exam prep

Scientific Method

• Observations lead to research questions.

Variables in Research

• Definition of Variables: Anything that can change or take on different values.

  • Situational Variables: Environmental or contextual factors.

  • Response Variables: Outcomes measured.

  • Participant Variables: Characteristics of individuals (e.g., age, gender).

  • Independent Variable (IV): Manipulated by the researcher.

  • Dependent Variable (DV): Measured to assess the effect of the IV.

Experimental Design

• Purpose: Manipulating the IV and measuring the DV establishes cause-and-effect relationships.

  • Types of Experimental Designs:

  • Between-Subjects Design: Different participants in different conditions.

  • Within-Subjects Design: Same participants in all conditions.

Statistical Analysis

• Types of Statistics:

  • Descriptive Statistics:

  • Summarizing data (e.g., mean, median, mode).

  • Inferential Statistics:

  • Making inferences about populations (e.g., hypothesis testing).

• Probability Distributions and Z-scores: Tools for standardizing data.

Hypothesis Testing

• Null Hypothesis (H0): Assumes no effect or relationship.

• Alternative Hypotheses: Proposes differences or effects.

• **Errors in Hypothesis Testing:

**

• Type I Error: Incorrectly rejecting the null hypothesis.

• Type II Error: Incorrectly accepting the null hypothesis.

Correlation vs Causation

• Correlations do not imply causation.

Validity Threats

• Internal Validity Threats:

  • Address confounding variables and randomization.

• External Validity:

  • Generalizability across contexts and populations.

Causality in Research

• Experiments Purpose: Establish cause and effect.

• Requirements for Determining Cause:

  • Temporal Precedence: The cause must precede the effect in time.

  • Covariation: The effect occurs when the cause is present and does not occur when the cause is absent.

  • Elimination of Alternatives: No other plausible explanations should remain for the relationship.

Internal Validity

• Researcher controls the amount of time participants spend with dogs to study effects.

• Internal validity refers to the degree to which conclusions can be drawn about causal relationships based on data.

• Essential to ensure that variations in the dependent variable (DV) are solely due to the IV and not other factors.

Controlling Extraneous Variables

• Confounds: Occurs when an extraneous variable varies systematically with the IV.

  • This correlation threatens internal validity, potentially causing misinterpretations of the DV's changes.

• Constancy: Keeping key extraneous variables consistent across all experimental conditions.

• Randomisation: Essential to assign participants randomly to Conditions for equal representation of participant variables (e.g., gender, age).

Experimental Designs

• Between-Subjects Design:

  • Different participants are required in each condition.

  • Equal chance assignment ensures participant variables are evenly distributed.

  • Matching: Participants are matched on relevant characteristics to maintain control.

• Within-Subjects Design:

  • Same participants undergo all conditions but must account for order effects.

  • Order Effects: Changes in performance due to learning, fatigue, or other factors.

  • Counterbalancing: Presenting conditions in various orders to mitigate bias from order effects.

Quasi-Experimental Research

• When researchers lack control over condition assignment or causal variable manipulation.

  • Example: Measuring happiness before and after introducing dogs in a nursing home context.

• Important to recognize challenges to internal validity when interpreting results.

Threats to Internal Validity

• Selection Bias: Differences in groups before the experiment.

• History: External events occurring between measurements.

• Maturation: Changes in participants over time.

• Testing: Impact of repeated measures on assessment.

• Instrumentation: Variability in measurement tools over time.

• Mortality: Participant dropout rates.

• Expectancy Effects: Researcher biases influencing results.

External Validity

• Definition: The degree to which research results generalize across different contexts or populations.

• Replication is crucial to validate findings in varied settings.

Guidelines for Research with Indigenous Peoples

• Historical Context: Previous non-Indigenous research methods have often been culturally insensitive towards Indigenous communities (Gower, 2012).

• Setting the Scene: Misguided policies result from mistreatment and lack of understanding of Indigenous cultures.

• Ethics Development: Established guidelines are necessary to safeguard Indigenous participants during research projects.

NHMRC Guidelines

• Updated ethical guidelines focusing on improving engagement with Aboriginal and Torres Strait Islander Peoples.

• Emphasizes respect for rights, promoting partnerships, collaboration, and equitable responsibility.

Core Values of NHMRC Guidelines

1. Spirit and Integrity: Connection between past and future generations; respectful behaviors and genuine intentions.

2. Cultural Continuity: Maintains identity through relationships and cultural practices.

3. Equity: Fair partnerships respecting Aboriginal culture.

4. Reciprocity: Mutual benefits and shared responsibilities in research.

5. Respect: Acknowledging cultural heritage and ensuring informed consent.

6. Responsibility: Caring for community welfare and avoiding harm.

Informed Consent

• Participation must be voluntary, well-communicated, and culturally understood.

AIATSIS Code of Ethics

• Provides clear pathways for ethical review in Indigenous research.

• Considers the cultural context and prioritizes Indigenous engagement.

Indigenous Engagement Strategies

• Forms of engagement: Inform, Consult, Involve, Collaborate, and Empower Indigenous communities.

Data Management

• Indigenous Data Governance: Ensures Indigenous control over data, legality, and benefit distribution.

Indigenous Research Methods

• Ganma: Knowledge sharing, symbolizing two cultures mingling.

• Yarning: An informal dialogue fostering personal connection and understanding.

  • Four types: Social, Collaborative, Research Topic, and Therapeutic Yarning.

• Dadirri: Represents deep listening in the research conversation.

