Biostatistics Final Exam Definitions UTA
Bonferroni-Holm Multiple Comparisons - ANSWER>>-In the context of an
ANOVA, rejecting the null hypothesis means there is a statistical difference
between at least two means, but it won't tell you where it is. You use this to
discover exactly which means are different.
-Only used for Model I ANOVAs
-A t-statistic for a two sample t-test assuming equal variance
Steps to Applying the Bonferroni-Holm Multiple Comparison Test -
ANSWER>>Step 1: Calculate test statistics and corresponding P values for each
of the m comparisons
Step 2: Order the P values from smallest to largest: p1,p2,...,pm. Label the
corresponding comparisons: C1,C2,...Cm
Step 3: Compare p1 and alpha(a)/m
(a) If p1 > a/m, then stop. Conclude that there is no evidence of differences
between any of the means. Procedure is done
(b) p1 < or = a/m, then reject Ho for C1. Continue to next step.
Step 4: Compare p2 and a/(m-1)
(a) If p2 > a/(m-1), then stop. There is no evidence of differences between any
of the means in the remaining comparisons. Procedure is done.
(b) p2 < or = a/(m-1), then reject Ho for C2. Continue to next step.
Step 5: Compare p3 and a/(m-2)
(a) If p3 > a/(m-2), then stop. There is no evidence of differences between any
of the means in the remaining comparisons. Procedure is done.
, (b) p3 < or = a/(m-2), then reject Ho for C3. Continue to next step
Continue until procedure requires you to stop or until all P values have been
compared
Kruskal-Wallis Test - ANSWER>>The nonparametric analog to a Model I One-
Way ANOVA. We would use if it we reject the assumption of normality for the
data.
Randomized-Complete Block Design ANOVA - ANSWER>>Used to extend paired
experimental designs to accommodate making more than just two
measurements on the same individuals. Also called Repeated Measures ANOVA.
Model Assumptions:
1. Each observation constitutes a random, independent sample from a
population with mean u_ij. There are k x b of these populations sampled.
2. Each of the k x b populations is normal and with the same variance.
3. The treatment and block effects are additive, that is, there is no interaction
(synergy or interference) between blocks and treatments.
Factorial-Design Two-Way ANOVA - ANSWER>>Model Assumptions:
1. The observations in each cell constitute an independent random sample of
size n from a population with mean u_ij
2. Each of the population represented by the cell samples is normal and has the
same variance.
Friedman k-sample Test: Matched Data - ANSWER>>The nonparametric analog
to the Randomized-Complete Block Design ANOVA
Linear Regression - ANSWER>>Examines the amount of variability in one
variable (Y) that is explained by the changes in another variable (X). Typically
used in situations in which we have control of X and can measure it essentially
without error.
Bonferroni-Holm Multiple Comparisons - ANSWER>>-In the context of an
ANOVA, rejecting the null hypothesis means there is a statistical difference
between at least two means, but it won't tell you where it is. You use this to
discover exactly which means are different.
-Only used for Model I ANOVAs
-A t-statistic for a two sample t-test assuming equal variance
Steps to Applying the Bonferroni-Holm Multiple Comparison Test -
ANSWER>>Step 1: Calculate test statistics and corresponding P values for each
of the m comparisons
Step 2: Order the P values from smallest to largest: p1,p2,...,pm. Label the
corresponding comparisons: C1,C2,...Cm
Step 3: Compare p1 and alpha(a)/m
(a) If p1 > a/m, then stop. Conclude that there is no evidence of differences
between any of the means. Procedure is done
(b) p1 < or = a/m, then reject Ho for C1. Continue to next step.
Step 4: Compare p2 and a/(m-1)
(a) If p2 > a/(m-1), then stop. There is no evidence of differences between any
of the means in the remaining comparisons. Procedure is done.
(b) p2 < or = a/(m-1), then reject Ho for C2. Continue to next step.
Step 5: Compare p3 and a/(m-2)
(a) If p3 > a/(m-2), then stop. There is no evidence of differences between any
of the means in the remaining comparisons. Procedure is done.
, (b) p3 < or = a/(m-2), then reject Ho for C3. Continue to next step
Continue until procedure requires you to stop or until all P values have been
compared
Kruskal-Wallis Test - ANSWER>>The nonparametric analog to a Model I One-
Way ANOVA. We would use if it we reject the assumption of normality for the
data.
Randomized-Complete Block Design ANOVA - ANSWER>>Used to extend paired
experimental designs to accommodate making more than just two
measurements on the same individuals. Also called Repeated Measures ANOVA.
Model Assumptions:
1. Each observation constitutes a random, independent sample from a
population with mean u_ij. There are k x b of these populations sampled.
2. Each of the k x b populations is normal and with the same variance.
3. The treatment and block effects are additive, that is, there is no interaction
(synergy or interference) between blocks and treatments.
Factorial-Design Two-Way ANOVA - ANSWER>>Model Assumptions:
1. The observations in each cell constitute an independent random sample of
size n from a population with mean u_ij
2. Each of the population represented by the cell samples is normal and has the
same variance.
Friedman k-sample Test: Matched Data - ANSWER>>The nonparametric analog
to the Randomized-Complete Block Design ANOVA
Linear Regression - ANSWER>>Examines the amount of variability in one
variable (Y) that is explained by the changes in another variable (X). Typically
used in situations in which we have control of X and can measure it essentially
without error.
