Correlation and Regression

Comprehensive review flashcards covering correlation, regression, statistical inference, reliability, and validity from Lecture 3.

According to Donnellan & Lucas (2008), which Big Five personality traits are positively associated with age, and which are negatively associated?

Agreeableness and Conscientiousness are positively associated with age, whereas Extraversion and Openness are negatively associated with age.

According to Pavot, Diener, & Fujita (1990), what relationship is highlighted as one of the most consistently replicated and robust findings in subjective well-being (SWB) literature?

The relationship between extraversion and happiness (or subjective well-being).

According to Wilmot & Ones (2019), what personality trait is the most potent noncognitive predictor of occupational performance?

Conscientiousness.

What two key parameters of a linear association does Pearson's correlation coefficient ($r$) quantify?

Direction of association (positive or negative) and degree of association (strength).

What is the numerical range of Pearson's correlation coefficient ($r$), and what do the extreme values represent?

The range is from $-1$ to $1$, where $1$ is a perfect positive correlation, $-1$ is a perfect negative correlation, and $0$ indicates no linear association.

According to Cohen's (1988) rules of thumb, what values of $r$ correspond to small, medium, and large effect sizes?

Small effect: $r \times .10$; Medium effect: $r \times .30$; Large effect: $r \times .50$.

According to Richard et al. (2003), what is the average correlation coefficient ($r$) found in personality and social psychology literature?

$r = .21$.

Why can Pearson's correlation coefficient ($r$) yield a value of $0.00$ even when two variables have a very strong relationship?

Pearson's $r$ only quantifies linear relationships, so strong non-linear or curvilinear relationships can result in $r = 0.00$.

How does increasing the sample size ($N$) impact the effect of extreme scores or outliers on correlation estimates?

As sample size ($N$) increases, the influence of extreme scores decreases, and correlation estimates stabilize.

What is the formula for calculating Pearson's correlation coefficient ($r$) using Sum of Products ($SP$) and Sum of Squares ($SS$)?

$r = \frac{SP}{\sqrt{SS_X \times SS_Y}}$, where $SP$ represents covariance and $SS_X$ and $SS_Y$ represent separate variances.

In null hypothesis significance testing for correlation, what is the null hypothesis ($H_0$)?

$H_0: \rho = 0$, assuming that the true correlation in the population ($\rho$) is zero.

What is the standard threshold ($\alpha$ level) used in psychology to reject the null hypothesis, and what error rate does it represent?

The threshold is $p < .05$, representing a willingness to tolerate being wrong $5$ times out of $100$.

How are degrees of freedom ($df$) calculated when testing the statistical significance of a correlation coefficient?

$df = N - 2$, where $N$ is the sample size.

How does Spearman's correlation ($r_s$) differ from Pearson's correlation ($r$) in how data is processed?

Spearman's correlation converts raw data into ranks before calculation, measuring monotonic relationships and making it less sensitive to non-linearity and outliers.

What is the primary conceptual difference between correlation analysis and regression analysis?

Correlation quantifies bivariate patterns of association between variables, whereas regression involves predicting values of a criterion variable ($Y$) based on a predictor variable ($X$).

In the regression equation $Y = a + bX + e$, what do $a$, $b$, and $e$ represent?

$a$ is the intercept (predicted value of $Y$ when $X = 0$), $b$ is the slope (change in $Y$ for a $1$-unit change in $X$), and $e$ is the residual error term.

What three key assumptions are made regarding residuals ($e$) in a linear regression model?

Residuals are assumed to be independent, normally distributed with a mean of zero, and homoscedastic.

How are the slope ($b$) and intercept ($a$) calculated in least squares linear regression?

Slope $b = \frac{SP}{SS_X}$ and intercept $a = \bar{Y} - b\bar{X}$, which minimize the total squared error $\sum (Y - \hat{Y})^2$.

What is the difference between homoscedasticity and heteroscedasticity in regression diagnostics?

Homoscedasticity means residual error variance is equal across all predicted values of $Y$, whereas heteroscedasticity means error variance systematically changes or spreads unequally.

What does the coefficient of determination ($R^2$) measure in regression, and what statistical test evaluates if $R^2$ is significantly greater than zero?

$R^2$ measures the proportion of variance in $Y$ explained by the regression model, and an ANOVA $F$-test evaluates whether $R^2$ is significantly different from zero.

In a simple linear regression model ANOVA $F$-test, what are the two reported degrees of freedom ($df$) terms?

Model degrees of freedom ($df_{\text{Model}} = 1$) and Error degrees of freedom ($df_{\text{Error}} = N - 2$).

What is the theoretical equation for the general model of measurement reliability?

$X = T + E$, where $X$ is the observed score, $T$ is the true score, and $E$ is measurement error.

What is Cronbach's alpha ($\alpha$), and what threshold is widely accepted as indicating sufficient internal consistency reliability?

Cronbach's alpha is the average of all possible split-half reliabilities for a scale, with $\alpha \ge .70$ generally considered acceptable.

What effect does measurement unreliability have on observed correlation coefficients?

Unreliability attenuates correlations, causing observed correlation coefficients to be lower and less trustworthy than the true underlying relationship.

What is the difference between convergent validity and divergent validity in construct validation?

Convergent validity requires a measure to correlate significantly with relevant related measures, while divergent validity requires it to show weak or zero correlations with irrelevant measures.

Why does a statistically significant correlation between two variables not establish causation?

Correlation only demonstrates an association; it cannot determine directionality (reverse causation) or rule out the influence of unmeasured third variables.