Module 3: Statistical Inference Practice Flashcards

This set covers vocabulary and foundational concepts for Null Hypothesis Significance Testing, correlation, t-tests, and statistical errors based on the Module 3 lecture notes.

Inferential Statistics

Statistical methods used to make conclusions about a population based on data collected from a sample.

Null Hypothesis ($H_0$)

A hypothesis that assumes no effect or relationship exists, and any observed difference is due to random chance or sampling variation.

Alternative Hypothesis ($H_1$ / $H_a$)

A hypothesis that assumes a real effect or relationship exists and is not due to chance alone.

Directional Hypothesis

An alternative hypothesis that specifies the direction of an effect, such as Group A being greater than Group B ($A > B$).

Non-directional Hypothesis

An alternative hypothesis that specifies a difference exists but does not state the direction, such as Group A not equaling Group B ($A \neq B$).

p-value

The probability of obtaining the observed result, or more extreme, if the null hypothesis is true; used to determine if data is surprising.

Alpha ($\alpha$)

The threshold—usually set at $.05$—against which the p-value is compared to decide whether to reject the null hypothesis.

Statistical Significance

A conclusion based on the p-value indicating whether an effect likely exists in the population ($p < .05$).

Practical Significance

A conclusion based on effect size indicating whether the observed effect is meaningful or important in real-world contexts.

Effect Size

A number showing the magnitude or strength of an effect, rather than just whether it exists.

Cohen’s d

A type of effect size from the d family that measures the difference between groups, where $.20$ is small, $.50$ is medium, and $.80+$ is large.

Power ($1 - \beta$)

The probability of detecting a real effect when one actually exists in the population.

Type I Error

A false positive error that occurs when the researcher rejects a true null hypothesis ($H_0$).

Type II Error ($\beta$)

A false negative error that occurs when a researcher fails to reject a false null hypothesis, thus missing a real effect.

Test statistic

A single number summarizing the relationship between sample results and the null hypothesis; larger values indicate greater deviation from the null.

Degrees of freedom ($df$)

How many values in a calculation are free to change without breaking the mathematical rules of that calculation.

Pearson’s r

A measure of the strength and direction of the linear relationship between two continuous variables, ranging from $-1$ to $+1$.

Restricted Range

A situation where the variability of data is limited, which typically weakens the observed correlation.

Heterogeneous Samples

A problem where subgroups within a sample distort results, requiring the subgroups to be analyzed separately.

Coefficient of Determination ($r^2$)

The square of the correlation coefficient, representing the percentage of variance in one variable explained by the other.

Bivariate Normality

An assumption for correlation that both variables are normally distributed, often checked using the Shapiro-Wilk test.

Linearity

The assumption that the relationship between two variables is effectively represented by a straight line, checked using a scatterplot.

One-sample t-test

A statistical test used to compare a sample mean to a known population mean or a specific test value.

Independent Samples t-test

A test used to compare the means of two different groups of participants in a between-subjects design.

Paired Samples t-test

A test used to compare the means of the same participants across two different times or conditions in a within-subjects design.

Homogeneity of Variance

The assumption that the groups being compared have similar variance, typically checked using Levene's test.

Levene’s test

A test used to check the assumption of homogeneity of variance where a result of $p > .05$ indicates the assumption is met.

Welch’s t-test

A variation of the t-test used when the assumption of homogeneity of variance is violated.

Shapiro-Wilk test

A statistical test for normality where a outcome of $p > .05$ suggests the data does not significantly deviate from a normal distribution.