Psych Stats

• One-Tailed Test:

  • Used when the hypothesis predicts a specific direction of the effect
  • Critical region for rejection is on one side of the distribution curve
  • Example:
  • Null Hypothesis (H0): There is no difference
  • Alternative Hypothesis (H1): The mean is greater than (or less than) a specific value
• Two-Tailed Test:

  • Used when the hypothesis does not specify the direction of the effect
  • Critical region for rejection is on both sides of the distribution curve
  • Example:
  • Null Hypothesis (H0): There is no difference
  • Alternative Hypothesis (H1): The mean is not equal to a specific value
• Parametric Statistics:

  • Based on specific assumptions about the population distribution
  • Common assumptions include normality and homogeneity of variances
  • Examples of parametric tests: t-tests, ANOVA, correlation, regression
• Non-Parametric Statistics:

  • Do not rely on specific assumptions about the population distribution
  • Used when data does not meet parametric test assumptions
  • Examples of non-parametric tests: Mann-Whitney U test, Wilcoxon signed-rank test, Kruskal-Wallis test, chi-square test
• 1. Test for Independent Samples:

  • Compares means of two independent groups
  • Example: Comparing test scores of students who took a preparation course vs. those who did not
• 1. Test for Dependent Samples:

  • Compares means of two related groups
  • Example: Comparing blood pressure before and after an exercise program
• One-Way Analysis of Variance (ANOVA):

  • Assesses if means of three or more groups are statistically different
  • Example: Comparing scores of students taught by different methods
• Two-Way Analysis of Variance (ANOVA) F-Test:

  • Assesses the influence of two categorical independent variables on a dependent variable
  • Example: Studying the impact of gender and diet on weight loss
• F Test for Repeated Measures/Dependent Samples:

  • Assesses differences between means of related observations
  • Example: Comparing student performance across different test sessions
• Analysis of Covariance (ANCOVA):

  • Compares means of different groups while considering the influence of continuous variables (covariates)
• Covariance:

  • Indicates the degree to which two variables vary together
  • Positive covariance: variables tend to increase or decrease together
  • Negative covariance: one variable tends to increase while the other decreases
• Covariate:

  • Scale variable associated with the independent variable of interest
• • Homogeneity of Group Variances: variances of dependent variable should be roughly equal across all groups
  • Random Sampling (or Random Assignment): data should ideally come from a random sample or random assignment to groups
• Assumptions:

  • Linearity: relationship between dependent variable and each independent variable should be linear
  • Homogeneity of Regression Slopes: slopes of regression lines relating dependent variable to covariate should be approximately equal across all levels of categorical independent variable
  • Homogeneity of Variances: variances of residuals should be roughly equal across all groups
  • Normality of Residuals: residuals should be approximately normally distributed
  • Independence: observations should be independent of each other
• Difference from ANOVA:

  • ANOVA focuses on comparing group means without considering additional variables
  • ANCOVA extends ANOVA by including covariates to control for the effects of continuous variables
• Chi-Square Test of Independence:

  • Determines significant association between two categorical variables
  • Compares observed frequencies of categories in a contingency table to expected frequencies if variables were independent
• Chi-Square Goodness of Fit Test:

  • Determines if distribution of observed categorical data matches expected distribution
  • Checks if observed data fits a particular expected pattern or distribution
• One-Way ANOVA vs. F Test for Repeated Measures:

  • Independence: One-Way ANOVA compares independent groups, F Test for Repeated Measures compares related groups or repeated measures on the same subjects
  • Design: One-Way ANOVA is suitable for between-group designs, F Test for Repeated Measures is suitable for within-subject or repeated-measures designs
  • Data Structure: One-Way ANOVA assumes independence between groups, F Test for Repeated Measures assumes dependence between measures on the same subject
• T Test for Dependent vs. F Test for Repeated Measures:

  • T Test for Dependent Samples compares means of two related groups
  • F Test for Repeated Measures compares means of three or more sets of related observations
• Two-Way ANOVA F-Test:

  • Assesses how two variables affect an outcome together
  • Determines interaction effect between variables
• McNemar's Test:

  • Determines significant change in proportions between two related groups with categorical data
  • Assumptions:
  • Nominal Variable with Two Categories
  • Independent Variable with Two Connected Groups
  • Mutually Exclusive Groups
  • Random Sample
  • Matched Pairs
  • No Assumption of Normality
• McNemar's Test:

