Question

A psychologist was interested in the effects of age and stress on memory. Her rationale was that memory would become impaired following a stressor, and this would be excerbated with increasing. She recruited 48 participants: 24 young (ages between 18 - 35) and 24 old (ages between 55 - 72). Both young and old participants were randomly assigned to one of three stress conditions: Control (sitting in a quiet room); Low stress (listening to a 1 hour Hillary Clionton speech); High stress (listening to a 1 hour Donald Trump speech). Memory was measured on a simple memory recall test in which participants had to recall a list of presented words. The stressors were were administered prior to the initial presentation of the word list. The participants were scored on the percentage of correctly recalled words. The data are presented below.         

	High stress	Low Stress	Control
	30.00	65.00	70.00
	30.00	70.00	65.00
	30.00	95.00	80.00
Old	55.00	75.00	65.00
	35.00	80.00	70.00
	20.00	80.00	75.00
	45.00	90.00	85.00
	40.00	70.00	65.00
	55.00	80.00	85.00
	65.00	75.00	70.00
	70.00	70.00	80.00
Young	55.00	80.00	70.00
	55.00	75.00	70.00
	60.00	70.00	75.00
	50.00	70.00	70.00
	50.00	60.00	75.00

1. Graph the data.
2. Perform the appropriate analysis at an alpha level of .05. (Make sure to atach your SPSS output, and include the following: descriptive statistics, Levene’s test, ANOVA table, the marginal means for age and stress levels)
3. Is the homogeneity of variance assumption violated?
4. If your results are significant perform the appropriate post-hoc tests (Tukey’s and pairwise comparisons with Bonferroni corrections) to identify where the differences lie. Do this for both significant main and interaction effects. Make sure to include the results of these comparisons in your conclusion. (Make sure to include the post-hoc results in your attached SPSS output)
5. What is the effect size of the study(find for each effect)?
6. Summarize your results (i.e. 3 or 4 lines) in journal format.

Answer 1

Based on the given data, running a two way ANOVA using excel,

View Data Transform Analyze Direct Marketing Graphs Utilities Add-ons Window Help Reports Descriptive Statistics Tables Compare Means General Linear ModelUnivariate.. Generalized Linear Models Mixed Models Correlate Regression Loglinear Neural Networks var var var Score 30 30 30 Multivariate... Repeated Measures... Variance Components... 35 20 45 40

Univariate Dependent Variable Model... Memory_Score Contrasts Fixed Factor(s): Plots... Post Hoc... Save... Options... Bootstrap Age Stress level Random Factor(s) Covariate(s) WLS Weight: OK Paste Reset CancelHelp

a. Graphing the data:

Univariate: Profile Plots Factors Age Stress_level Horizontal Axis Age Separate Lines Stress level Separate Plots Change Remove Add Continue Cancel Help

Univariate: Profile Plots Factors Horizontal Axis Age Stress level Separate Lines Separate Plots Add Change Remove Age Stress_level Continue Cancel Help

We get the output:

Profile Plots Estimated Marginal Means of Memory_Score Stress_level 80 High Stress Low stress Control 70 r 60 50 40 30 Old Young Age

b. The 2-way ANOVA gives the following result:

We get the output:

Tests of Between-Subjects Effects Dependent Variable Memory_Score Source Type Ill Sum of Squares Partial Eta Squared df Mean Square 2052.500 Si Corrected Model Intercept Age Stress_ level AgeStress_level Error Tota Corrected Total 30.381 1202800.000 3001.797 6.938 60.664 11.818 783 986 142 743 360 10262.500 202800.000 468.750 8196.875 1596.875 2837.500 215900.000 13100.000 468.750 4098.437 798.437 67.560 012 42 48 47 a. R Squared 783 (Adjusted R Squared- .758)

Estimated Marginal Mean:s 1. Age Estimates Dependent Variable Memory_Score Age 95% Confidence Interval Old Young Mean Std. Error Lower BoundUpper Bound 65.261 71.511 61.875 1.678 58.489 64.739 ng 68.125 1.678 Pairwise Comparisons Dependent Variable Memory_Score (Age (J) Age 95% Confidence Interval for Difference Mean Difference( J) Old Young Old Based on estimated marginal means Error Sig. 2.373 2.373 012 012 Lower Bound 11.038 1.462 Upper Bound 1.462 1.038 Young 6.250 6.250 t. The mean difference is significant at the .05 level a. Adjustment for multiple comparisons: Bonferroni

Univariate Tests Dependent Variable Memory_Score Sum of Squares Partial Eta Squared df Mean Square 468.750 67.560 Si 468.750 012 Contrast Error The F tests the effect of Age. This test is based on the linearly independent pairwise comparisons 6.938 142 2837.500 42 among the estimated marginal means.

