## One-Way ANOVA

ANOVA |
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Stanford Achievement Test NCE scores in Reading Before | |||||

Sum of Squares | df | Mean Square | F | Sig. | |

Between Groups | 2341.061 | 2 | 1170.530 | 3.426 | .036 |

Within Groups | 42360.337 | 124 | 341.616 | ||

Total | 44701.397 | 126 |

Interpretations: “A one-way between subjects ANOVA was conducted to compare the difference in the Pre-SAT reading scores among different races. There was a statistical significant difference in the Pre-SAT reading scores of the three different race with (F=3.426, p=0.036).

C. t tests - Means: Difference between two independent means (two groups)

Analysis: A priori: Compute required sample size

Input: Tail(s) = Two

Effect size d = 0.5

α err prob = 0.05

Power (1-β err prob) = 0.80

Allocation ratio N2/N1 = 1

Output: Noncentrality parameter δ = 2.8284271

Critical t = 1.9789706

Df = 126

Sample size group 1 = 64

Sample size group 2 = 64

Total sample size = 128

Actual power = 0.8014596

Using G-power analysis the required sample size is 64 for group 1 and 64 for group 2 which will amount to 128 total sample size.

## Two-Way ANOVA

A. Two- Way ANOVA is the appropriate statistical level to use. The two-way ANOVA is used to estimate how the mean of a quantitative variable changes according to the levels of two categorical variables. In this question both race and group are the categorical variables while the Pre-SAT reading scores is the dependent variable.

B.

a. R Squared = .080 (Adjusted R Squared = .042)

Tests of Between-Subjects Effects |
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Dependent Variable: Stanford Achievement Test NCE scores in Reading Before | |||||

Source | Type III Sum of Squares | df | Mean Square | F | Sig. |

Corrected Model | 3596.055^{a} |
5 | 719.211 | 2.117 | .068 |

Intercept | 333707.428 | 1 | 333707.428 | 982.320 | .000 |

group | 84.123 | 1 | 84.123 | .248 | .620 |

race | 2976.851 | 2 | 1488.425 | 4.381 | .015 |

group * race | 1064.266 | 2 | 532.133 | 1.566 | .213 |

Error | 41105.342 | 121 | 339.714 | ||

Total | 486021.730 | 127 | |||

Corrected Total | 44701.397 | 126 |

Multiple Comparisons |
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Dependent Variable: Stanford Achievement Test NCE scores in Reading Before Tukey HSD | ||||||

(I) race | (J) race | Mean Difference (I-J) | Std. Error | Sig. | 95% Confidence Interval | |

Lower Bound | Upper Bound | |||||

African American | White | -9.505^{*} |
3.6212 | .026 | -18.098 | -.913 |

Others | -5.740 | 4.9706 | .482 | -17.535 | 6.054 | |

White | African American | 9.505^{*} |
3.6212 | .026 | .913 | 18.098 |

Others | 3.765 | 4.7305 | .706 | -7.460 | 14.990 | |

Others | African American | 5.740 | 4.9706 | .482 | -6.054 | 17.535 |

White | -3.765 | 4.7305 | .706 | -14.990 | 7.460 |

Correlations |
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Stanford Achievement Test NCE scores in Reading After | Stanford Achievement Test NCE scores in Language After | Stanford Achievement Test NCE scores in Math After | ||

Stanford Achievement Test NCE scores in Reading After | Pearson Correlation | 1 | .737^{**} |
.789^{**} |

Sig. (2-tailed) | .000 | .000 | ||

N | 148 | 148 | 148 | |

Stanford Achievement Test NCE scores in Language After | Pearson Correlation | .737^{**} |
1 | .738^{**} |

Sig. (2-tailed) | .000 | .000 | ||

N | 148 | 148 | 148 | |

Stanford Achievement Test NCE scores in Math After | Pearson Correlation | .789^{**} |
.738^{**} |
1 |

Sig. (2-tailed) | .000 | .000 | ||

N | 148 | 148 | 148 |