Interpreting hypothesis test results

Introduction to Statistics

George Boorman

Curriculum Manager, DataCamp

Life expectancy in Chicago vs. Bangkok

Null hypothesis:
- There is no difference in life expectancy between Chicago residents and Bangkok residents
Alternative hypothesis:
- Chicago residents have a longer life expectancy than Bangkok residents

Chicago

Bangkok

sampling_histogram_of_life_expectancy_in_Chicago_and_Bangkok.png

second_sample_histogram_of_life_expectancy_in_Chicago_and_Bangkok.png

sampling_distribution_of_mean_life_expectancy_per_city_following_two_bell_curve_shapes.png

$p$
- Probability of achieving this result, assuming the null hypothesis is true

chicacgo_sample_means_distribution_annotated_with_p_value_for_mean_of_eighty_two.png

bangkok_and_chicago_sample_mean_distributions_with_p_value_annotated_as_the_overlap_between_the_two.png

To reduce the risk of drawing a false conclusion:
- Set a probability threshold for rejecting the null hypothesis
Known as $\alpha$ or significance level
Decided before data collection to minimize bias:
- Otherwise they could choose a different $\alpha$ to serve their interests
A typical threshold is 0.05
- 5% chance of wrongly concluding that Chicago residents live longer than Bangkok residents
If $p\leq\alpha$, reject the null hypothesis
These results are said to be statistically significant

sampling_distribution_of_mean_life_expectancy_per_city_following_two_bell_curve_shapes_with_overlap_annotated.png

Introduction to Statistics