A psychologist is interested whether or not students will learn more effectively
ID: 3223454 • Letter: A
Question
A psychologist is interested whether or not students will learn more effectively with a constant background sound, as opposed to a soothing music or no sound at all. She randomly divides twenty-four students into three groups of eight. All students study a passage of text for 30 minutes. Those in group 1 study with background sound at a constant volume in the background. Those in group 2 study with noise that changes volume periodically. Those in group 3 study with no sound at all. After studying, all students take a 10 point multiple choice test over the material. Their test scores follow:
Group 1: constant sound: 7, 4, 6, 8, 6, 6, 2, 9
Group 2: Soothing music: 5, 5, 3, 4, 4, 7, 2, 2
Group 3: No sound: 2, 4, 7, 1, 2, 1, 5, 5
a. If the F is significant, follow with the Tukey HSD post hoc follow up analysis.
b. Explain all results and write a statement as to your conclusions.
Note. This is a One-Way ANOVA (i.e., 1 IV). The one IV (factor) has three levels and one ther is one DV (score on the test).
Explanation / Answer
a) Null HYpothesis H0: mew1=mew2=mew3 i.e there is no significance difference between the average test scores of three groups.(all are equal scores)
Alternative hypothesis H1: at least two of them not equal to zero(two tailed test)
Descriptives
Treatment
N Mean Std. Deviation Std. Error
Group1 8 6.0000 2.20389 .77919
Group2 8 4.0000 1.69031 .59761
Group3 8 3.3750 2.19984 .77776
Total 24 4.4583 2.26465 .46227
ANOVA one-way classification table
Treatment
Sum of Squares df Mean Square F Sig.
Between Groups 30.083 2 15.042 3.595 .045
Within Groups 87.875 21 4.185
Total 117.958 23
From F- tables the critical value of F at 5% level with (2,21) df is 3.46
therefore caculated value >table value(3.595>3.46)
therefore H0 is rejected i.e there is signficant difference between the test mean scores of three groups
b) Multiple Comparisons
POST HOC analysis
Treatment
Tukey HSD
(I) Factor (J) Factor Mean Difference (I-J) Std. Error Sig.
Group1 Group2 2.00000 1.02281 .148
Group3 2.62500* 1.02281 .045
Group2 Group1 -2.00000 1.02281 .148
Group3 .62500 1.02281 .816
Group3 Group1 -2.62500* 1.02281 .045
Group2 -.62500 1.02281 .816
From the above table we observe that individual groups
Group 1 to group 2 is not significant since (0148>0.05)
Group 1 to group 3 is significant since (0.045<0.05)
Group 2 to group 1 and groupe are not significant because 0.148,0.816>0.05
Group 3 to group 1 is significant (0.045<0.05)
Group 3 to group 2 is not significant since (0.816>0.05)
overall comparision for all groups the result is significant at p-value (0.045426) < 0.05.
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