Question

Following is a one-way ANOVA. 30 participants were randomly assigned into three different groups, with 10 participants in each group. The means and sample standard deviations for each group are shown below

n | X_bar | Sample standard deviation | |

Group 1 | 10 | 18 | 1.5 |

Group 2 | 10 | 14 | 2 |

Group 3 | 10 | 22 | 3 |

What is the value of η 2 for this ANOVA? Round your answer to two decimal places.

What is the value of ω 2 for this ANOVA? Round your answer to two decimal places.

Answer #1

paint | n_{i} |
x̅_{i} |
S^{2}_{i} |
n_{i}*(X_{i}-X_{grand})^{2} |
(n_{i}-1)*S^{2}_{i} |

Group 1 | 10 | 18.000 | 2.250 | 0.000 | 20.25 |

Group 2 | 10 | 14.000 | 4.000 | 160.000 | 36.00 |

Group 3 | 10 | 22.000 | 9.000 | 160.000 | 81.00 |

grand mean= | 18.000 | 320.000 | 137.25 | ||

SSTr | SSE | ||||

Source of variation | SS | df | MS | F | |

between | 320.00 | 2 | 160.00 | 31.475 | |

within | 137.25 | 27 | 5.08 | ||

total | 457.25 | 29 |

1)

^{2}
=SSbg/SSttoal =320/457.25 =0.70

ω^{2}
=(k-1)*(F-1)/((k-1)*(F-1)+nk) |
=0.67 |

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