Hypothesis Testing

Hypothesis Testing Assignment Help

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Hypothesis testing

Hypothesis tests can be one sided or two sided tests as explained below.

One tailed tests are directional in nature:

H0: µ1 - μ2 ≤ 0
H1: μ1 - μ2 > 0

This is a one-tailed test in which the critical region lies in the right-tail of the test statistic.

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Two tailed tests are not directional:

H0: μ1 - μ2 = 0
H1: μ1 - μ2 ≠ 0

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Significance of P-value:

P-value ≤ α ⇒ Reject H0 at level α
P-value > α ⇒ Do not reject H0 at level α

When to Reject H0

Denoting our subject probability as follows:

Level of significance, α:It is defined before doing hypothesis test and is used to decide rejection region
Rejection region: Region outside the confidence interval as shown below.

When to use what?

Comparison of meansParametric TestsNon-parametric Tests
Differences between the means of two independent groupsIndependent t-testMann-Whitney test
Differences between paired (matched) samples e.g. weight before and after a diet for each subjectPaired t-testWilcoxon signed rank test
Differences in the means of 3+ independent groups for one variableOne-way ANOVAOne-way ANOVA
Differences between 3+ measurements on the same subjectRepeated Measures ANOVAFriedman test
Strength of a relationship between 2 continuous variablesPearson's Correlation Co-efficientSpearman's Correlation co-efficient
Predicting the value of one variable given the value of a predictor variableSimple Linear Regression
Assessing the relationship between two categorical variables.Chi-squared test


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