2. Stress level Estimates Dependent Variable Memory_Score Stress level 95% Confidence Interval High Stress Low stress Control Mean 46.563 75.313 73.125 Std. Error Lower BoundUpper Bound 50.709 79.459 77.272 2.055 2.055 2.055 42.416 71.166 68.978 Pairwise Comparisons Dependent Variable Memory_Score () Stress_level (J) Stress_level 95% Confidence Interval for Difference Mean Difference( J) 28.750 26.562 28.750 Error Sig. 2.906 2.906 2.906 2.906 2.906 2.906 Lower Bound 35.997 33.809 21.503 5.059 19.316 9.434 Upper Bound 21.503 19.316 35.997 9.434 33.809 5.059 High Stress Low stress Control High Stress Control High Stress Low stress Low stress 2.188 1.000 Control 26.562 2.188 1.000 Based on estimated marginal means t. The mean difference is significant at the .05 level a. Adjustment for multiple comparisons: Bonferroni

Univariate Tests Dependent Variable Memory_Score Sum of Squares Partial Eta Squared df Sig Contrast Error The F tests the effect of Stress_level. This test is based on the linearly independent pairwise Mean Square 4098.437 67.560 8196.875 60.664 743 2837.500 42 comparisons among the estimated marginal means 3. Age * Stress level Dependent Variable Memory_Score Age Stress_level 95% Confidence Interval MeanStd. Error Lower BoundUpper Bound 41.490 83.990 77.740 63.365 78.365 80.240 2.906 2.906 2.906 2.906 2.906 2.906 29.760 72.260 66.010 51.635 66.635 68.510 Old 35.625 78.125 71.875 Young High Stress 57.500 72.500 74.375 High Stress Low stress Control Low stress Control

Descriptive Statistics Dependent Variable Memory_Score Age Old Stress level High Stress Low stress Control Total Mean 35.63 78.13 71.87 61.88 57.50 72.50 74.38 68.13 46.56 75.31 73.13 65.00 Std. Deviation 10.836 10.329 7.530 21.255 7.071 6.547 5.630 9.870 14.343 8.845 6.551 16.695 24 Young High Stress Low stress Control Total High Stress Low stress Control Total 24 Total 16 48 Levene's Test of Equality of Error Variancesa Dependent Variable Memory_Score df1 df2 Sig 1.029 413 Tests the null hypothesis that the error variance of the dependent variable is equal across groups a. Design: Intercept+Age Stress_level +Age Stress_level

c. Since the p-value obtained for levene's test (p = 0.413 > 0.05) is not significant, we may conclude that homogeneity of variance assumption is not violated.

d. Since the variable 'Age' has two categories only, there is no need to go for post hoc for Age.

: Univariate: Post Hoc Multiple Comparisons for Observed Me....X Factor(s) Age Stress_level Post Hoc Tests for Stress_level Equal Variances Assumed Waller-Duncan Type I/Type ll Error Ratio: 100 Dunnett Control Category Bonferroni Tukey □ Tukey's-b Duncan Sidak | □ Scheffe D RE-G-VV-F ] Hochberg's GT2「Test □ R-E-G-W-Q □ Gabriel 02-sided <Control > Control Equal Variances Not Assumed Tamhane's T2Dunnetts T3Games-Howell Dunnetts C Continue Cancel Help

We get the output:

Stress level Multiple Comparisons Dependent Variable Memory_Score ()Stress_level (J) Stress_level 95% Confidence Interval Mean Difference ( J) Std. Error 2.906 2.906 2.906 2.906 2.906 2.906 2.906 2.906 2.906 2.906 2.906 2.906 Si Lower Bound Upper Bound 21.69 19.50 35.81 9.25 33.62 4.87 21.50 19.32 36.00 9.43 33.81 5.06 35.81 33.62 21.69 4.87 19.50 9.25 36.00 33.81 21.50 5.06 19.32 9.43 Tukey HSD High Stress Low stress Control High Stress Control High Stress Low stress Low stress Control High Stress Control High Stress Low stress 28.75 26.56 28.75 Low stress 2.19 734 Control 26.56 2.19 28.75 26.56 28.75 734 Bonferroni High Stress Low stress 2.19 1.000 Control 26.56 2.19 1.000 Based on observed means The error term is Mean Square(Error) 67.560 t. The mean difference is significant at the .05 level

Homogeneous Subsets Memory_Score Tukey HSDb Stress_level Subset 16 16 16 46.56 High Stress Control Low stress Sig 73.13 75.31 734 1.000 Means for groups in homogeneous subsets are displayec Based on observed means. The error term is Mean Square(Err) 67.560. a. Uses Harmonic Mean Sample Size- 16.000. b. Alpha-.05

We observe a statistically significant difference in memory scores between the stress levels except for 'Control and 'low stress' pair.

e. From the output obtained, the effect size for:

Age = 0.142 = 14.2%

Stress level = 0.743 = 74.3%

Interaction = 0.360 = 36%

d. Conclusion:

A two way ANOVA conducted to compare the main effects of Age(Levels: Old and Young) and stress levels (Levels: High, low, Control) and their interaction effect on Memory yielded the following results:

Both the main effects of Age and Stress level, as well as their interaction effect was found to be statistically significant at 5% level.The factor Age had a significant effect on memory (F_1,42 = 6.938, p = 0.012 < 0.05, partial eta square = 14.2%); so did Stress levels (F_2,42 = 60.664, p = 0.000 < 0.05, partial eta square = 74.3%). The interaction effect was also found to be significant (F_2,42 = 11.818, p = 0.000 < 0.05, partial eta square = 36%).