Lab 2 instruction

a collection of statistical methods to compare several groups according to their means on a quantitative response variable

One-Way ANOVAa special case of ANOVA when a single

factor is used

Response: LSA value (lipid-bound sialic acid)

4 groups: 1(Control), 2(benign), 3(Primary), 4(Recurrent)

350 patients in each group

Independence: both within and across the groups

Normality: population distributions of all groups are normal

the populations have equal standard deviations

Independence: setup of the experiment

Normality: boxplot / Q-Q plot

Equal std devs: ◦ Boxplot◦ Descriptive summary “Rule of thumb”: the ratio of the largest sd and the

smallest sd < 2◦ Levene’s test

In Levene’s test

Levene’s test of equal Levene’s test of equal variancevariancess

equal are variancesallnot :

: 24

23

22

210

AH

H

p-value>0.05

Analyze -> Descriptive stats -> explore

Descriptive summary;boxplot;Q-Q plot;Levene’s test.

differ means least twoat :

: 43210

AH

H

One-way ANOVA

Analyze -> Compare Means -> One-Way ANOVA

Full model: different group meanReduced model: grand mean

Calculate F by hand:

F (SSRreduced SSR full ) /(dfreduced df full )

SSR full /df full

Multiple comparisons: test the difference between each pair of means

Tukey test Scheffe test

Multiple ComparisonMultiple Comparison

In Post Hoc..

Multiple ComparisonMultiple Comparison number of pairwise comparisons Look at p-value of the hypothesis test of equalit

y of two means Check whether the confidence interval contains

zero or not

compare cancer patients (group 2, 3 and 4 ) with healthy individuals (group 1).

03:

03:

,lyequivalent

3/)(:

3/)(:

4321

43210

4321

43210

A

A

H

H

H

H

In Contrasts..

Another tool in SPSS:Another tool in SPSS:ScatterPlotScatterPlot

If two variables are somehow related, there would be some trend in the scatter plot.

Scatter plot of “LSA” V.S. “ID”--LSA in Y axisID in X axis

Different groups can be denoted using different markers

Scatter plotScatter plot