Means Tests

HypothesisTesting

AssumptionsTesting

(Normality)

Normality Tests

Many Statistical Tests require normal dataYou must verify normality with a test

Testing for NormalityHow do we test for normality?

Compute the linear correlation coefficient between the sample data and normal scores

Weight

Perc

ent

6005004003002001000-100-200

99.9

99

95

90

80706050403020

10

5

1

0.1

Mean

<0.010

192.2StDev 110.5N 143RJ 0.955P-Value

Probability Plot of WeightNormal

H0: (null hypothesis): data normally distributed

Ha: (alternative hypothesis): Data not normal

Hypothesis TestingNormality Test

Weight

Perc

ent

6005004003002001000-100-200

99.9

99

95

90

80706050403020

10

5

1

0.1

Mean

<0.010

192.2StDev 110.5N 143RJ 0.955P-Value

Probability Plot of WeightNormal

Hypothesis TestingNormality Test

Test Statistic

P-value

Critical Value (Alpha ɑ) = ??

How to we use p?

Compare p-value from test to specified significance level (alpha, α=0.05)

If the p-value is less than or equal to α=0.05, reject the null hypothesis,

Otherwise, do not reject (fail to) the null hypothesis

Hypothesis TestingNormality Test

P-value: <0.01Alpha (ɑ) = 0.05

Since p is < ɑ Reject the null hypothesis

Since we reject the null hypothesis

H0: (null hypothesis): data normally distributed

We accept the alternative hypothesis

Ha: (alternative hypothesis): Data not normal

…and determine that data are not normallydistributed

Hypothesis TestingNormality Test