Hypothesis Testing

Why is hypothesis testing useful?

1. Compare a population measure to a specified value

2. Compare measures for 2 populations

3. Determine whether a population follows a specified distribution

What are the steps of hypothesis testing?

1. State the null hypothesis (H_o) – that there is no relationship between two or more objects of comparison

2. State the alternative hypothesis (H_a) – the statement that the null hypothesis is false

3. Set the significance (α) – the statistical strength of the hypothesis test

4. Collect data

5. Calculate a test statistic (p-value)

6. Accept or reject the hypothesis (compare p-value to α)

7. Draw a conclusion about the null hypothesis 

What is type I error?

Rejecting the null hypothesis when it is true (false positive)

What is type II error?

Don’t reject the null hypothesis when the alternative is true (False negative)

What is the p value?

The probability of obtaining a test statistic as extreme or more extreme than the one calculated if the null hypothesis (H_o) is true

What is a 1 sample t-test?

1. Compares the sample mean to a hypothesized value

2. Compares the sample mean to the hypothesized value to assess variability in the sample

3. The results indicate whether the difference between the values is statistically significant, using the p-value

What is a 2 sample t test?

1. A test for two population means to determine whether there is a significantly difference between the two populations

2. The two populations must be independent of the other (i.e., observations for the two populations should have occurred at different times)

3. The results indicate whether the difference between the two populations are statistically significant, using the p-value

What assumptions do we make when doing a 2 sample t test?

1. The two populations are independent

2. The data is normal

3. The two populations have equal variances

What is a paired t test?

1. A hypothesis test for the mean difference between paired observations that are related or dependent

2. The paired t-test is useful for assessing differences in before-and-after measurements on the same subject when a treatment is applied to the after measurements

What assumptions do we make when doing paired t tests?

1. Each data point collected are independent of the others

2. The data is normal

What is correlation?

Linear relationship between 2 continuous variables

What is indicative of strong correlation?

R² value is greater than .5