Statistical Analysis: Normality, Correlation, and Regression
What does skewness indicate in a distribution?
The aysmmetry of the distribution; positive values indicate a build-up of high scores, while negative values indicate too low scores
what does kurtosis indicate in a distribution?
The heaviness of the tails in the distribution; positive values indicate a heavy-tailed distribution, while negative values indicate a light-tailed distribution
What is the significance of a skewness or a kurtosis value further from 0?
The more likely it is that the data are not nromally distributed
What is the significance level for determining if a score is significant in normality tests?
a significance level greater than 1.96 indicates significance (p<.05)
What is the purpose of the Kolmogorov-Smirnov (K-S) test?
assesses whether scores are significantly different from a normal distribution
What is the Shapiro-Wilk test used for?
to detect differences from normality and has more power than the K-S test
What is homogeneity of variance (homoscedasticity)?
the assumption that the spread of scores is roughly equal at different parts of the predictor variable
How can homogeneity of variance be evaluated?
by plotting standardised values against standardised residuals
What is Levene's test used for?
to test the assumption of homogeneity of variance
What does a significant result (sig.<.o5) in Levene's test indicate?
indicates that the variances are significantly different across groups
What is the variance ratio in the context of homogeneity of variance?
the largest group variance divided by the smallest, and it should be smaller than critical values for homogeneity to be assumed
What is Pearson's correlation coefficient, r?
a standardised measure of the linear relationship between two variables ranging from -1 to +1
What do the values of Pearson's correlation coefficient represent
the strength and direction of the relationship: +1 indicates a perfect positive relationship, -1 indicates a perfect negative relationship, 0 indicates no linear relationship
what is the effect size interpretation for correlation coefficients?
+/-0.1 represents a small effect, +/-0.3 is a medium effect, and +/-0.5 is a large effect
What is Spearman's correlation coefficient?
a non-parametric statistic used to assess the relationship between two ordinal variables
What is the point-biserial correlation coefficient?
quantifies the relationship between a continuous variable and a discrete dichotomy
What is the biserial correlation coefficient?
quantifies the relationship between a continuous variable and a continuous dichotomy
What does partial correlation quantify?
the relationship between two variables while accounting for the effects of a third variable
What does semi-partial correlation quantify?
the relationship between two variables while accounting for the effects of a third variable on only one of the original variables
What is a scatterplot used for in correlation research?
visualises the relationship between two variables and helps identify outliers that might bias the relationship
What is the purpose of the chi-square test in correlation analysis?
assesses the significance of the relationship between two categorical
What indicates a significant relationship in a chi-square test?
if the exact sig. value is less than 0.05
What should be checked in a contingency table for chi-square tests?
ensure that no expected frequencies are less than 5
What does the odds ratio indicate in hypothesis?
the strength of the relationship; values greater than 1 suggest a shift towards the alternative hypothesis
What is the purpose of a linear regression model?
predicts the outcome variable based on one or more predictor variables
What does R(2) represent in a regression model?
the proportion of variance in the outcome variable that is explained by the predictor variable
What is multicollinearity in regression analysis?
when predictor variables correlate too highly with each other, which can distort the results
What is the significance of VIF values in assessing multicollinearity?
values less than 10 indicate no cause for concern regarding multicollinearity
What should be checked in residual analysis of a regression model?
standardised residuals that exceed absolute values of 2 or 2.5, which may indicate outliers