Lecture One Way ANOVA

7/27/2019 Lecture One Way ANOVA

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ANOVA

One-Way Analysis of Variance

Two-Way Analysis of Variance


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ONE WAY ANOVA


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Overview

Compares two or more populations of interval

data

Extension of independent T-Test

ANOVA (Analysis of Variance) determines

whether differences exist between population

means.

This procedure works by analyzing the sample

variance, hence the name.


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AIM

Whether means from several (>2)

independent groups differ

E.g. if a researcher is interested whether four

ethnic groups differ in their IQ scores.


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Checklist of Requirements for

ONE-WAY ANOVA

One IV (e.g., ethnicity) with more than two

levels

More than two levels for IV (e.g., Australian,

American, Chinese and African)

One DV...that is to be measured like IQ scores,

calories consumed, time taken to solve

problem.


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Assumptions

The populations from which the samples were

taken are normally distributed.

Homogeneity of variance

The observations are all independent of one

another.


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Example

A researcher is interested in finding out whether

the intensity of electric shock will affect the time

required to solve a set of difficult problems.

Eighteen subjects are randomly assigned to

three experimental conditions of low shock,

medium shock and high shock. The total time (in

minutes) required to solve all the problems isthe measure recorded for each subject.


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Dataset

Shock Intensity

Low Medium High

15 30 40

10 15 35

25 20 50

15 25 43

20 23 45

18 20 40


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State the Hypotheses

H0: The time taken to solve problems in each

shock level is same.

Ha

: The time taken to solve problems in each

shock level is not same., at least one is

different from the others.

H0: m1= m2= m3

Ha: Not all ms are equal


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Checking for the assumptions

INDEPENDENCE is judged through the problemstatement

NORMALITY: if sample size is large: the datatends to normal checked through Graphically (histograms, normality plots)

Numerically (Kolmogrov, Shapiro Wilk (when samplesize is less than 50))

HOMOGENEITY OF VARIANCES Checked through levenestest


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NORMALITY

The data is said to be normally distributed, as assessedby Shapiro-Wilk Test (p>.05), so the assumption ofnormality is satisfied.

Note: for sample size less than 50, Shapiro-Wilk test is displayed automatically and weinterpret through this test. For sample size larger than 50, Kolmogrov-Smirnov test isinterpreted.


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HOMOGENEITY OF VARIANCES

The significance value exceeds .05, suggesting

that the variances for the three shock levelsare equal, so the assumption of homogeneity

of variance is satisfied.


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Output and interpretation


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In one-way ANOVA, the total variation is partitioned into

two components. Between Groups represents variation of the group means

around the overall mean.

Within Groups represents variation of the individual scoresaround their respective group means.

Sigindicates the significance level of the F-test. Small significance values (


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Total Variability

Should besmall

Should belarge

Within group, response is

not exactly the same dueto;

1. Individual differences

2. Experimental error

different treatments

exposed to differentgroups and each

group responded

differently


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Interpretaion

The results from the analysis indicate that theintensity of the electric shock has a significanteffect on the time taken to solve the problem,

F(2,15)= 40.14,p


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Post Hoc Comparisons (when ANOVA

results are significant)

H1 supported, then researcher is interested to

know which of the two groups differ?

Post hoc comparisons provide the answer.


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Post Hoc Comparisons

Although the highly significant F-ratio (p


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Post Hoc Test


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Interpretation

The results indicate that the high shock level is

significantly different from both the low shock

and medium shock levels.

The low and medium shock levels do not differ

significantly.


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Graphical Representation


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Conclusion

These results show that overall difference in

the time taken to solve complex problems

between the three shock intensity levels is

because of significantly greater amount of

time taken by the subjects in high shock

conditions.

Lecture One Way ANOVA

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