STATS 615

PSY 615 Exam 1 MS I/O

Characteristics of the normal distribution

• Bell shaped

• Symmetrical

• Central tendency

• Asymptotic tails

Assumptions for Pearson’s r

• Normality

• Linearity

• Independence

Which correlation coefficient is appropriate for two continuous variables

Pearson's r

Which correlation coefficient is appropriate for two ordinal (ranked) variables

Spearman's rs

Which correlation coefficient is appropriate for two dichotomous variables (e.g., yes/no)

Phi coefficient (Φ)

Which correlation coefficient is appropriate for one continuous and one dichotomous variable

Point-biserial

What does homoscedasticity mean?

Homoscedasticity means that the variability of prediction errors (residuals) remains relatively constant across all values of X.

What do degrees of freedom tell us?

Degrees of freedom tell us how many values can vary independently after accounting for constraints.

What is the difference between a population and a sample?

A population is the entire group of interest. A sample is a subset drawn from that population.

What distinguishes nominal variables

Categories without an inherent order i.e., hair color or department

What distinguishes interval variables

Equal intervals, but no true zero i.e., Likert scale

What distinguishes ordinal variables

Meaningful order, but unknown distances between values ex. quality of life ranking, places in a race

What distinguishes ratio variables

Equal intervals and a true zero i.e., seconds, salaries

Why are cumulative percentages inappropriate for nominal variables

Nominal categories have no meaningful order, so cumulative percentages depend on an arbitrary arrangement of categories

What can frequency distributions reveal about a dataset?

Frequencies, proportions, missing values, outliers, skewness, and other potential problems with the distribution

What is the difference between positive and negative skewness?

Positive skewness has a longer right tail toward higher values. Negative skewness has a longer left tail toward lower values

What is the difference between variance and standard deviation?

Variance measures the spread of scores using squared deviations from the mean. Standard deviation is the square root of variance and is expressed in the original units.

Why does sample variance use n − 1 rather than n?

Because deviations from the sample mean must sum to zero, only n − 1 deviations are free to vary. Dividing by n − 1 also corrects for bias when estimating population variance.

What does a z-score of −1.5 indicate?

The observation is 1.5 standard deviations below the mean.

What is the 68–95–99.7 rule?

In a normal distribution, approximately 68% of observations fall within ±1 standard deviation, 95% within ±2 standard deviations, and 99.7% within ±3 standard deviations of the mean.

What is the difference between leptokurtic and platykurtic distributions?

Leptokurtic distributions have greater tail weight than a normal distribution. Platykurtic distributions have lighter tails than a normal distribution.

What do the sign and magnitude of Pearson's r indicate?

The sign indicates the direction of the relationship (positive or negative), while the absolute magnitude indicates the strength of the linear relationship.

What does r² represent?

The proportion of variance shared by two variables. In simple linear regression, it represents the proportion of outcome variation explained by the predictor.

What are the three assumptions for computing a Pearson correlation?

• X and Y are normally distributed.

• X and Y are linearly related.

• Observations are independent.

How does range restriction affect a correlation?

Restricting the range of scores on X or Y generally reduces the observed correlation, potentially underestimating the strength of the relationship.

What is the difference between Type I and Type II errors?

• Type I error: Rejecting a true null hypothesis (false positive).

• Type II error: Failing to reject a false null hypothesis (false negative).

What is the purpose of a Bonferroni correction?

To control the risk of Type I error when conducting multiple statistical tests by dividing the significance level (α) by the number of tes

What do the slope and intercept represent in the unstandardized regression equation?

• Slope (b): The change in predicted Y for every one-unit increase in X.

• Intercept (a): The predicted value of Y when X equals zero.

What is a residual, and what does its sign indicate?

• A residual is the difference between the observed and predicted score:

• Residual = Y − Y′

• A positive residual indicates underprediction, while a negative residual indicates overpredictio

What does the standard error of estimate measure?

The overall scatter of observed Y scores around their predicted Y′ values. A smaller standard error of estimate indicates more precise predictions.

What is homoscedasticity?

The assumption that the variability of residuals remains approximately constant across all values of the predictor variable (X).

What is the relationship between SS Total, SS Regression, and SS Error?

SS Total = SS Regression + SS Error.

Degrees of Freedom for a Correlation Test

2 df; (N-2)

What question does Standard Error of Estimate answer?

How far off are my predictions from the actual scores?

What question does standard error answer?

How much might my statistic change if I collected another sample?

For a two-tailed test with (alpha=.05) what is the critical value?

-1.96 and +1.96

Our test-statistics tells us

How unusual our sample result would be if the null hypothesis were true.