Critical Value

How are the degrees of freedom ($df$) calculated when conducting a one-sample $t$-test?

If a researcher conducts a one-sample $t$-test with 30 participants, the exact shape of the $t$ distribution used to identify the $p$ value is dictated by 30 degrees of freedom.

Match the sample size ($N$) of each psychology study with the correct degrees of freedom ($df$) required to find the $p$ value in a one-sample $t$-test.

A researcher is conducting a one-sample $t$-test. Arrange the following steps in the correct logical sequence to demonstrate how the degrees of freedom ($df$) analytically connect the sample data to the final probability ($p$ value).

In a one-sample $t$-test, which parameter dictates the exact shape of the $t$ distribution used to identify the $p$ value?

In a one-sample $t$-test, which statistical value dictates the exact shape of the $t$ distribution, allowing researchers to identify the associated $p$ value?

In a peer review of a one-sample $t$-test, you are asked to judge whether the researcher's findings are statistically valid. You find that the researcher looked up their results using the total sample size ($N$) instead of $N - 1$. By failing to use the correct _____, the researcher used a distribution shape that was too narrow, leading to a biased $p$ value.

A psychologist conducts a one-sample $t$-test to determine whether the mean daily study time of college students at her university ($N = 20$) differs from the national average. She uses $df = 19$ when consulting the $t$ distribution to find the $p$ value. Her degrees of freedom are correct.

A one-sample $t$-test involves several connected components that together link sample data to a $p$ value. Match each component on the left to the role it plays in that process.

A researcher argues that because her sample is reasonably large ($N = 16$), it makes little practical difference whether she uses $df = 15$ or $df = 16$ to find the $p$ value for her one-sample $t$-test. You evaluate this reasoning as _____, because the exact shape of the $t$ distribution—and therefore the accuracy of the $p$ value—depends on using precisely $N - 1$ degrees of freedom.

State the formula used to calculate the degrees of freedom ($df$) when conducting a one-sample $t$-test, and recall how this calculated value is used by researchers to determine the significance of their test statistic.

Explain why the student's method of using the total sample size instead of calculating the degrees of freedom is incorrect. Describe what the degrees of freedom should be for this study and how this value affects the distribution used to find the $p$ value.

A psychology researcher is analyzing memory recall scores from a sample of $N = 40$ participants using a one-sample $t$-test. Calculate the degrees of freedom ($df$) for this study, and state what specific parameter of the analysis is dictated by this number.