Performing ANOVA Statistics
Tests of Normality |
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Kolmogorov-Smirnov^{a} | Shapiro-Wilk | |||||
Statistic | df | Sig. | Statistic | df | Sig. | |
Exam Mark | .139 | 30 | .142 | .937 | 30 | .075 |
a. Lilliefors Significance Correction |
Test of Homogeneity of Variances |
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Levene Statistic | df1 | df2 | Sig. | ||
Exam Mark | Based on Mean | 2.569 | 2 | 27 | .095 |
Based on Median | 1.734 | 2 | 27 | .196 | |
Based on Median and with adjusted df | 1.734 | 2 | 19.176 | .203 | |
Based on trimmed mean | 2.527 | 2 | 27 | .099 |
ANOVA |
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Exam Mark | |||||
Sum of Squares | df | Mean Square | F | Sig. | |
Between Groups | 1205.067 | 2 | 602.533 | 21.008 | .000 |
Within Groups | 774.400 | 27 | 28.681 | ||
Total | 1979.467 | 29 |
4. Based on the research questions, I would like to plan orthogonal contrasts as below.
Q4 (2 pts): Fill in the table below to specify the weights for the corresponding contrasts
Groups | Contrast 1 | Contrast 2 | Product of group weights |
Punish | |||
Indifferent | |||
Reward | |||
Sum |
Groups | Contrast 1 | Contrast 2 | Product of group weights |
Punish | |||
Indifferent | |||
Reward | 0 | 0 | |
Sum | 0 | 0 | 0 |
Note: use the five rules for assigning weights for contrasts and the requirement of orthogonal contrast.
Q5 (1 pt): Interpret the results of contrast testing. E.g., is the value of contrast significantly different from zero? What does it mean?
Ans: The contrast testing for contrast 1 yields statistically significant result but the contrast 2 does not. The interpretation is that exam scores of teaching method Reward is statistically different from that of the average of Punish and Indifferent.
However, the test yields insignificant result for difference between Punish and Indifferent. This indicates that the difference between exam scores of teaching methods Punish and Indifferent are not different, but they are different from Reward.
Contrast Coefficients |
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Contrast | Type of Teaching Method | ||
Punish | Indifferent | Reward | |
1 | -.4 | -.4 | .8 |
2 | -.7 | .7 | 0 |
Contrast Tests | |||||||
Contrast | Value of Contrast | Std. Error | t | df | Sig. (2-tailed) | ||
Exam Mark | Assume equal variances | 1 | 9.9200 | 1.65934 | 5.978 | 27 | .000 |
2 | 4.2000 | 1.67654 | 2.505 | 27 | .019 | ||
Does not assume equal variances | 1 | 9.9200 | 1.50472 | 6.593 | 21.696 | .000 | |
2 | 4.2000 | 1.81940 | 2.308 | 14.476 | .036 |
6. Test the difference between all possible pairs of group means using post hoc comparisons.
In One-Way ANOVA, Post Hoc check Tukey and Scheffe, and any other tests you prefer.
Q6 (1 pt): Which means are different based on Tukey (HSD) test?
Ans: In Tukey’s test, we have different findings that the exam scores of teaching methods Punish and Indifferent are different, and they are different from Reward at 5% level of significance. All p-values are <0.05.
Multiple Comparisons |
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Dependent Variable: Exam Mark | |||||
(I) Type of Teaching Method | (J) Type of Teaching Method | Mean Difference (I-J) | Std. Error | Sig. | |
Tukey HSD | Punish | Indifferent | -6.00000^{*} | 2.39506 | .047 |
Reward | -15.40000^{*} | 2.39506 | .000 | ||
Indifferent | Punish | 6.00000^{*} | 2.39506 | .047 | |
Reward | -9.40000^{*} | 2.39506 | .002 | ||
Reward | Punish | 15.40000^{*} | 2.39506 | .000 | |
Indifferent | 9.40000^{*} | 2.39506 | .002 | ||
Scheffe | Punish | Indifferent | -6.00000 | 2.39506 | .060 |
Reward | -15.40000^{*} | 2.39506 | .000 | ||
Indifferent | Punish | 6.00000 | 2.39506 | .060 | |
Reward | -9.40000^{*} | 2.39506 | .002 | ||
Reward | Punish | 15.40000^{*} | 2.39506 | .000 | |
Indifferent | 9.40000^{*} | 2.39506 | .002 | ||
*. The mean difference is significant at the 0.05 level. |