Glossary
Hypothesis Testing
A statistical method used to make decisions about a population parameter based on sample data. It involves setting up competing hypotheses and using data to determine which one is more likely.
Example:
Before launching a new app, a company uses hypothesis testing to determine if the average user engagement time is significantly different from their previous app.
Null Hypothesis (H₀)
The statement of no effect, no difference, or no change that is assumed to be true until evidence suggests otherwise. It's the baseline assumption in a hypothesis test.
Example:
In a study testing a new fertilizer, the null hypothesis would be that the fertilizer has no effect on crop yield.
Power
The probability of correctly rejecting a false null hypothesis. It measures the test's ability to detect a real effect or difference when one truly exists.
Example:
A high power in a clinical trial means the study is very likely to detect if a new treatment is truly effective, rather than missing its benefits.
Sample Size
The number of observations or individuals included in a statistical study. Increasing it generally improves the precision of estimates and the power of a test.
Example:
To increase the chance of detecting a small but real difference in customer satisfaction, a company should increase their sample size for the survey.
Significance Level (α)
The predetermined probability of making a Type I error, often set at 0.05 or 0.01. It represents the threshold for rejecting the null hypothesis.
Example:
If a researcher sets the significance level (α) at 0.05, they are willing to accept a 5% chance of incorrectly rejecting a true null hypothesis.
Standard Error
A measure of the variability or dispersion of sample means (or other sample statistics) around the true population mean. A smaller standard error indicates more precise estimates.
Example:
If a survey has a small standard error, it means that repeated samples would likely produce very similar average results, indicating high precision.
Type I Error
Occurs when a true null hypothesis is incorrectly rejected. It's a 'false positive,' concluding an effect exists when it doesn't.
Example:
A pharmaceutical company commits a Type I error if they conclude their new drug lowers blood pressure when, in reality, it has no effect, potentially leading to an ineffective drug being marketed.
Type II Error
Occurs when a false null hypothesis is incorrectly failed to be rejected. It's a 'false negative,' missing a real effect or difference.
Example:
A medical test makes a Type II error if it fails to detect a disease that is actually present in a patient, leading to a missed diagnosis.