Probability - Binomial

Principles of BiostatisticsANOVADietWeight Gain (grams)Standard91010108Junk Food1010131312Organic91012910Table shows weight gains for mice on 3 diets.Test the following hypothesis at the = 0.05 sig level.

DietWeight Gain (grams)Standard91010108Junk Food1010131312Organic91012910Table shows weight gains for mice on 3 diets.Test the following hypothesis at the = 0.05 sig level.

ANOVA (Analysis of Variance)

Assumptions: Samples are independent (within and among groups) Population variances are equal Populations are normally distributedTable shows weight gains for mice on 3 diets.Test the following hypothesis at the = 0.05 sig level.

DietWeight Gain (grams)MeanStandard910101089.4Junk Food101013131211.6Organic910129101010.33Table shows weight gains for mice on 3 diets.Test the following hypothesis at the = 0.05 sig level.

DietWeight Gain (grams)MeanStandard910101089.4Junk Food101013131211.6Organic910129101010.33DietSquare Deviations (within groups)Standard(9-9.4)2(10-9.4)2(10-9.4)2(10-9.4)2(8-9.4)2Junk Food(10-11.6)2(10-11.6)2(13-11.6)2(13-11.6)2(12-11.6)2Organic(9-10)2(10-10)2(12-10)2(9-10)2(10-10)2DietSquare Deviations (within groups)Standard0.160.360.360.361.96Junk Food2.562.561.961.960.16Organic10410Table shows weight gains for mice on 3 diets.Test the following hypothesis at the = 0.05 sig level.

DietWeight Gain (grams)MeanStandard910101089.4Junk Food101013131211.6Organic910129101010.33DietSquare Deviations (within groups)Standard0.160.360.360.361.96Junk Food2.562.561.961.960.16Organic10410

Table shows weight gains for mice on 3 diets.Test the following hypothesis at the = 0.05 sig level.

DietWeight Gain (grams)MeanStandard910101089.4Junk Food101013131211.6Organic910129101010.33DietSquare Deviations (between groups)Standard(9.4-10.33)2Junk Food(11.6-10.33)2Organic(10-10.33)2DietSquare Deviations (between groups)Standard0.87Junk Food1.60Organic0.11Table shows weight gains for mice on 3 diets.Test the following hypothesis at the = 0.05 sig level.

DietWeight Gain (grams)MeanStandard910101089.4Junk Food101013131211.6Organic910129101010.33DietSquare Deviations (between groups)Standard0.87Junk Food1.60Organic0.11

Table shows weight gains for mice on 3 diets.Test the following hypothesis at the = 0.05 sig level.

DietWeight Gai (grams)MeanStandard910101089.4Junk Food101013131211.6Organic910129101010.33

Table shows weight gains for mice on 3 diets.Test the following hypothesis at the = 0.05 sig level.

DietWeight Gai (grams)MeanStandard910101089.4Junk Food101013131211.6Organic910129101010.33

Calculating the p-value

Post-hoc TestsDietWeight Gain (grams)Standard91010108Junk Food1010131312Organic91012910

Post-hoc TestsDietWeight Gain (grams)Standard91010108Junk Food1010131312Organic91012910

Post-hoc TestsDietWeight Gain (grams)Standard91010108Junk Food1010131312Organic91012910

Assumptions Samples are independent Population variances are equal Populations are normally distributed

Not paired samplesEstimating the Pooled VarianceDietWeight Gain (grams)St DevStandard910101080.89Junk Food10101313121.52Organic910129101.22

Back to the Post-hoc TestsDietWeight Gain (grams)MeanStandard910101089.4Junk Food101013131211.6Organic9101291010

Post-hoc Confidence IntervalDietWeight Gain (grams)MeanStandard910101089.4Junk Food101013131211.6Organic9101291010

Post-hoc SummaryDietWeight Gain (grams)MeanStandard910101089.4Junk Food101013131211.6Organic9101291010t-statisticDecision-2.81Reject H0-0.77Retain H02.04Retain H0

Confidence Interval(-3.91, -0.49)(-2.31, 1.11)(-0.11, 3.31)SPSS Output

Bonferronis Correction

Example A study has 3 groups. 3 comparisons must be made.

1 to 2, 1 to 3, 2 to 3

If the pairwise error rate is 5%, approximate the overall error rate

Answer: 15%Bonferronis Correction

Example A study has 4 groups. 6 comparisons must be made.

1 to 2, 1 to 3, 1 to 4, 2 to 3, 2 to 4, 3 to 4

If the pairwise error rate is 5%, approximate the overall error rate

Answer: 30%Bonferronis Correction

Example A study has 3 groups. 3 comparisons must be made.

1 to 2, 1 to 3, 2 to 3

If the overall error rate is 5%, approximate the pairwise error rate

Answer:

Bonferronis Correction

Example A study has 4 groups. 6 comparisons must be made.

1 to 2, 1 to 3, 1 to 4, 2 to 3, 2 to 4, 3 to 4

If the overall error rate is 5%, approximate the pairwise error rate

Answer:

Formula for # of Comparisons

Post-hoc Confidence Intervals with Bonferronis Correction

Post-hoc Confidence Intervals with Bonferronis Correction

Post-hoc Confidence Intervals with Bonferronis CorrectionDietWeight Gain (grams)MeanStandard910101089.4Junk Food101013131211.6Organic9101291010

SPSS Output