Psychological Statistics || Module 1-10

Linear Regression

Statistical method to model relationship between variables

Prediction

Using known data to estimate unknown data

Line of Best Fit

Line expressing relationship in scatter plot data

Least Squares Method

Technique to minimize sum of squared differences

ANOVA Table

Table showing variance components in analysis

Hypothesis Testing

Statistical method to test relationships in data

Geometric Equation

Equation representing line in scatter plot

Intercept

Point where line crosses Y-axis

Slope

Steepness and direction of the line

Parameter Estimates

Approximations of true population values

Correlation

Measure of relationship between variables

Covariance

Measure of joint variability between variables

Variance

Measure of variability or spread of data

Pearson Correlation Coefficient

Measure of linear correlation between variables

Simple Regression Assumptions

Conditions for valid application of regression

Null Hypothesis

Statement of no effect or relationship in data

Alternative Hypothesis

Statement of effect or relationship in data

Critical Value

Value to determine statistical significance

Degrees of Freedom

Number of values free to vary in analysis

F Statistic

Statistic to compare variances in groups

Linear Regression Model

Statistical model explaining variance between variables

Four-Step Hypothesis-Testing Procedure

Process to test for statistically significant relationships between variables

Test Statistics

Values calculated to assess significance of regression model

Means, Standard Deviations, Sum of Products

Calculated values for X and Y variables in regression analysis

Slope of the Line

Rate of change in Y for a unit change in X

Equation for Line of Best Fit

Mathematical representation of the regression model

Effect Size in Regression

Measure of how much variance is explained by the model

Obtained F Statistic

Calculated value used to test hypothesis in ANOVA

Analysis of Variance

Method to identify variability sources in data sets

Variability

Spread of scores around the mean

ANOVA Table

Displays sources of variability, degrees of freedom, and F-statistic

Between-Groups Sum of Squares

Variability between groups in ANOVA

Within-Groups Sum of Squares

Variability within each group in ANOVA

Total Sum of Squares

Sum of between-groups and within-groups sums of squares

Hypothesis in ANOVA

Testing differences in group means using ANOVA

Grouping Variable

Predictor or independent variable in ANOVA

Outcome Variable

Variable based on group differences in ANOVA

Individual Group Means

Means of each group in ANOVA

Grand Mean

Overall mean across all groups in ANOVA

Degrees of Freedom

Number of values in the final calculation of a statistic

F-Statistic

Ratio of two variances in ANOVA hypothesis testing

Critical Values

Values from F distribution table for hypothesis testing

Mean Square

Sum of squares divided by degrees of freedom

Test Statistic

Statistic used to make decisions in hypothesis testing

Correlation

Statistical measure of relationship size and direction

Covariance

Tool to determine relationship between random variables

Variability and Covariance

Significance in statistical analysis and understanding data patterns

Pearson's Correlation Coefficient

Formula to calculate and interpret correlation between variables

Visualizing Relationships

Importance of graphical representation in understanding variables

Form, Direction, Magnitude

Concepts in interpreting relationships between variables

Correlation vs. Causation

Distinguishing between relationship and cause-effect in statistics

Variance

Measure of how spread out a set of values are from the mean

Sum of Products

Result of multiplying deviations of paired values and summing them

Scatterplot

Visual representation of relationship between two variables

Positive Correlation

Relationship where both variables increase/decrease together

Negative Correlation

Relationship where one variable increases as the other decreases

Form

Shape of a relation in a scatterplot

Linear Relation

Relation best represented by a straight line in a scatterplot

Curvilinear Relation

Relation represented by a curved line in a scatterplot

No Relation

Points in a plot show no consistent relationship

Direction

Indicates how variables change together (positively or negatively)

Magnitude

Strength or consistency of the relationship between variables

Pearson's r

Popular correlation coefficient for linear relationships

Assumptions for Pearson Correlation

Conditions to check before performing a Pearson correlation test

Critical Value

Value used to determine statistical significance in hypothesis testing

Test Statistics

Calculations used to assess the relationship between variables

Standard Deviation

Measure of the amount of variation or dispersion of a set of values

Causation

Relationship where one action causes another

Hypothesis

Presumptive statement seeking proof in an investigation.

Assumption

Taking things for granted to simplify logical procedures.

Postulate

Working belief accepted at face value in scientific activity.

Null Hypothesis

Assumed true unless data convincingly prove it false.

Alternative Hypothesis

Accepted only if data convincingly support its truth.

Significance Level

Threshold set pre-data collection to determine hypothesis rejection.

Rejection Region

Values of test statistic leading to null hypothesis rejection.

One Tailed Test

Alternative hypothesis is directional, specifying a single direction.

Two Tailed Test

Alternative hypothesis does not specify departure from null hypothesis.

Critical Value

Value corresponding to a specific rejection region in hypothesis testing.

Test Statistic

Inferential statistic used to test a null hypothesis.

Z-Score

Measure of how many standard deviations a data point is from the mean.

Hypothesis Testing Process

Four-step procedure to test hypotheses in a structured manner.

Population Mean

Average value of a specific group in a population

Population Standard Deviation

Measure of the amount of variation in a population

Critical Values

Values used to determine rejection of the null hypothesis

Two-Tailed Test

Hypothesis test looking for differences in both directions

P-Value

Probability of obtaining results at least as extreme as the observed results

T-Statistic

Statistic used in T tests to support or reject the null hypothesis

Degrees of Freedom

Number of independent values or quantities which can be assigned to a statistical distribution

T Distribution Table

Table listing critical values for T tests at different levels of significance

One Sample T-Test

Test to compare one population mean using a single sample

Dependent Samples

Samples that are related or paired in some way

Independent Samples

Samples that are not related or paired

Longitudinal Data

Data from same participants at different time points

Dependent Samples T-Test

Compares means from the same group measured twice

Difference Scores

Scores calculated by subtracting paired values

Assumptions for Dependent Samples T-Test

Continuous dependent variable, matched pairs, no outliers

Independent Samples T-Test

Compares means from two separate groups

Homogeneity of Variances

Equality of variances in different groups being compared

Pooled Variance

Combined variance of two independent samples

Standard Error

Measure of the variability of sample statistic