In null hypothesis testing, which two main considerations determine the $p$ value?

If two separate studies observe the exact same strength of relationship between variables, the study with the larger sample size will typically yield a lower $p$ value.

A researcher is evaluating the results of three different experimental studies in psychology. Rank these study scenarios in order from the one expected to yield the lowest $p$ value (rank 1) to the one expected to yield the highest $p$ value (rank 3).

In psychological research, the $p$ value is influenced by the characteristics of the sample and the data collected. Match each research scenario modification to the logical shift in the $p$ value and the statistical reason behind that change.

A clinical psychologist is developing a research protocol to test the efficacy of a new mindfulness-based therapy for anxiety. To construct a study design that most effectively minimizes the resulting $p$ value by optimizing the two primary determinants of this statistic, which strategy should be proposed?

A team of psychologists is studying how sleep duration affects cognitive performance. They analyze three different data sets. Based on the determinants of the $p$ value, rank these data sets in order from the lowest $p$ value (most statistically significant) to the highest $p$ value (least statistically significant).

A reviewer is evaluating two psychological studies that both report a $p$ value of $.03$. Study A utilized a sample size of $N = 20$, while Study B utilized a sample size of $N = 400$. The reviewer correctly concludes that for Study A to reach the same level of significance as Study B, it must have observed a much higher ______ of relationship.

A researcher is comparing different study outcomes to determine how sample characteristics influence statistical significance. Analyze the following scenarios and match each one with the correct explanation for its relative $p$ value.

In null hypothesis testing, a stronger sample relationship and a larger sample size both decrease the ______ of obtaining the observed result if the null hypothesis were true, thereby resulting in a lower $p$ value.

Which two main considerations determine the $p$ value in null hypothesis testing?

If two separate studies observe the exact same strength of relationship in their data, the study with the larger sample size will generally yield a higher $p$ value.

When evaluating a psychology study that failed to reach statistical significance ($p > .05$) despite an extremely large sample size, a researcher would conclude that the primary determinant responsible for the high $p$ value was the low _____ of the sample relationship.

A psychology researcher wants to design a study comparing a new memory training technique with a control condition. Explain how the researcher can apply their understanding of the two determinants of the $p$ value to maximize the likelihood of obtaining a lower, statistically significant $p$ value. Specifically describe how they should address both determinants in their study design.

Analyze the difference between Study A and Study B. Identify which determinant of the $p$ value explains the difference in their statistical significance, and explain the statistical mechanism behind why this determinant led to a lower $p$ value for Study B.

A student researcher claims: 'If our study yields a high $p$ value, it must be because our sample size was too small, since sample size is the only factor that determines how likely our results are under the null hypothesis.' Evaluate the validity of the student's statement based on the determinants of the $p$ value.