Paired Sample t Test,
p value

For this activity, the terms "Null Hypothesis Distribution" and "Ho: Null Distribution" are both used to indicate a distribution of sample means as specified by the null hypothesis.  

Paired Sample t Test: How and Why

Does a difference exist?  Take two measurements (e.g., art appreciation and writing appreciation), and it is unlikely that they will exactly equal each other.  But, is the difference found in the sample so large that we can confidently conclude that it is true for the population?

For a paired sample t test, we typically start with one group, and make two measurements per person (e.g., appreciation of art, appreciation of writing). Each person contributes a pair of scores.  Next, for each participant, the value from one variable is subtracted from the value of the other variable.  For example, let's say people's appreciation of art and writing is ranked on a scale of 1 - 7 (and treated as interval data).  We could, for each participant, subtract their appreciation of writing from their appreciation of art, and get a difference score.  Next, we'd calculate the average of the difference scores.  

For a two-tailed test, the null hypothesis would be that the average difference score will not differ significantly from zero (i.e., appreciation of art = appreciation of writing).  A statistically significant result would indicate that the difference between appreciation of art and writing is so large in the sample, that we must reject the null hypothesis of no difference in the population.

While appreciation of art and writing may be correlated, our purpose is to evaluate whether a difference exists between them (e.g., Art < > Writing appreciation).  That these two variables are likely correlated is at the forefront of our thinking - that is why we would go with a paired sample t test versus using the independent sample t test.  The stronger the correlation, the more sensitive the paired sample t test will be to a difference between the variables.

t test and p value

One-tail vs Two-tail Hypothesis Test: The P-value

Alpha Level & Hypothesis Testing

For this game, you will always work with a two-tail test.  What does it mean?  You, the end user, must take into consideration whether it is a one-tailed or two-tailed hypothesis test.

If a two-tailed test, then...

• • • • • Reject the null hypothesis when the 'p-value (2-tailed)' ≤ .05

If a one-tailed test (e.g., "Pre-test >= Post-test"), then...

• • 1. Retain the null hypothesis if the results are consistent with the null hypothesis

    2. Otherwise, reject the null hypothesis:

• • • • If 'p-value (2-tailed)' ≤ (2 x alpha level). 
        For a one-tailed test, with the sample mean in the direction opposite of that predicted by the null hypothesis, with a p-value (2-tailed) of .09, and an alpha level of .05, we would reject the null hypothesis.

      • Which can also be stated as: reject the null if ('p-value (2-tailed)' / 2) ≤ .05.

That is to say, for a one-tailed hypothesis, if the results are consistent with the null hypothesis, then retain it.  Otherwise, compare the 'p-value. (2-tailed)' to a value that is double the alpha level (e.g., 2 * .05 = .10); for an alpha of .05, reject the null if the 'p-value (2-tailed)' ≤ .10.  Alternatively, one could halve the 'p-value (2-tailed)' and compare it to the alpha level (e.g., .05).  Mathematically, these two methods will give the same result, so pick whichever approach you find easier to apply.

Resource/Options

• View the video tutorial for this game

• Open the game in Full Screen mode

To earn credit for this activity:

1. Click the 'Accommodations' button on the game menu.

2. Using the number pad (in the Accommodation dialog box), type the passcode provided by your instructor.

3. Click the 'Continue' button.  Doing so will return you back to the game menu.

4. Then click 'Start' to begin the game. 

5. When you complete the task with a score of 85% or greater, you will be given a completion code.  To view this completion code, click on the 'Completion Code' button.

6. To get credit for having completed the activity,  provide the completion code as your answer (e.g., to a quiz question).  If the completion code is not yet available (e.g., performance was less than 85%), then click the 'Continue' button to re-do the activity. 

Accommodations include: 

• Screen Reader (click the 'Screen Reader' button)

• Unlimited decision time (e.g., Click the 'Accommodations' button, then type #17 by itself or at the end of a passcode.  Click 'Continue').

Please notify your instructor if requesting these accommodations.

Instructors can modify games and set up quizzes rather easily.  Check out game modifications.