Statistics: Hypothesis Testing Flashcards

Question 1

Define Hypothesis Test.

Accepted Answer

A formal procedure that uses sample data to judge whether evidence against a stated claim about a population is strong enough to reject that claim.

Question 2

Define Null Hypothesis (H0).

Accepted Answer

The default statement of no effect or no difference, assumed true during the calculation and always containing an equality about a population parameter.

Question 3

Define Alternative Hypothesis (Ha).

Accepted Answer

The competing statement a study seeks evidence for, claiming a population parameter is greater than, less than, or different from the null value.

Question 4

Define Test Statistic.

Accepted Answer

A number computed from sample data that measures how far the estimate lies from the null value, usually in units of standard error.

Question 5

What is P-Value?

Accepted Answer

The probability, calculated assuming the null hypothesis is true, of obtaining a test statistic at least as extreme as the one actually observed.

Question 6

Define Significance Level (Alpha).

Accepted Answer

The threshold chosen before collecting data that sets the largest acceptable probability of rejecting a null hypothesis that is actually true.

Question 7

Define Statistically Significant.

Accepted Answer

A description of a result whose p-value falls at or below the chosen alpha, meaning random variation alone is an unconvincing explanation under the null.

Question 8

Define Fail to Reject H0.

Accepted Answer

The decision made when evidence is too weak to overturn the null hypothesis, which leaves it unproven rather than confirming it as true.

Question 9

Define Type I Error.

Accepted Answer

A false positive: concluding that an effect exists by rejecting a null hypothesis that is in reality true, with probability equal to alpha.

Question 10

Define Type II Error.

Accepted Answer

A false negative: failing to detect a real effect by not rejecting a null hypothesis that is in reality false, with probability called beta.

Question 11

What is Beta?

Accepted Answer

The probability that a study fails to reject a false null hypothesis, which depends on the true effect size, sample size, variability and alpha.

Question 12

Define Statistical Power.

Accepted Answer

The probability that a test correctly rejects a false null hypothesis, equal to one minus beta for a specific true effect size.

Question 13

Define One-Tailed Test.

Accepted Answer

A test whose alternative hypothesis specifies one direction, placing the entire rejection region in either the upper or the lower tail of the distribution.

Question 14

Define Two-Tailed Test.

Accepted Answer

A test whose alternative hypothesis allows a difference in either direction, dividing the rejection region equally between both tails of the distribution.

Question 15

Define Critical Value.

Accepted Answer

The cutoff on the test statistic's distribution that separates outcomes leading to rejection of the null from outcomes that do not.

Question 16

Define Rejection Region.

Accepted Answer

The set of test statistic values extreme enough that, if observed, the analyst rejects the null hypothesis at the chosen significance level.

Question 17

Define Standard Error.

Accepted Answer

The standard deviation of a statistic's sampling distribution, describing how much that statistic typically varies from one random sample to another.

Question 18

Define Sampling Distribution.

Accepted Answer

The probability distribution of a statistic across all possible random samples of a fixed size drawn from the same population.

Question 19

Define Central Limit Theorem.

Accepted Answer

The result that the sampling distribution of a mean becomes approximately normal as sample size grows, whatever the shape of a population with finite variance.

Question 20

Define Degrees of Freedom.

Accepted Answer

The number of independent values free to vary in a calculation, which determines the exact shape of distributions such as t and chi-square.

Question 21

Define One-Sample Z Test for a Mean.

Accepted Answer

A procedure comparing a sample mean with a claimed population mean when the population standard deviation is known and the sampling distribution is approximately normal.

Question 22

Define One-Sample T Test.

Accepted Answer

A procedure comparing a sample mean with a claimed population mean when the population standard deviation is unknown and must be estimated from the sample.

Question 23

Define Two-Sample T Test.

Accepted Answer

A procedure comparing the means of two independent groups, using their sample standard deviations to judge whether the population means differ.

Question 24

Define Paired T Test.

Accepted Answer

A procedure for matched or repeated measurements that computes each pair's difference and tests whether the mean of those differences equals zero.

Question 25

Define One-Proportion Z Test.

Accepted Answer

A procedure comparing a sample proportion with a claimed population proportion, valid when expected counts of successes and failures are large enough.

Question 26

Define Two-Proportion Z Test.

Accepted Answer

A procedure comparing proportions from two independent groups, typically pooling them under a null hypothesis that the population proportions are equal.

Question 27

Define Chi-Square Goodness-of-Fit Test.

Accepted Answer

A procedure comparing observed category counts of one categorical variable with the counts expected under a specified distribution.

Question 28

Define Chi-Square Test of Independence.

Accepted Answer

A procedure using a two-way table of counts from one sample to assess whether two categorical variables are associated in the population.

Question 29

Define One-Way ANOVA.

Accepted Answer

A procedure using an F statistic to compare variation between group means with variation within groups, testing whether several population means are all equal.

Question 30

Define Effect Size.

Accepted Answer

A quantitative measure of how large a difference or relationship is, reported independently of whether the result reached statistical significance.

Question 31

Define Cohen's d.

Accepted Answer

A standardized effect size expressing the gap between two means in pooled standard deviation units, with 0.2, 0.5 and 0.8 as conventional benchmarks.

Question 32

Define Bonferroni Correction.

Accepted Answer

An adjustment for running many tests that divides the overall alpha by the number of comparisons to limit the family-wise false positive rate.