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ANOVA Procedures Homework Help Using SPSS
Performing ANOVA Statistics
The author of our textbook (Andy) did an experiment in his own statistics courses where he taught the same material but with different teaching methods. The first group of students got punished by asking draft questions or giving wrong answers (punish teaching method); the second group received reward for participating in discussions and working hard (reward teaching method); the third group received neither punishment nor rewards so that Andy remained indifferent to students’ efforts (indifferent teaching method). Students took exams at the end of semester which reflected their learning outcome.
Research Question: Examine the effect of different teaching methods on students’ exam scores. In particular, we would like to know (a) if there is any difference in exam scores across three groups, (b) if reward teaching would produce the best learning, and (c) if punishment would retard learning and be even worse than indifferent approach.
Comparing Mean Differences Using One-way
ANOVA
1. Download Teach.sav from Blackboard and open in SPSS
2. Examine normality assumption
Analyze Descriptive Statistics, Explore, Plots, Check histogram and normality plots with test Continue, OK
Q1 (1 pt): Is the normality assumption violated? Justify your answer.
Ans: No. The normality assumption is not violated as the KS test as well as Shapiro-Wilk test both are statistically insignificant at 5% level of significance.
Tests of Normality |
| |
Kolmogorov-Smirnova |
Shapiro-Wilk |
| Statistic |
df |
Sig. |
Statistic |
df |
Sig. |
| Exam Mark |
.139 |
30 |
.142 |
.937 |
30 |
.075 |
| a. Lilliefors Significance Correction |
3. Examine homogeneity of variance assumption and run one-way
ANOVA
Analyze Compare Means One-way ANOVA Move exam to “Dependent” Move group to “Factor” Options Check Descriptive, Homogeneity of variance test, and Means plot Continue OK
Q2 (1 pt): Is the homogeneity of variances assumption violated? Justify your answer.
Ans: No. The test of homogeneity of variances yields statistically insignificant result based on mean, median, and trimmed mean.
Test of Homogeneity of Variances |
| |
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 |
Q3 (2 pts):Is there a significant difference in students’ exam scores between three groups that received different teaching methods? Report the F test results in APA format.
ANS: Yes. There is statistically significant difference between the exam scores of three groups. The F-statistic was obtained as 21.0 (p-value < 0.001) indicating that null hypothesis of no difference in exam scores should be rejected in favor of alternative.
Hence, we conclude that the data contains enough evidence that exam scores of three different teaching methods are different.
ANOVA |
| 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 |
|
|
|
Note: use the five rules for assigning weights for contrasts and the requirement of orthogonal contrast.
5. Run the planned contrasts specified in the previous step.
In One-Way ANOVA, Contrasts Type in weights as coefficients (pay close attention to the sequence)
| 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
|
| 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
|
| 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. |
Q7 (1 pt): Which means are different based on Scheffe test?
Ans: In Scheffe’s test, we have same result as our contrast that exam scores of teaching methods Punish and Indifferent are not different, but they are different from Reward at 5% level of significance.
P-value for difference between Punish and Indifferent are >0.05 but with Rewards, it is <0.05
Q8 (1 pt): Were the results different based on Tukey (HSD) and Scheffe tests? Did you expect that? Why or why not?
Ans: Yes the results in Tukey’s HSD and Scheffee’s tests are different. This is not surprising given they use different methods in controlling the type 1 error and Tukey HSD favors power of the test, hence, it rejects the null hypothesis more often than Scheffe’s which is quite conservative in power.