Research Methods II Exam 3

nominal

categorical data used for naming or labeling without numerical value 🏷️

ordinal

data that can be ranked in order but distance between values is unknown 🥇

interval

ordered data with equal spacing between points but no true zero 🌡️

ratio

data with equal spacing and a true zero allowing for relative comparisons ⚖️

discrete

variables that can only take specific, separate values like whole numbers 🔢

continuous

variables that can take any infinite value within a range like time ⏱️

descriptive statistics

numerical summaries used to characterize and simplify sample data 📊

inferential statistics

procedures used to draw conclusions about a population from a sample 🔮

statistics

summary numbers describing a sample usually shown with Latin letters like M or s 📝

parameters

summary numbers describing a population shown with Greek letters like µ or σ 🏛️

mode

the most frequently occurring score in a data set 🔝

median

the middle score in a rank-ordered distribution or the 50th percentile 📍

mean

the arithmetic average calculated by dividing the sum of scores by the total count ➗

range

the difference between the highest and lowest scores in a distribution ↔️

variance

a measure of how much scores deviate from the mean squared 📐

standard deviation

the average amount scores vary from the mean in original units 📏

z-scores

standard scores used to compare values from different scales by showing distance from the mean in standard deviations 🎯

probability

the likelihood or chance that a specific event will occur 🎲

p

the mathematical abbreviation for probability expressed as a proportion between 0 and 1 🔢

inferential statistics

procedures used to determine if findings are reliable or due to chance 🔮

null hypothesis

the prediction that there is no effect or no difference between groups ⚪

alternative hypothesis

the prediction that a specific effect or difference exists 🎯

reject the null

concluding that an effect is unlikely to be due to chance alone ✅

fail to reject the null

concluding there is not enough evidence to claim an effect exists 🛑

nondirectional hypothesis

a prediction that a difference exists without specifying which group will be higher (two-tailed test) ↔️

directional hypothesis

a prediction that specifies which group will be higher or lower (one-tailed test) ➡️

type i error

mistakenly rejecting a true null hypothesis (false positive) ⚠️

type ii error

failing to reject a false null hypothesis (false negative) 📉

alpha

the probability of making a Type I error, usually set at .05 📏

critical value

the threshold a test statistic must exceed to reject the null hypothesis 🚧

statistically significant

a result unlikely to have occurred by chance based on the alpha level 🌟

statistical power

the ability to correctly reject a false null hypothesis and detect a real effect 💪

effect size

a measure of the magnitude of a difference independent of sample size 📏

sample size

the number of observations in a study; larger samples increase power by reducing error 👥

measurement reliability

the consistency of a measure; higher reliability reduces noise and increases power 🛠️

single-sample t-test

compares a sample mean to a specific hypothesized population value when the population standard deviation is unknown 🎯

dependent samples t-test

compares means from the same group tested twice or matched pairs (also called repeated measures) 👯

independent samples t-test

compares means from two separate, unrelated groups to see if they differ significantly 👥

degrees of freedom (df)

the number of values in a calculation that are free to vary; typically N - 1 for one sample or (N1 + N2) - 2 for two samples ⛓️

t-distribution

a family of probability distributions that look like the normal curve but have "fatter tails" for smaller sample sizes 📉

homogeneity of variance

the assumption that the amount of variability is roughly equal across the groups being compared ⚖️

standard error of the difference

the denominator in a t-test representing the estimated standard deviation of the difference between means 📏

two-tailed test

used when a researcher predicts a difference in either direction (greater than or less than) ↔️

one-tailed test

used when a researcher predicts a specific direction for the effect (e.g., "Group A will be higher than Group B") ➡️

sampling distribution of t

the theoretical distribution of all possible t-values if the null hypothesis were true 🔮

robustness

the ability of a statistical test to remain accurate even if certain assumptions (like normality) are slightly violated 🛡️

one-way anova

a test used to compare means across three or more levels of a single independent variable 🧪

f-ratio

the test statistic for anova calculated by dividing the variance between groups by the variance within groups 📊

between-groups variance

measure of how much the group means differ from each other (due to the IV) ↔️

within-groups variance

measure of the spread of scores within each group (due to chance or error) 🎲

post-hoc tests

follow-up tests conducted after a significant anova to find which specific groups differ from each other 🔍

factorial anova

an extension of anova used when there are two or more independent variables (factors) 🧩

