Dep-Ss t WS2 - Romantic Love - WORKSHEET - revised 2023

WORKSHEET : Dependent-Samples t Test – Example 2 (Romantic Love) Aron et al. (2005) were interested in examining the brain systems involved in human romantic love. They wanted to determine whether romantic love changes brain activity, so they measured neuronal activity in a part of the brain called the caudate while participants viewed two different pictures. They recruited participants who had recently fallen madly in love. Participants were asked to bring one picture of their beloved and one picture of a familiar, neutral person of the same age and sex as their love interest. Participants then had fMRI scans that measured scores indicating activity in the caudate while they looked at each picture for 30 seconds. Step 1. State your hypotheses. a. Is it a one-tailed or two-tailed test? Answer: Two-tailed When the prediction is that scores on the dependent variable (in this case, the scores indicating activity in the caudate) will be different in the different conditions (which they will be if romantic love changes brain activity), this indicates that you are going to conduct a two-tailed test. b. Research hypotheses H A : When participants view pictures of their beloved, they will have different scores than when they view pictures of a familiar, neutral person of the same age and sex as their love interest. H 0 : When participants view pictures of their beloved, they will NOT have different scores than when they view pictures of a familiar, neutral person of the same age and sex as their love interest. When conducting a true experiment , hypotheses are written in the future tense because, at the time they are written, the researcher does not yet know whether the expectation of a different amount of activity will be supported or not. c. Statistical hypotheses H A : µ D ≠ 0 H 0 : µ D = 0 Step 2. Set the significance level (  = .05). Determine the critical value of t. df = 9 t crit = +/- 2.262

Step 3. Complete the cells in the columns labeled D and ¿ They are filled in light blue. Then compute the appropriate statistical test using the data provided in the table. Participant # Beloved’s picture Neutral picture D (Beloved – Neutral) D D − D ¿ 1 8 8 0 1.200 -1.200 1.44 2 8 2 6 1.200 4.800 23.04 3 7 6 1 1.200 -0.200 0.04 4 3 4 -1 1.200 -2.200 4.84 5 9 8 1 1.200 -0.200 0.04 6 4 4 0 1.200 -1.200 1.44 7 5 4 1 1.200 -0.200 0.04 8 4 3 1 1.200 -0.200 0.04 9 2 1 1 1.200 -0.200 0.04 10 8 6 2 1.200 0.800 0.64 ΣX =58 ΣX=42 ΣD = 12 n pairs = 10 X=5.8 X=4.2 D = ∑ D n = 1.200 ∑ of Squares = ¿ ∑ ¿¿ Notice that the cells in which you could choose to calculate the sample mean when participants are in the beloved condition and the neutral condition are not filled in. That’s because, in a dependent-samples t test, the difference scores for each pair are calculated first, then the mean difference score is calculated (see Column 4). It is unnecessary to know what the means of each sample are because the raw scores are only meaningful in the context of each pair’s matching score in the other condition. Note the sum of squared deviations of the difference scores from the mean of the difference scores (copied from above): SS D = 31.600 Calculate the variance of the difference scores (be careful to use the correct number for sample size—the number of pairs): s D 2 = ∑ ( D − D ) 2 n − 1 = 31.600 10 − 1 = 31.600 9 = 3.51 Calculate the standard error of the difference (be careful to use the correct number for the sample sizes): s D = √ s D 2 n = √ 3.51 10 = √ 0.351 = 0.592 Calculate t -obtained (remember that μ D equals 0):

Step 6. Write a complete APA-style conclusion. When participants view pictures of their beloved, they have higher scores than when they view pictures of a familiar, neutral person of the same age and sex as their love interest. Romantic love did not change brain activity ( M diff = 5.80, SD diff = 0.59), t (9) = 2.03 , p < .05. The first sentence addresses the operational definition of the construct (scores on a measure of neuronal activity in the caudate); the second addresses the hypothetical construct (brain activity). As shown here, the first sentence contains the comparison between the measure of the DV in both conditions. The second sentence translates that comparison into plain English. The statistical information (mean difference, SD of the difference, and the statistical conclusion) can go at the end of either sentence, but the first two must stay together. At the end of the second sentence come the statistical results . Use a comma (rather than a period) before the statistical results, write the statistical results exactly as in Step 5, and end everything with a period. There should be a space on both sides of each = symbol and of the < or > symbol (I’m not telling you which one to use this time). Round the mean difference and the SD of the difference to 2 decimal places even when that requires adding an ending 0. Italicize the symbol M (for mean) and SD (for standard deviation). The conclusion should be written in the past tense because this is a true experiment. Step 7. Compute the estimated d if it’s appropriate. If it’s not appropriate, please explain why. estimated d = D s D = D √ s D 2 = 1.200 √ 3.51 = 1.200 1.87 = 0.64 Step 8. Compute r 2 and write a conclusion for this measure of effect size if it’s appropriate. If it’s not appropriate, please explain why. r 2 = t 2 t 2 + df = ¿¿ Approximately 31.41% of the variance in the difference of scores indicating activity in the caudate can be attributed to whether romantic love changes brain activity.