Perform a 1-d and 2-d chi squared test
| How well is it to study/work not being in school/work? | How have your grades been impacted from switching to online learning? | How has your productivity been impacted in how your online classes are structured? |
| 5 | 5 | 5 |
| 4 | 3 | 5 |
| 5 | 3 | 5 |
| 5 | 3 | 5 |
| 3 | 2 | 5 |
| 1 | 1 | 2 |
| 2 | 4 | 5 |
| 4 | 2 | 4 |
| 5 | 3 | 3 |
| 5 | 3 | 5 |
| 5 | 3 | 4 |
| 4 | 3 | 4 |
| 5 | 2 | 4 |
| 5 | 5 | 5 |
| 3 | 3 | 3 |
| 4 | 3 | 2 |
| 2 | 2 | 2 |
| 4 | 4 | 2 |
| 2 | 3 | 3 |
| 3 | 3 | 4 |
| 2 | 4 | 4 |
| 3 | 2 | 4 |
| 5 | 4 | 5 |
| 5 | 3 | 5 |
| 5 | 4 | 5 |
| 5 | 4 | 5 |
| 5 | 4 | 5 |
| 5 | 4 | 4 |
| 4 | 4 | 5 |
| 5 | 3 | 5 |
| 5 | 3 | 5 |
| 5 | 3 | 5 |
| 5 | 3 | 4 |
| 5 | 3 | 5 |
| 3 | 4 | 5 |
| 5 | 4 | 5 |
| 5 | 3 | 5 |
| 5 | 3 | 5 |
| 5 | 4 | 4 |
| 4 | 4 | 4 |
| 5 | 3 | 5 |
| 5 | 3 | 5 |
| 4 | 5 | 4 |
| 5 | 4 | 5 |
| 4 | 3 | 4 |
| 5 | 4 | 5 |
| 5 | 3 | 5 |
| 3 | 3 | 3 |
| 3 | 3 | 3 |
| 2 | 3 | 2 |
The hypothesis being tested is:
H0: µ1 = µ2 = µ3
Ha: Not all means are equal
| Mean | n | Std. Dev | |||
| 4.2 | 50 | 1.13 | How well is it to study/work no | ||
| 3.3 | 50 | 0.81 | How have your grades been impac | ||
| 4.2 | 50 | 1.00 | How has your productivity been | ||
| 3.9 | 150 | 1.08 | Total | ||
| ANOVA table | |||||
| Source | SS | df | MS | F | p-value |
| Treatment | 28.37 | 2 | 14.187 | 14.49 | 1.80E-06 |
| Error | 143.92 | 147 | 0.979 | ||
| Total | 172.29 | 149 |
The p-value is 0.0000.
Since the p-value (0.0000) is less than the significance level (0.05), we can reject the null hypothesis.
Therefore, we can conclude that not all means are equal.
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