main effect

the separate effect of one independent variable on the dependent variable, ignoring other variables 💡

interaction

occurs when the effect of one independent variable depends on the level of another independent variable 🤝

f-distribution

a right-skewed distribution of all possible f-ratios; it varies based on numerator and denominator degrees of freedom 📈

anova table

a standard way to report sums of squares (ss), degrees of freedom (df), mean squares (ms), and f-ratios 📋

mixed design anova

a study design that includes both between-subjects and within-subjects independent variables 🔄

type i error inflation

the increased risk of a false positive that occurs when running multiple t-tests instead of one anova ⚠️

correlational design

a research method where two or more variables are measured without manipulation to describe their relationship 🤝

bivariate correlation

a measure of the association between exactly two variables ranging from -1.00 to 1.00 🔢

positive correlation

a relationship where both variables increase or decrease together 📈

negative correlation

a relationship where one variable increases as the other decreases 📉

scatterplot

a graph where each point represents an individual, used to visualize the relationship between variables 🌌

effect size

the strength of an association; in correlation, the coefficient r itself is the effect size 📏

coefficient of determination (r^2)

the proportion of variability in the criterion variable explained by the predictor variable 🍰

restriction of range

when a sample lacks the full range of scores present in the population, artificially lowering the correlation 🤏

outlier

an extreme score that can disproportionately strengthen or weaken a correlation coefficient 🚀

curvilinear relationship

a relationship where the data follows a curve rather than a straight line, making Pearson’s r misleading 🎢

pearson’s r

a correlation coefficient used when both variables are measured on an interval or ratio scale 📏

spearman’s r

a correlation coefficient used when both variables consist of ordinal (ranked) data 🥇

point-biserial r

used when one variable is dichotomous (two categories) and the other is interval or ratio 🌓

linear regression

a statistical method for finding the best-fitting line to predict a criterion variable from a predictor variable 📐

predictor variable

the variable used to make a prediction (the X variable) 🔮

criterion variable

the variable being predicted or explained (the Y variable) 🎯

multiple regression

a technique using two or more predictor variables to explain a single criterion variable and control for third variables 🏗️

beta (\beta)

a standardized coefficient in regression that shows the relationship between a predictor and criterion while holding other predictors constant ⚖️

parametric test

statistical tests that assume data follows a specific distribution (like the normal distribution) and estimate population parameters 📏

non-parametric test

"distribution-free" tests used when data is skewed, nominal, or ordinal and doesn't meet parametric assumptions 🆓

chi-square (\chi^2) test of independence

used to see if two categorical (nominal) variables are related, like major and political party 📊

chi-square (\chi^2) goodness-of-fit

compares observed frequencies in categories to what is expected by chance 🎲

spearman’s rho

a non-parametric correlation used for ordinal (ranked) data 🥇

mann-whitney u test

the non-parametric alternative to the independent-samples t-test for comparing two groups 👥

wilcoxon t test

the non-parametric alternative to the related-samples t-test for dependent groups 🔄

kruskal-wallis h test

the non-parametric alternative to a one-way anova for three or more independent groups 🏗️

friedman chi-square

the non-parametric alternative to a repeated measures anova for three or more conditions 🔁

mcnemar test

a non-parametric test for nominal data in a repeated measures design 📉

non-robust

assumptions that must be strictly met for the statistical result to be valid ⛔

normally distributed

the assumption that the population follows a bell-shaped curve 🔔

random sample

a group where every member of the population had an equal chance of being chosen 🎲

independence of observations

the assumption that one person's data does not influence another's 👤

standard error

the estimated standard deviation of a sampling distribution (the denominator in many tests) 📏

apa format

the standard style for reporting statistics (e.g., t(df) = value, p < .05) 📝

latin letters

italicized symbols (like M or s) used to represent sample statistics ✍️

greek letters

symbols (like \bm{\mu} or \bm{\sigma}) used to represent population parameters 🏛️

standard scores

another name for z-scores, used to compare different scales 🎯

coefficient of determination

the \bm{r^2} value showing how much one variable explains another 🍰

principle of least squares

the math used to find a line that minimizes the distance to all data points 📐

predictor variable

the independent variable (\bm{X}) used to forecast an outcome 🔮

criterion variable

the dependent variable (\bm{Y}) being predicted in a regression 🎯