Consider the following data from a repeated-measures design. You want to use a repeated-measures t test to test the null hypothesis H₀: μDD = 0 (the null hypothesis states that the mean difference for the general population is zero). The data consist of five observations, each with two measurements, A and B, taken before and after a treatment. Assume the population of the differences in these measurements are normally distributed. Complete the following table by calculating the differences and the squared differences: Observation A B Difference Score Squared Difference Score (D = B – A) (D²) 1 12 10 2 11 12 3 17 16 4 10 11 5 16 18 The mean difference score is MDD = . For a repeated-measures t test, you need to calculate the t statistic, which requires you to calculate s and sMDMD. What is the estimated standard deviation of the difference scores? s = √ / = √ 10.80 / = What is the estimated standard error of the mean difference scores? (Note: For best results, retain at least six decimal places from your calculation of s.) sMDMD = s / = What is the t statistic for the repeated-measures t test to test the null hypothesis H₀: μDD = 0? t = MDD – / = 0.27 t Distribution Degrees of Freedom = 7 -4.0-3.0-2.0-1.00.01.02.03.04.0t.2500.5000.2500-0.7110.711 You conduct a two-tailed test at α = .05. To use the Distributions tool to find the critical values, you first need to set the degrees of freedom in the tool. The degrees of freedom are . The critical values (the values for t scores that separate the tails from the main body of the distribution, forming the critical region) are . Finally, since the t statistic in the critical region, you the null hypothesis.

MATLAB: An Introduction with Applications

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3. A step-by-step hypothesis test for a repeated-measures design

Consider the following data from a repeated-measures design. You want to use a repeated-measures t test to test the null hypothesis H₀: μDD = 0 (the null hypothesis states that the mean difference for the general population is zero). The data consist of five observations, each with two measurements, A and B, taken before and after a treatment. Assume the population of the differences in these measurements are normally distributed.

Complete the following table by calculating the differences and the squared differences:

Observation	A	B
(D = B – A)	(D²)
1	12	10
2	11	12
3	17	16
4	10	11
5	16	18

The mean difference score is MDD = .

For a repeated-measures t test, you need to calculate the t statistic, which requires you to calculate s and sMDMD.

What is the estimated standard deviation of the difference scores?

√

10.80 /

What is the estimated standard error of the mean difference scores? (Note: For best results, retain at least six decimal places from your calculation of s.)

sMDMD

s /

What is the t statistic for the repeated-measures t test to test the null hypothesis H₀: μDD = 0?

MDD – /

0.27

t Distribution

Degrees of Freedom = 7

-4.0-3.0-2.0-1.00.01.02.03.04.0t.2500.5000.2500-0.7110.711

You conduct a two-tailed test at α = .05. To use the Distributions tool to find the critical values, you first need to set the degrees of freedom in the tool. The degrees of freedom are .

The critical values (the values for t scores that separate the tails from the main body of the distribution, forming the critical region) are .

Finally, since the t statistic in the critical region, you the null hypothesis.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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