# Hypothesis Testing: Testing an Association

Learn about hypothesis tests that can be used to evaluate whether there is an association between two variables.

Start## Key Concepts

Review core concepts you need to learn to master this subject

Two-Sample T-Test

Multiple Two-Sample T-Tests

Analysis of Variance

Tukey’s Range Test

Hypothesis Testing Assumptions

Chi-Square Test

Chi-Square Assumptions

Two-Sample T-Test

Two-Sample T-Test

```
from scipy.stats import ttest_ind
#separate out claw lengths for two species
grizzly_bear = data.claw_length[data.species=='grizzly']
black_bear = data.claw_length[data.species=='black']
#run the t-test here:
tstat, pval = ttest_ind(grizzly_bear, black_bear)
```

We can test an association between a quantitative variable and a binary categorical variable by using a two-sample t-test. The null hypothesis for a two-sample t-test is that the difference in group means is equal to zero. A two-sample t-test can be implemented in Python using the `ttest_ind()`

function from `scipy.stats`

. The example code shows a two-sample t-test for testing an association between claw length and species of bear (grizzly or black).

- 1In this lesson, we’ll use hypothesis tests to make inference about population-level associations between two variables. We will cover four different hypothesis tests: * Two Sample T-Tests (for a…
- 2Suppose that a company is considering a new color-scheme for their website. They think that visitors will spend more time on the site if it is brightly colored. To test this theory, the company sho…
- 3In the previous exercise, we used a two-sample t-test to investigate an association between a quantitative variable (time spent on a website) and a binary categorical variable (an old color scheme …
- 5Let’s say that we have performed an ANOVA to compare sales at the three VeryAnts stores. We calculated a p-value less than 0.05 and concluded that there is a significant difference between at least…
- 6Before we use a two sample t-test, ANOVA, or Tukey’s range test, we need to be sure that the following things are true: #### 1. The observations should be independently randomly sampled from the p…
- 7If we want to understand whether the outcomes of two categorical variables are associated, we can use a Chi-Square test. It is useful in situations like: * An A/B test where half of users were sho…
- 8Before we use a Chi-Square test, we need to be sure that the following things are true: #### 1. The observations should be independently randomly sampled from the population This is also true of 2…

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