# Homework 3

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Name: Ann-Koraly Jean-Bart Homework #3: ANOVA and Post-Hoc LSD (worth 35 points) Instructions: Read the scenario and answer the questions. Print out one copy to turn in and print another copy to check during class. In addition to this document, you should turn in: All relevant SPSS outputs Word document with write up Figure (either from Excel or pasted into this Word document) A researcher is interested in how long people can retain information in short term memory. He makes a list of three-letter strings (for example "GSZ" is a letter string) with 50 items on it. He randomly assigns 40 participants into one of four memory conditions: 3 seconds, 5 seconds, 7 seconds and 9 seconds. In the 3 second memory condition, participants try to recall the letter string 3 seconds after seeing it on a screen; in the 5 second condition, they wait 5 seconds before recalling, and so forth. Participants were told not to repeat the letters silently to themselves. The number of correctly recalled letter strings (out of 50) was recorded for each participant. The data can be found in the Excel file "Memory.xlsx". 1). Check assumptions in SPSS using histograms and box plots. Are any assumptions violated?
- Assumptions: Normality and homogeneity of variance were assessed by examining histograms and box plots for each of the dependent variables. This revealed that variable memory had a slightly non-normal distribution. Because ANOVA is robust to violations of normality, the analysis was conducted on the non-transformed variable. Visual inspection did not indicate a violation of homogeneity of variance. There were also several outliers present in the data; these cases were 14 and 18. 2). Run the ANOVA in SPSS. Tests of Between-Subjects Effects Dependent Variable: memory Source Type III Sum of Squares df Mean Square F Sig. Corrected Model 785.075 a 3 261.692 10.984 .000 Intercept 21022.225 1 21022.225 882.360 .000 conditions 785.075 3 261.692 10.984 .000 Error 857.700 36 23.825 Total 22665.000 40 Corrected Total 1642.775 39 3). Fill in the source table using information from your SPSS output. SOURCE SS df MS F p BG 785.075 3 261.692 10.984 <.000 WG 857.700 36 23.825 TOTAL 1642.775 39 ANSWER QUESTION: Did the researcher reject the null hypothesis? (yes or no) ________ 4). Calculate the LSD by hand and answer the questions that follow (SHOW ALL WORK; YOU CAN CHECK YOURSELF IN EXCEL OR SPSS):
df error = tcrit (df error) MS error = s = LSD = _______ Mean Comparisons: -Mean 3 sec vs. Mean 9 sec = | | = ______ Greater than (>) LSD value? __ Significant?__ ___ Mean 3 sec vs. Mean 7 sec = |__ _| = _____ Greater than (>) LSD value? ___ __ Significant?__ __ Mean sec vs. Mean 5 sec = |__ __ ___| = _____ Greater than (>) LSD value? _ __ Significant?__ __ 5). Run LSD and Bonnferoni post hoc tests in SPSS. Multiple Comparisons Dependent Variable: memory (I) conditions (J) conditions Mean Difference (I-J) Std. Error Sig. 95% Confidence Interval Lower Bound LSD 3 seconds 5 seconds .6000 2.18289 .785 -3.8271 7 seconds 5.5000 * 2.18289 .016 1.0729 9 seconds 11.0000 * 2.18289 .000 6.5729 5 seconds 3 seconds -.6000 2.18289 .785 -5.0271 7 seconds 4.9000 * 2.18289 .031 .4729 9 seconds 10.4000 * 2.18289 .000 5.9729 7 seconds 3 seconds -5.5000 * 2.18289 .016 -9.9271 5 seconds -4.9000 * 2.18289 .031 -9.3271 9 seconds 5.5000 * 2.18289 .016 1.0729 9 seconds 3 seconds -11.0000 * 2.18289 .000 -15.4271