  • Used for paired categorical data
  • Compares proportions or frequencies within paired observations
  • Focuses on understanding if there is a significant change in proportions within paired observations
• McNemar's Test Example:

  • Scenario: Testing the effectiveness of a new drug
  • Data: Blood pressure measurements before and after administering the drug
  • Question: Is there a significant difference in blood pressure before and after the treatment?
• Fisher's Exact Test:

  • Used for paired categorical data
  • Compares proportions or frequencies within paired observations
  • Helps determine if the observed associations between categorical variables are likely due to chance or if there is a meaningful relationship
• Fisher's Exact Test Example:

  • Scenario: Comparing the success rates of a medical treatment before and after a new intervention
  • Data: Binary outcomes (success/failure) for each participant before and after the intervention
  • Question: Is there a significant difference in treatment success?
• Use McNemar's test when you have paired categorical data and want to compare proportions or frequencies within those pairs
• Use Fisher's Exact Test when you have paired categorical data and want to compare proportions or frequencies within those pairs
• Fisher's Exact Test:

  • Definition: Statistical method to determine significant association between two categorical variables, especially with small sample sizes
  • Used when dealing with around 5 cells or less in the table or sample size less than 20 with expected cell count 5 or greater less than 80% of the cell
• Pearson Product-Moment Correlation Coefficient:

  • Measures strength and direction of linear relationship between two continuous variables
  • Ranges from -1 to +1, where -1 indicates perfect negative linear relationship, +1 indicates perfect positive linear relationship, and 0 indicates no linear relationship
• Pearson Product-Moment Correlation Coefficient Example:

  • Scenario: Investigating the relationship between study hours and exam scores
  • Data: Study hours and exam scores of 10 students
  • Calculation: Pearson correlation formula yields a value of r
  • Interpretation: Positive value of r indicates a strong positive linear relationship between study hours and exam scores
• Multiple Correlation:

  • Measures overall relationship between one dependent variable and multiple independent variables taken together
  • Assesses combined influence of multiple independent variables on one dependent variable
• Multiple Correlation Example:

  • Scenario: Assessing the combined influence of temperature, advertising expenditures, and day of the week on ice cream sales
• Multiple Correlation:

  • Assesses how effectively the combination of marketing spending, competitor prices, and economic indicators predicts the monthly sales of a business
  • Examines the overall relationship between one variable and a set of other variables
• Partial Correlation:

  • Examines the relationship between two variables while controlling for the influence of one or more additional variables
  • Isolates the relationship between two variables while controlling for the impact of one or more additional variables
• Spearman Rank Order Correlation:

  • Assesses the strength and direction of the monotonic relationship between two variables based on their ranks
  • Coefficient between -1 and less than 0 indicates negative correlation, while a coefficient between greater than 0 and 1 indicates positive correlation
• Assumptions for Spearman Rank Order Correlation:

  • Monotonic Relationship: As one variable increases, the other tends to consistently increase or decrease, not necessarily at a constant rate
  • Ordinal Data or Continuous Data Approximating Ordinal Scale: Suitable for ordinal data or continuous data that can be converted into ranks
  • No Extreme Outliers: Extreme outliers can still influence results
  • No Ties or Address Ties Appropriately: Assumes no ties or that any ties are appropriately addressed in the analysis
• Pearson Correlation vs. Spearman Rank Order:

  • Pearson Correlation measures linear relationships, while Spearman Rank Order assesses monotonic relationships
  • Pearson Correlation is suitable for continuous, interval, or ratio data, while Spearman Rank Order is appropriate for ordinal or ranked data
  • Pearson Correlation involves the actual values of the variables, while Spearman Rank Order involves the ranks or order of the values
• Linear vs. Monotonic Relationship:

  • Spearman Rank Order Correlation assesses monotonic relationships where variables tend to move together in a systematic way, not necessarily in a straight line
  • Pearson Correlation is commonly used for linear relationships between continuous variables
• Kendall’s W (Kendall's coefficient of concordance):

  • Assesses the agreement between different raters or observers when ranking or scoring multiple items
  • Ranges from 0 to 1, with 1 indicating perfect agreement among raters and 0 suggesting no agreement beyond what would be expected by chance
• Random Sampling (for inferential statistics):

  • Data for making inferences about a population based on Kendall's W results should be obtained through a random sampling process