Assignment # 2

Problem Set-up

Clearly describe the link between the biological hypothesis, the statistical hypothesis and the data collected

Example

This study measured the tumour volume in mice randomly assigned to four groups, three receiving different anti-cancer drugs and one control receiving no drugs, to test if the drugs were effective in reducing tumour size

If a drug was effective, then mice that received it should have a mean tumour volume that was significantly LOWER THAN the control (i.e. one-tailed).

Efficiency among drugs was tested by determining which, if any, drug had a significantly LOWER tumour volume (i.e. on tailed)

Statistical Hypothesis

Ho: No difference among group means

Ha: Difference among group means

Significant ANOVA does not indicate that drugs were effective against cancer;

Difference could be smaller control tumour volume

Need to do multiple comparisons with one-tailed hypothesis

Ho: µT≥µC

Ha: µT<µC

Analysis

1. Examine raw data first 2. Present results of ANOVA, then test

assumptions3. Try a transformation before doing

non-Parametric4. Be sure to explicitly identify if plots

and tests are of residuals or raw data

Power Considerations

Power a concern when you do not reject Ho i.e. pair-wise comparisons Not the ANOVA

Power was low for C-T, C-X comparisons

Perhaps due to the higher variation in tumoursize in those groups, especially in the control

Consequence of low power: fail to detect truedifferences between C – T, C – X, accepted afalse null (Type II error)

Discussion

Many people provide very little discussion of results, and answers to questions.

Many people simply concluded that, “the data were appropriate”.

Thanks for the vote of confidence, but we are looking for a little more intellectual zeal than that!

Discussion points

1. Logical inconsistency in pair-wise comparisons and ;

V > C, but V = T,X and T, X = C

V = C ???

1. That there was difference in mortality rates among groups (many dead mice in V).

a. may explain the smaller variation in tumour size among V group and the higher power to detect a difference in C – V

b. the usefulness of V in treating cancer if it has a high mortality rate

Discussion Points

Differences in starting tumour size: measure tumour shrinkage, as opposed to final tumour volume to reduce some of the variation and increase power

Variation among individuals; why does the drug work in some but not others?

Any other reasonable suggestion

Discussion Points

Simply suggesting more samples was not sufficient

Especially for those who didn’t talk about problems with low power!!

Writing Style

Try to write in the more formal style demanded in science.

Use paragraphs that explain what you did, interpret the result refer reader to appropriate statistical result,

graphic, table that supports your conclusion. Include statistical output, in appendix if

necessary

Example

Visual examination of residuals from the initial ANOVA, comparing tumour volumes among groups, showed evidence of non-normality (Figure 1). This result was confirmed by the K-S test on the residuals (K-S: 0.1083, p = 0.0315).

Example # 2

Tumour volume was significantly different among groups (ANOVA: F = 7.78, df = 3,70, p <0.0001), with post-hoc comparisons indicating this was due solely to a significant difference between the C and V groups (Figure 2). There was no significant difference between the control and the other two treatments or among the treatments themselves (Figure 2)