deviation is unknown. The distribution's shape is determined by the degrees of freedom, usually calculated as the sample size minus one (n - 1), which reflects the amount of information available to estimate the variability in the sample.

Null and Alternative Hypotheses

In hypothesis testing, the null hypothesis (H?) typically states that there is no difference or no effect – in this context, that the true mean PTSD score is equal to a specific value. The alternative hypothesis (H?) is what the researcher aims to establish, such as the true mean being less than that value, which determines the direction of the test (a one-tailed test in this case).

Hypothesis Testing

Hypothesis testing is the process of making inferences about population parameters based on sample data. In this method, researchers propose a null hypothesis (representing a default position) and an alternative hypothesis (representing a competing claim), and then use statistical methods to assess whether the sample data provide sufficient evidence to reject the null hypothesis.

One-Sample t-Test

A one-sample t-test is used to compare the mean of a sample to a known or hypothesized population mean when the population standard deviation is unknown and the sample size is relatively small. This test calculates a t-statistic, which is then used to determine whether the observed sample mean significantly differs from the target population value.

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