CCJ4746 Statistics in Criminology - Exam 3 Study Guide

Vocabulary practice flashcards covering Chapters 8, 9, and 12 of Statistics in Criminology (CCJ4746), including one-sample tests, two-sample tests, correlation, and linear regression.

Null hypothesis ($H_0$)

The hypothesis stating that there is no difference between groups or no relationship between variables.

Alternative hypothesis ($H_1$)

The research hypothesis stating that a difference or relationship exists.

Alpha level ($\alpha$)

The significance threshold (commonly set at $.05$) that sets the risk of a Type I error to $5\%$.

Statistical significance ($p < .05$)

The conclusion reached when an observed test statistic is sufficiently unlikely under $H_0$, leading the researcher to reject the null hypothesis.

Effect size

A standardized measure that answers "how big is the difference or relationship?", which does not automatically grow just because a sample size is larger.

Two-tailed (nondirectional) test

A hypothesis test evaluating any difference in either a positive or negative direction ($\ne$).

One-tailed (directional) test

A hypothesis test evaluating an outcome specifically higher ($>$) or lower ($<$).

Test statistic

A metric indicating how far an observed sample result is from what $H_0$ predicts relative to sampling uncertainty.

One-sample $z$ test

A hypothesis test used to compare ONE sample mean ($\bar{x}$) to a known population mean ($\mu$) when the population standard deviation ($\sigma$) is known.

Standard error of the mean (SEM)

The expected variability in sample means due to chance, calculated as $\text{SEM} = \frac{\sigma}{\sqrt{n}}$ when $\sigma$ is known, or $\text{SEM} = \frac{s}{\sqrt{n}}$ when $\sigma$ is unknown.

One-sample $t$ test

A hypothesis test used to compare ONE sample mean ($\bar{x}$) to a known benchmark or population mean ($\mu$) when the population standard deviation ($\sigma$) is unknown and estimated using the sample standard deviation ($s$).

Degrees of freedom ($df$) for a one-sample $t$ test

The parameter used to locate critical values on the $t$ distribution, calculated as $df = n - 1$.

Cohen's $d$

A standardized measure of effect size expressing the practical size of a difference, calculated as $d = \frac{\bar{x} - \mu}{\text{SD}}$ using standard deviation rather than SEM.

Cohen's $d$ rules of thumb

Standard guidelines for interpreting effect sizes: small ($\sim 0 - .2$), medium ($\sim .2 - .8$), and large (above $.8$).

Independent-samples $t$ test

A test used to compare the means of TWO separate, independent groups (e.g., comparing scores between males and females).

Pooled variance ($s_p^2$)

The combined variance estimate calculated from two independent samples: $s_p^2 = \frac{(n_1 - 1)s_1^2 + (n_2 - 1)s_2^2}{n_1 + n_2 - 2}$.

Degrees of freedom ($df$) for an independent-samples $t$ test

The degrees of freedom calculated for two independent groups: $df = n_1 + n_2 - 2$.

Paired-samples $t$ test

A test used to compare two related measurements taken from the SAME participants (e.g., pretest vs. posttest) or matched pairs.

Difference score ($D$)

In a paired-samples design, the change measured within each subject or pair, defined as $D = \text{posttest} - \text{pretest}$.

Degrees of freedom ($df$) for a paired-samples $t$ test

The degrees of freedom calculated from the number of pairs: $df = n - 1$, where $n$ is the number of pairs.

Pearson's $r$

A correlation coefficient ranging from $-1$ to $+1$ that describes the direction and strength of a linear relationship between two numeric variables.

Correlation significance test

A test evaluating whether a population correlation ($\rho$) differs from zero, evaluated using a $t$ statistic calculated as $t = r \times \sqrt{\frac{n - 2}{1 - r^2}}$ with $df = n - 2$.

Coefficient of determination ($r^2$)

The squared correlation coefficient ($r \times r$), representing the proportion of variation shared or explained in a simple linear model.

Simple linear regression

A statistical method used to predict an outcome variable ($Y$) from ONE numeric predictor ($X$) using the line of best fit equation $Y' = bX + a$.

Slope ($b$)

The expected change in predicted $Y$ ($Y'$) for a one-unit change in $X$.

Intercept ($a$ or _cons)

The predicted value of $Y$ ($Y'$) when the predictor variable $X$ equals zero.

Residual (prediction error)

The vertical distance from an observed data point to the regression line, computed as $\text{actual } Y - \text{predicted } Y'$.

Standard error of estimate

The overall typical size or spread of prediction errors (residuals) around the regression line.

Multiple linear regression

A statistical technique predicting an outcome ($Y$) from two or more predictors ($X_1, X_2, \dots$), showing each predictor's unique association with $Y$ while controlling for other variables.

Standardized Beta

A regression slope expressed in standard deviation units rather than original measurement units, used to compare the relative importance of predictors on different scales.

Model $R^2$

The proportion of total variation in the outcome variable explained simultaneously by all predictors in a multiple regression model.

Stata command pwcorr ..., sig

The Stata command used to calculate pairwise correlation coefficients between variables along with their statistical significance ($p$ values).

Stata regress variable ordering rule

In Stata syntax (e.g., regress selfc delpeers), the variable listed immediately after regress is always the dependent outcome variable ($Y$).