Glossary
Alternative Hypothesis (Ha)
A statement that contradicts the null hypothesis, proposing that there is an effect, difference, or relationship.
Example:
If the null hypothesis states a coin is fair, the alternative hypothesis might be that the coin is biased (not fair).
Left-tailed test
A hypothesis test where the alternative hypothesis specifies that the population parameter is less than a hypothesized value.
Example:
Investigating if a new diet decreases average weight would typically use a left-tailed test.
Null Hypothesis (H0)
A statement of no effect, no difference, or no relationship, which is assumed to be true until evidence suggests otherwise.
Example:
In a study testing if a new fertilizer increases crop yield, the null hypothesis would be that the fertilizer has no effect on yield.
One-Sample Proportion Test
A statistical test used to compare an observed sample proportion to a hypothesized population proportion.
Example:
To determine if the proportion of students who prefer online learning in a specific school is different from the national average, you would use a one-sample proportion test.
P-value
The probability of observing a sample result as extreme as, or more extreme than, what was observed, assuming the null hypothesis is true.
Example:
If a study on a new drug yields a p-value of 0.02, it means there's a 2% chance of seeing such a positive effect if the drug actually has no effect.
Right-tailed test
A hypothesis test where the alternative hypothesis specifies that the population parameter is greater than a hypothesized value.
Example:
Testing if a new teaching method increases test scores would involve a right-tailed test.
Significance Level (Alpha Level)
The predetermined threshold (often 0.05) used to decide whether to reject the null hypothesis; if the p-value is less than this level, the result is considered statistically significant.
Example:
Setting the significance level at 0.05 means you're willing to accept a 5% chance of making a Type I error (rejecting a true null hypothesis).
Test Statistic
A standardized value calculated from sample data during a hypothesis test, used to determine the p-value and make a decision about the null hypothesis.
Example:
In a t-test, the calculated test statistic (t-score) tells you how many standard errors your sample mean is away from the hypothesized population mean.
Two-tailed test
A hypothesis test where the alternative hypothesis specifies that the population parameter is different from (either greater than or less than) a hypothesized value.
Example:
If you're checking whether a machine's output differs from a standard 100 units (it could be more or less), you'd use a two-tailed test.
Type II Error
Occurs when a hypothesis test fails to reject a false null hypothesis, meaning you conclude there is no effect when one actually exists.
Example:
A medical test commits a Type II error if it concludes a patient is healthy when they actually have the disease.