SPSS and Anova

8/8/2019 SPSS and Anova

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SPSS

t-test and ANOVA

By the end of this lecture you shouldunderstand

Carrying out a t-test

Why we need ANOVA

Entering data and running a 1-way ANOVA

Interpreting a 1-way ANOVA

H0 : =

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Basic Stats. RevisionH0 : =

Assumptions and requirements

All data are independent (no data point canappear twice) (APPLIES TO ALL TESTS)

Variances must be homogenous (can be fixedusing transformations)

For ANOVA and t tests the assumption of anormal distribution of the data is least importantand can effectively be ignored


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Errors

Null Hyp. True

Null Hyp. False

Accept Reject

Type I errorby conventionp(type I) =

= 0.05

Type II error

p (type II) =

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Comparing 2 means (t test), robust, reliable.

A t-test

A B

H0 : =


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A Basic t-testH0 : =

Investigation into group size in kangaroos. Theliterature says that the average group size is 10

Model: You are testing the model that yourgroup is representative of other studies

Hypothesis is that your mean is statistically notdifferent from 10

Collect data from 25 groups

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2 ways of doing this

1. Excel using the formula, with n-1 degrees offreedom


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Use a statistical programme

Good example is SPSS

Is NOT a spreadsheet

1. copy and paste data into cells, then namecells


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10

Then double click on

var00001


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Code Label(will appear in print-outs) Grouping

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Mean is significantly less than10, t24 = 9.28, P < 0.001


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2-sample t-test to compare 2 means

Model: You are testing the model that yourgroups are different from another 20 groups fromdifferent habitats

Hypothesis is that the average group size differsbetween groups seen in area A ) (bush) and areaB (grass

Collect data from 20 groups in each habitat

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Need to code the groups


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So, the mean size of groups of kangaroos ineach habitat was not significantly differentt38 = 0.662, NS

P > 0.05

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ANOVA

By the end of this lecture you shouldunderstand

Why we need ANOVA

Entering data and running a 1-way ANOVA

Interpreting a 1-way ANOVA

Entering data and running a 2 wayorthogonal ANOVA

Interpretation of such an ANOVA

H0 : =


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Basic Stats. RevisionH0 : =

Assumptions and requirements

All data are independent (no data point canappear twice) (APPLIES TO ALL TESTS)

Variances must be homogenous (can be fixedusing transformations)

For ANOVA and t tests the assumption of anormal distribution of the data is least importantand can effectively be ignored

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Comparing 2 means (t test), robust, reliable.

What happens for 3 levels of a treatment,e.g. 3 diets affecting growth of shrimps?

t tests look for differences in treatmentmeans, consider overlap of tails

Why ANOVA?

A B

H0 : =


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3 means, now have 11 possible tails......OW!

Instead of using 1 test, could use 3 tests

A vs B, A vs C, and B vs C

This approach... 2 problems...

1. Problems of independence

2. Increased probability of type I error (on 3tests rises to 0.14 from 0.05)

Can get round pt 2 by corrections(Bonferroni), but this increases probability oftype II error and gives reduced power

t testsH0 : =

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ANOVA

Can use an ANOVA for >2 means

Allows development of complex designs

H0 : =


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Language Break!

Response variable: the thing you are measuringMost people think in terms of treatment(s)

Clumsy and ambiguous term

Example.... To investigate the effect of growthenhancers on the cattle.

Treatment (T) effect:Diet

T1 = normal dietT2 = diet + xT3 = diet + 2x

Factor: Diet3 Levels

L1 = normal dietL2 = diet + xL3 = diet + 2x

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1-way ANOVA on SPSS

Model: Temperature controls themetamorphosis rate of barnacles cyprids

Hypothesis: If temperature increases, timetaken for metamorphosis is reduced (H1:

time at high T0C < time at medium T0C 0.31.1397.332194.7Ve x Di> 0.50.6959.112118.2Disturbance Di

< 0.00152.904556.2514556.3Vegetation Ve

PFMSdfSSSource

Effect of Vegetation Type on Success Rates of Foraging Kestrels

Vegetation

Grass Complex

SuccessR

ates(Killsperday)

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5

10

15

20

25

30

35

40

High Dist

Med Dist

Low dist

Interpret?

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2-way Factorial ANOVA : SPSS

Too simplistic?

Madeitup, I (1989) redid the experiment

Kestrels 2 data set,


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3613269.0Total

97.63302928.8Residual

< 0.017.15697.8621395.7Ve x Di

< 0.054.3420.192840.4Disturbance Di

< 0.018.71850.691850.7Vegetation Ve

PFMSdfSSSource

2-way Factorial ANOVA : SPSS

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Effect of Vegetation Type on Success Rates of Foraging Kestrels

Vegetation

Grass Complex

SuccessRates(Killsperday)

0

5

10

15

20

25

30

low Dist

Med Dist

High dist


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2-way Factorial ANOVA on

SPSSWhat have I missed?

Assumptions of independence.. DESIGN

Assumptions of Homogeneity of Variance..Test data

stat, ANOVA, Homogeneity of Variance

use Levenes test?

H0 : =

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Homogeneity of Variance

Do ANOVAand Interpret

Non SignificantResult

YesDo ANOVAand interpret

ANOVA NSAbsolutely Fine

YesProbably OK

NoInterpret with

caution, treat as pilot

Design Large?N > 30, a > 6

ANOVA Sig.

NoDo ANOVA

Fixed Problemof heterogeneity?

Transform Dataand re-test

SignificantResult

Test Homogeneity ofVariance


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Summary and survival guide

ANOVA is more powerful in terms of flexibility data must be independent

variances must be homogeneous

Normality is not important

Nearly all biological hypotheses are aboutinteractions... Know what that means!

SPSS is useful for general purposes

All detailed in your refs + Dytham, C. (1999)

Choosing and using statistics. Blackwell. (note heis wrong about assumptions of normality.. Ignore it!)

Documents

SPSS and Anova