Quantitate Comps

Four Types of Data & Definitions

N: Nominal: Categorical identity - Mutually exclusive data. Example: Freshmen, Sophomore, Junior, Senior.

O: Ordinal: Order - Interval isn't consistent. Always starts with 1. Example: Top 3 candidates for a job

I: Interval: Assesses a degree of quantity in addition to identity and order. Zero doesn't mean nothing. Example: Temperature

R: Ratio: Assesses quantity, identity, order, and Zero means nothing. Example: Distance, Mass.

T Tests

Compare two means from two seperate populations. Outcome variable is ratio or interval. Results in a T score (like effect size) and p value (significant indicates a meaningful difference between groups)

Chi Squared Tests

Compare two categories, or two nominal forms of data (if three groups, use ANOVA). Results in a p value and X squared effect size indicator

Independent Samples T-test

Between subjects test (there are multiple groups, or different populations. 1 control doesn't receive the IV, and you compare their results to another group that does)

Paired Samples T-Test

Within subjects test (you're assessing something within one population, usually measuring something, applying the IV, then measuring the same thing again)

How to check for normality (and what is distribution)

Shapiro Wilk Test (If p > .05 assume normal distribution) or QQ plot (straight line equals normal distribution)

Distribution: the overall shape of the data, shown via graph. Think entire mountain range, peaks & valleys

How to check for variance (and what is variance)

Levene’s test: Assesses if two populations have equal variances. if p > .05 assume equal. If p < .05 assume different variances. If unequal variances, use Welch's test

Variance: A single numerical value that quantifies the dispersion of a distribution. A low variance indicates that data points cluster closely around the mean, while a high variance means the data points are scattered far away from the mean. Think: 1 number indicates the degree of flatness

Cohen’s D

Think visually, it's the distance between the mean/peak of two curves. It's measuring the strength (significance) of the relationship between two variables

Cohen’s D

Measures the standardized difference between two group means, expressed in units of standard deviation. A d of 0.5 means the group averages differ by half a standard deviation

Around .2 = small

Around .5 = medium

Around .8 = large

Chi Squared goodness of fit test vs test of independence and Cramer’s V

• Goodness-of-fit: Tests if a single categorical variable's frequency distribution matches a theoretical, hypothesized, or uniform distribution (1 variable, 1 sample). Even distribution of M&Ms

• Independence: Tests if two categorical variables are related or associated with each other (2 variables, 1 sample) Does left handedness relate to eye color?

Cramer’s V: Effect Size for Chi Square test.

.5 < High association

.3-.5 = moderate

.1-.3 = low association

0-.1 = no association

Factor vs Levels

F: IV (diet vs excercise)

Levels: Groups within a factor (keto, gluten-free, vegetarian)

Omnibus test & Post-hoc tests

O: Doesn’t share which groups differ, just states that groups differ

PHT: Outlines specifics: Holm

Anova & effect size of anova

Used when you have more than one factor and you want to compare the variance of 3 different groups.

eta squared = one way anova (factor with more than 2 levels)

partial eta squared = factorial anova (more than 1 factor)

Factorial Design (2×3×4)

3 IVs

1st has 2 levels

2nd has 3 levels

3rd has 4 levels

Main Effect and Interactions

The effect of one factor, ignoring the effect of other factors

Can only be as many MEs as there are Factors (IVs)

Interaction: When the effect of one factor depends on the level of another factor

If P is significant the the graph isn’t parallel, there’s an interaction. Formula to calculate number of interactions 2(to the k power) - k - 1 (K = # of factors)

Factorial ANOVA assumptions

Normality (QQ plot or shapiro wilk), Homogeneity of variance (Levene’s), independence

Pearson’s R / Correlation coefficient

r = 0 mean's there's no relationship

r = 0 - .2 weak or no relationship

r = .2 - .4 weak

r = .4 - .6 moderate

r = .6 - .8 strong

r = .6 - .8 Very strong

Can be negative. Ratio or integral data only. Describes relationship between two variables

Heavily influenced by outliers

Coefficient of determination

How much variance in Y can be accounted for by variation in X

Regression. Simple vs multiple

Find the best fitting line for a set of data that allows you to predict one variable from another.

Simple: 1 IV

Multiple: Several IVs

Unstandardized Beta Coefficient vs Standardized BC (or standardized estimate)

Unstandardized betas measure the direct, absolute change in a dependent variable for a one-unit change in an independent variable (e.g., "$300 per square foot").

Standardized betas convert all variables to standard deviations, making them unitless and allowing you to directly compare which predictor has the strongest relative impact

Multiple Regression

1 DV, multiple IVs. How do HS GPA, parental income, and hours of sleep predict college gpa?

Adjusted R squared and AIC vs BIC

Compare regression models.

R2: Bigger is better

AIC/BIC: smaller is better

Multicollinearity

Occurs if VIF is greater than 10. Means that two IVs are so densely correlated you can’t parse out whether one is having an effect or the other. Must remove one IV if it occurs.

Dummy Coding

Assign nominal variables categorical ratios so you can use regression

Regression assumptions

Normal distribution

Linear relationship

Constant variance

Independence (random sampling)

No bad outliers

No multicollinearity

Validity