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Hypothesis Testing. Assumptions Testing (Normality). Means Tests. Normality Tests. Many Statistical Tests require normal data You must verify normality with a test. Testing for Normality. How do we test for normality?

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Means tests

Hypothesis

Testing

Assumptions

Testing

(Normality)

Means

Tests


Means tests

Normality Tests

Many Statistical Tests require normal data

You must verify normality with a test


Means tests

Testing for Normality

How do we test for normality?

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


Means tests

Hypothesis Testing

Normality Test

H0: (null hypothesis): data normally distributed

Ha: (alternative hypothesis): Data not normal


Means tests

Hypothesis Testing

Normality Test

Test Statistic

P-value

Critical Value (Alpha ɑ) = ??


Means tests

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


Means tests

Hypothesis Testing

Normality Test

P-value: <0.01

Alpha (ɑ) = 0.05

Since p is < ɑ

Reject the null

hypothesis


Means tests

Hypothesis Testing

Normality Test

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 normally

distributed