**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
**A**nalyze > 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** - Click the
**Post-Hoc****Tu****key**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**