ANOVA
T1 Scale of student's mathematics self-efficacy
	Sum of Squares	df	Mean Square	F	Sig.
Between Groups	3.684	3	1.228	1.271	.282
Within Groups	4509.796	4669	.966
Total	4513.480	4672

Multiple Comparisons
Dependent Variable: T1 Scale of student's mathematics self-efficacy
Tukey HSD
(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	-.00853	.03565	.995	-.1001	.0831
Town	.07693	.05069	.427	-.0534	.2072
Rural	.03513	.04032	.820	-.0685	.1387
Suburb	City	.00853	.03565	.995	-.0831	.1001
Town	.08546	.04908	.302	-.0407	.2116
Rural	.04366	.03827	.664	-.0547	.1420
Town	City	-.07693	.05069	.427	-.2072	.0534
Suburb	-.08546	.04908	.302	-.2116	.0407
Rural	-.04180	.05257	.857	-.1769	.0933
Rural	City	-.03513	.04032	.820	-.1387	.0685
Suburb	-.04366	.03827	.664	-.1420	.0547
Town	.04180	.05257	.857	-.0933	.1769

T1 Scale of student's mathematics self-efficacy
Tukey HSDa,b
T1 School locale (urbanicity)	N	Subset for alpha = 0.05
1
Town	521	-.0056
Rural	1062	.0362
City	1349	.0713
Suburb	1741	.0799
Sig.		.227
Means for groups in homogeneous subsets are displayed.
a. Uses Harmonic Mean Sample Size = 957.699.
b. The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error levels are not guaranteed.

Question: Is there a relationship between a student's school location and the student's mathematical proficiency?

Hypotheses

H0: School Location does not affect Students Mathematical Self Efficacy

H1: At Least One Location Affects Students Mathematical Self Efficacy.

From the ANOVA Output we observe that (F (3, 4669)= 1.271, p = 0.282). Because the P-Value was higher than the alpha value of 0.05, the null hypothesis is accepted, and I conclude that school location does not affect a student's Mathematics Self Efficacy . In the 2nd table, I performed a Tukey post-hoc test to determine the size of the effect. The table, Multiple Comparisons, shows which groups differ from each other. The Tukey post-hoc test is usually the preferred test for conducting a post-hoc test with a one-way ANOVA (Wagner, 2020). The table reveals that there is not a significant difference in Mathematics Self Efficacy between the location groups in the city and the town (p = .427), as well as between the city and the rural setting (p = .820) and city and suburb (p = .995). Continuing to the Suburbs, there is not a significant difference between suburb and town (p = .302) and suburb and rural (p = .664). Finally, no statistical meaningfulness showed up between town and rural (p = .857). Table 3 shows that the significance value is .227 which is greater than .05 for all the three cases so therefore we can say that there is no such relationship between students location and mathematical self efficacy.

Is this a good summary for the above tables? Does this make sense?