# Two Related Samples t Test

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1 Two Related Samples t Test In this example 1 students saw five pictures of attractive people and five pictures of unattractive people. For each picture, the students rated the friendliness of the person on a 1 point scale (where 1 was very unfriendly and 1 was very friendly.) The mean friendliness rating for the attractive and unattractive pictures was calculated. The researcher wants to know whether the attractiveness of the picture affects the perceived friendliness of the person. 1. Step 1: Write the null and alternative hypotheses and specify the probability of making a Type I error: H : µ D = H 1 : µ D α =.. Step : Sketch and determine the critical regions: Critical region Critical region df = n 1 = 1 1 = 9 From a table of critical t scores with α=., two-tailed, t critical (9) = ±. (The critical t is both positive and negative because we can reject H if μ is either > or <.) 3. Step 3: Calculate the test statistic: a. Open SPSS

2 b. Either type the data (see the last page for the data) or open a data set. The class data set (for homework) is available from < Save the data file somewhere and open it with SPSS. c. Analyze Compare Means Paired-Samples T Test d. Move the two dependent variables (that correspond to the control and treatment conditions) into the Paired Variables box. You can either drag the variable names into the box, or select the variables by clicking on them and then clicking on the arrow button between the two boxes.

3 e. Click the OK button f. The SPSS output viewer will open g. The first part of the output gives descriptive statistics for the dependent variable for each condition (level of the independent variable): Paired Samples Statistics Mean N Std. Deviation Std. Error Mean Pair 1 attractive unattractive h. This tells us that for the mean friendliness rating for the attractive faces is.1 (mean column and attractive row), the sample standard deviation (s) is 1.3, and the standard error of the means (s M ) is. (which should and does equal s / N = 1.3 / 1). Likewise, this tells us that for the unattractive faces there were 1 scores (in the N column of the unattractive row), that the sample mean ( ) is.9 (mean column and the unattractive row), the sample standard deviation (s) is 1.99, and the standard error of the means (s m ) is.3 (which should and does equal s / N = 1.99 / 1). i. The last part of the output gives us the value of the t-test: Paired Samples Test Paired Differences 9% Confidence Std. Interval of the Std. Error Difference Sig. (- Mean Deviation Mean Lower Upper t df tailed) Pair 1 attractive - unattractive n. This tells us the mean of the difference scores (1.), the standard deviation of the difference scores (1.), the standard error of the mean of the difference scores (.), the 9% confidence interval of the difference scores (from.1 to.), the value of t observed =.1, df = 9 and p =.3.

4 . Step : Make a decision: Find the p value for the t-test (in the column labeled Sig. (- tailed)). For this output, that value is.3. If the p value is less than or equal to the α level, then you should reject H. Otherwise, you should fail to reject H. Because p =.3 and α =., we reject H and conclude that it is likely the case that the perceived friendliness differs for attractive and unattractive pictures of people.. Cohen s d must be calculated by hand. Some of the values are from the SPSS output: Estimated value of Cohen s d = M D / s D = 1. / 1. =.13 This is a large effect (greater than.). r must be calculated by hand. Both values for the formula can be gotten from the SPSS output: r = t / (t + df) =.1 / (.1 + 9) =.3 This is a large effect (greater than.).

5 Steps 1 and are identical to those used with SPSS. Step 3: Calculate the test statistic: Attractive Unattractive Attractive - Unattractive Σ 1 n 1 1. SS 19. s D = SS D / df = 19. / 9 =.1 s MD = (S D / n) = (.1 / 1) =. t = M D / s MD = 1. /. =. Step : Decide: If the observed or calculated value of t (=.) is in one off the tails cut off by the critical t (from a table, ±.; see step above), then reject H, otherwise, fail to reject H. Reject H. It is likely the case that the perceived friendliness differs for attractive and unattractive pictures of people.

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