## Answers

treatment | G1 | G2 | G3 | G4 | G5 | |||

count, ni = | 8 | 8 | 8 | |||||

mean , x̅ i = | 3.000 | 8.25 | 5.38 | |||||

std. dev., si = | 1.8 | 1.0 | 1.1 | |||||

sample variances, si^2 = | 3.143 | 1.071 | 1.125 | |||||

total sum | 24 | 66 | 43 | 133 | (grand sum) | |||

grand mean , x̅̅ = | Σni*x̅i/Σni = | 5.54 | ||||||

( x̅ - x̅̅ )² | 6.460 | 7.335 | 0.028 | |||||

TOTAL | ||||||||

SS(between)= SSB = Σn( x̅ - x̅̅)² = | 51.681 | 58.681 | 0.222 | 110.5833333 | ||||

SS(within ) = SSW = Σ(n-1)s² = | 22.000 | 7.500 | 7.875 | 37.3750 |

no. of treatment , k = 3

df between = k-1 = 2

N = Σn = 24

df within = N-k = 21

mean square between groups , MSB = SSB/k-1 = 110.5833/2= 55.2917

mean square within groups , MSW = SSW/N-k = 37.375/21= 1.7798

F-stat = MSB/MSW = 55.2917/1.7798= 31.0669

anova table | ||||||

SS | df | MS | F | p-value | F-critical | |

Between: | 110.58 | 2.00 | 55.29 | 31.07 | 0.000 | 3.467 |

Within: | 37.38 | 21.00 | 1.78 | |||

Total: | 147.96 | 23.00 | ||||

α = | 0.05 |

F stat = 31.07

critical value at 0.05 = 3.467

f stat > critical value , reject Ho

................

TUKEY HSD/KRAMER | |

Level of significance | 0.05 |

no. of treatments,k | 3 |

DF error =N-k= | 21 |

MSE = | 1.7798 |

q-critical value(0.05,3,21)= | 3.5646 |

critical value = q*√(MSE/2*(1/ni+1/nj))

=1.68

confidence interval = mean difference ± critical value

if confidence interval do not contains zero, then means are significantly different.

critical value = q*√(MSE/n)

if absolute difference of means > critical value,means are significnantly different ,otherwise not

confidence interval | |||||||||

mean difference | absolute mean difference | critical value | lower limit | upper limit | result | ||||

µ1-µ2 | -5.25 | 5.25 | 1.68 | -6.93 | -3.57 | yes, means are different | |||

µ1-µ3 | -2.38 | 2.38 | 1.68 | -4.06 | -0.69 | yes, means are different | |||

µ2-µ3 | 2.88 | 2.88 | 1.68 | 1.19 | 4.56 | yes, means are different |

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