Longitudinal High school Study
Research Question
Does the school location affect Students Mathematical Efficacy?
Hypotheses
H0: School Location does not affect Students Mathematical Efficacy.
H1: At least one Location affects the Students Mathematical Efficacy.
Analysis Procedure
Press OK to produce output
- Click Analyze > Compare Means > One-Way ANOVA… on the main menu:
- Click on variable T1 Scale of student’s mathematics Self Efficacy and use the arrow button to move it to the Dependent list box.
- Click on variable T1 School Locale and use the arrow button to move it to the Factor box.
- Click the Post-Hoc button and check on the Tukey Option and Press Continue.
Output
| Sum of Squares | df | Mean Square | F | Sig. | |
| Between Groups | 37.676 | 3 | 12.559 | 12.705 | .000 |
|---|---|---|---|---|---|
| Within Groups | 18539.843 | 18755 | .989 | ||
| Total | 18577.519 | 18758 |
| (I) T1 School locale (urbanicity) | (J) T1 School locale (urbanicity) | Mean Difference (I-J) | Std. Error | Sig. | 95% Confidence Interval | |
|---|---|---|---|---|---|---|
| Lower Bound | Upper Bound | |||||
| City | Suburb | -.00558 | .01811 | .990 | -.0521 | .0409 |
| Town | .10415* | .02506 | .000 | .0398 | .1685 | |
| Rural | .08268* | .02024 | .000 | .0307 | .1347 | |
| Suburb | City | .00558 | .01811 | .990 | -.0409 | .0521 |
| Town | .10973* | .02434 | .000 | .0472 | .1723 | |
| Rural | .08826* | .01934 | .000 | .0386 | .1379 | |
| Town | City | -.10415* | .02506 | .000 | -.1685 | -.0398 |
| Suburb | -.10973* | .02434 | .000 | -.1723 | -.0472 | |
| Rural | -.02147 | .02596 | .842 | -.0882 | .0452 | |
| Rural | City | -.08268* | .02024 | .000 | -.1347 | -.0307 |
| Suburb | -.08826* | .01934 | .000 | -.1379 | -.0386 | |
| Town | .02147 | .02596 | .842 | -.0452 | .0882 | |
From the ANOVA Output, we observe that (F (3, 18755) = 12.705, p = .000). Since the P-Value is less than our alpha value of 0.05, the null hypothesis is rejected and we conclude that At least one Location affects the Students Mathematical Efficacy.
On the 2nd table, we perform a Tukey post-hoc test to determine the effect size. The table, Multiple Comparisons, shows which groups differed from each other. The Tukey post-hoc test is generally the preferred test for conducting post-hoc tests on a one-way ANOVA. We can see from the table that there is a significant difference in Mathematics Self Efficacy between the group in the City and that in Town (p = 0.000), as well as between that in the city and that in Rural setting (p = 0.000). Also significant difference was noted between the group in Suburb and that in Town (p = 0.000), and between those in Suburb and those in Rural areas (p = 0.000). However, there were no differences between the groups that Studied in the City and that in the Suburb (p = 0.990) and between that in town and that in Rural areas (p = 0.842).
Social Change
These results are important as they will help a parent or guardian to soundly decide where their children will be best motivated as much as Mathematics Self Efficacy is concerned.
Reference