Statistics Review for Research Methods

Flashcards covering core statistical terminology, descriptive vs. inferential statistics, t-test types, hypothesis testing, and effect sizes based on lecture notes.

Population

All individuals or items of interest in a research study, such as all US workers.

Sample

A subset selected from a broader population to be measured in a study.

Sampling Error

The natural variability that is expected from one sample to another.

Relationship between Population and Sample

A framework where a sample selected from a population provides a statistic, which is used through estimation and inference to draw conclusions about the population parameter.

Parameter

A numerical value that summarizes or describes a characteristic of an entire population.

Statistic

A numerical value that summarizes or describes a characteristic of a sample.

Between-Subjects Design

An experimental design that compares different groups of participants, measuring each participant only once.

Within-Subjects Design

An experimental design (also known as repeated measures) that assesses participants on the same measure more than once to reduce variability due to chance factors.

Mean ($M$)

A measure of central tendency representing the arithmetic average, calculated by dividing the sum of data by the sample size.

Median

A measure of central tendency representing the middle score in a data distribution.

Mode

A measure of central tendency representing the most frequently occurring score in a distribution.

Range

A measure of variability spanning from the lowest score to the highest score in a dataset.

Variance

A measure of variability calculated as the average squared distance of data points from the mean.

Standard Deviation ($SD$)

A measure of variability calculated as the square root of the variance.

Correlation Coefficient

A statistic measuring the association between variables, ranging in value from $-1.0$ to $+1.0$.

t-test

An inferential statistical test used to determine the significance of the mean difference between two scores or groups.

Analysis of Variance (ANOVA)

An inferential statistical test used to evaluate mean differences among three or more groups.

One-Sample t-test

A t-test that compares a single sample mean to a predetermined constant population value.

Independent Samples t-test

A t-test used to compare two sample means from groups that are completely independent of each other.

Dependent Samples t-test

A t-test used to compare two sample means from groups that are paired or dependent on each other.

Classic t-test Formula

The equation used to compute the t-statistic for sample comparisons: $t = \frac{(\bar{x}_1 - \bar{x}_2) - (\mu_1 - \mu_2)}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}$.

Degrees of Freedom ($df$)

The number of scores in a sample that are free to vary, calculated as $n - 1$ for a single sample mean.

Null Hypothesis ($H_0$)

A statement asserting that there is no significant difference between the sample statistic and the population parameter.

Alternative Hypothesis ($H_1$)

A statement asserting that there is a true difference between the sample statistic and the population parameter.

p-value

The probability of obtaining the observed sample outcome assuming that the null hypothesis is true, expressed as $p = P(\text{Data} \mid H_0: \text{True})$.

Statistically Significant Effect

A result deemed too unlikely to occur by chance alone, defined as a $p$-value less than $5\%$ ($.05$ as a proportion).

Cohen's d Standards

Standard benchmark values for evaluating effect size: $0.2$ for small, $0.5$ for medium, and $0.8$ for large.