Glossary
Alternative Hypothesis (Hₐ)
A statement that contradicts the null hypothesis, proposing that there is an effect, a difference, or a relationship. It is what the researcher is trying to find evidence for.
Example:
If the null hypothesis states a coin is fair, the alternative hypothesis (Hₐ) might be that the coin is biased towards heads (p > 0.5).
Context (in conclusions)
Referring to the real-world scenario or problem being investigated when stating the conclusion of a hypothesis test. It ensures the statistical findings are meaningful and understandable in practical terms.
Example:
When concluding a test about battery life, stating 'we have sufficient evidence to conclude the new battery lasts longer' provides context, rather than just saying 'we reject H₀'.
Empirical Rule
A rule stating that for a normal distribution, approximately 68% of data falls within one standard deviation, 95% within two standard deviations, and 99.7% within three standard deviations of the mean.
Example:
According to the Empirical Rule, if student heights are normally distributed with a mean of 68 inches and a standard deviation of 2 inches, about 95% of students will have heights between 64 and 72 inches.
Fail to reject the null hypothesis (H₀)
This decision is made when there is not enough statistical evidence to conclude that the null hypothesis is false. It does not mean the null hypothesis is true, only that the data does not provide compelling evidence against it.
Example:
After analyzing survey results, if the p-value is high, you might fail to reject the null hypothesis that a majority of students prefer online classes, meaning there isn't enough evidence to say otherwise.
Null Hypothesis (H₀)
A statement of no effect, no difference, or no relationship between variables, which is assumed to be true until evidence suggests otherwise. It is the statement being tested in a significance test.
Example:
The null hypothesis (H₀) for a new fertilizer might be that it has no effect on crop yield, meaning the average yield with the fertilizer is the same as without it.
P-value
The probability of observing a test statistic as extreme as, or more extreme than, the one calculated from the sample data, assuming the null hypothesis is true. It quantifies the 'surprise factor' of your data.
Example:
A p-value of 0.01 means there's only a 1% chance of seeing results like yours if the null hypothesis were true, making your data quite surprising.
Reject the null hypothesis (H₀)
This decision is made when there is sufficient statistical evidence to conclude that the null hypothesis is likely false. It implies that the observed data is too unlikely to have occurred if the null hypothesis were true.
Example:
If a study finds a very low p-value for a new drug, researchers might reject the null hypothesis that the drug has no effect, concluding it is effective.
Significance Level (α)
A predetermined threshold (e.g., 0.05 or 0.01) used to decide whether to reject the null hypothesis. If the p-value is less than or equal to alpha, the results are considered statistically significant.
Example:
Setting the significance level (α) at 0.05 means you are willing to accept a 5% chance of making a Type I error (rejecting a true null hypothesis).
Statistically Significant Evidence
Evidence from a sample that is unlikely to have occurred by random chance if the null hypothesis were true, typically indicated by a p-value less than or equal to the significance level.
Example:
Finding a p-value of 0.001 provides statistically significant evidence that the new teaching method improves test scores, as such a result is highly improbable by chance alone.
Test Statistic
A value calculated from sample data during a hypothesis test that measures how far the sample results deviate from what is expected under the null hypothesis. Examples include z-scores and t-scores.
Example:
In a study comparing two groups, the test statistic might be a t-value of 3.1, indicating a notable difference between the group means.
Z-score
A measure of how many standard deviations an element is from the mean. In hypothesis testing, it indicates how far a sample statistic is from the hypothesized population parameter under the null hypothesis.
Example:
If a student's test score has a z-score of 2.5, it means their score is 2.5 standard deviations above the class average, indicating a strong performance.