Research Design and Experimental Methodology

• Key Components of True Experiments:

  1. Manipulation of Independent Variable (IV):

     • Changes in the dependent variable (DV) must be caused by different levels or conditions of the IV.

  2. Random Assignment:

     • Participants are randomly allocated to groups/conditions to balance out differences, ensuring fair comparisons.

     • This helps control for extraneous variables which might bias results.

  3. Control of Extraneous Variables:

     • Extraneous Variables: Variables other than the IV that can affect the DV.

     • True experiments aim to eliminate or control these variables to avoid confounding results.

Determining Causality

1. Temporal Precedence:

   • The IV must precede the DV.

   • Example: Sleep must occur before measuring alertness.

2. Co-Variation:

   • Changes in the DV must correlate with changes in the IV.

   • Example: Good sleep leads to increased alertness; lack of sleep leads to no change in alertness.

3. Elimination of Alternative Explanations:

   • Must rule out other variables that could explain the effect (e.g., nutrition affecting alertness).

   • Control strategies include random assignment, holding variables constant, and counterbalancing.

Experimental Designs:

1. Between-Subjects Design:

   • Different participants in each condition.

   • Random allocation helps control for bias.

2. Within-Subjects Design:

   • Same participants experience all conditions.

   • Counterbalancing is used to control for order effects.

Statistical Tests - T-Test and ANOVA:

1. T-Test:

   • For comparing two conditions/groups.

   • Independent Samples T-Test: Different participants in each condition.

   • Paired Samples T-Test: Same participants in each condition.

2. ANOVA (Analysis of Variance):

   • Used for comparing three or more groups.

   • Types of ANOVA: One-way, repeated measures ANOVA depending on the number of IVs and groups.

   • F-Ratio: Compares between-groups variability to within-groups variability. A significant F indicates that differences exist between group means.

Hypothesis Testing Steps for ANOVA:

1. Formulate null and alternative hypotheses (no difference vs. at least one difference).

2. Determine alpha level (commonly 0.05).

3. Calculate degrees of freedom:

   • Between Groups: K - 1 (where K = number of groups).

   • Within Groups: N - K (N = total participants).

4. Compute sum of squares (SS) for total, between, and within groups.

5. Calculate mean squares (MS) and then the F-statistic (MS between / MS within).

6. Compare calculated F to critical F from F-distribution table to determine significance.

Assumptions for T-Tests and ANOVA:

• Normality: Distribution of the dependent variable should be normally distributed.

• Homogeneity of Variances: Variance among groups should be roughly equal. Tested with Levene's test.

• Independence of Observations: Each participant's score should be independent of others.

Practical Application (Example):

• Using ANOVA to compare the effectiveness of three levels of treatment for reducing depression symptoms:

  • Placebo, low dose, high dose groups.

  • Measure DV: Reduction in depression scores, assess via ANOVA.

Lecture Overview

• Revision on calculating the sum of squares (SS) and aspects of the ANOVA summary table.

• One-way between-subjects ANOVA using the Jamovi platform, with practice in tutorials.

Follow-Up Testing

• Follow-up testing occurs after a significant ANOVA result to identify which means differ.

• Types of follow-up tests depend on pre-set hypotheses:

  • Planned Comparison (a priori): Hypotheses defined before the experiment, e.g., CBT is expected to lower depression compared to placebo.

  • Unplanned Comparison (post hoc): Conducted after significant results are found.

Assumptions for ANOVA

1. Normality: Normal distribution of scores between groups, verified through tests (e.g., Shapiro-Wilk).

2. Homogeneity of Variances: Equal variances across groups, checked using Levene's test.

3. Data Measurement: Continuous scale required for dependent variable.

4. Independence of Observations: Each participant contributes one score only.

ANOVA Calculations

• Total variability calculated as: SS{total} = SS{between} + SS_ {within}

• Calculating degrees of freedom:

  • df_ {between} = k - 1 (where k = the number of groups)

  • df_ {within} = N - k (total participants - number of groups)

Effect Size

• eta-squared (η²): Percentage of variance explained by the independent variable. Calculated as:

  • η² = SS{between} / SS{total}

• Reporting effect size is important to show how strong the effect is beyond mere significance.

Example of Follow-Up Tests

• If ANOVA reveals significant results, plan for:

  • Contrasts (a priori): Hypotheses-driven comparisons.

  • Pairwise Comparisons (post hoc): Control type One error using methods like Bonferroni adjustments.

One-Way Repeated Measures ANOVA

• Concept: Involves repeated measures on the same participants across 3 or more conditions, violating the assumption of independence of observations from One-Way Between Subjects ANOVA, as each participant is measured multiple times.

• Calculating Variability: Involves calculating sums of squares and error differently to account for participant overlap.

• Null Hypothesis: No differences in mean scores across conditions, indicating identical condition scores.

F Statistic

• Formula: F = \frac{ \text{Mean Squares of Effect} }{ \text{Mean Squares of Error} }

• Mean Squares of Effect: Represents the experimental effect across conditions.

• Mean Squares of Error: Represents differences expected if no effect from the independent variable exists, including unsystematic differences.

Assumptions of Repeated Measures ANOVA

1. Normality: Distributions within each condition should be normally distributed. Robust to violations with a larger sample size (n > 30).

2. Interval/Ratio Level Data: Dependent variable should be measured at an interval or ratio level (continuous scale).

3. Sphericity: Equality of variances of differences between conditions. Assessed using Mauchly's Test.

   • A significant Mauchly’s test (< 0.05) indicates a violation of sphericity.

Assessing Normality

• Use Shapiro-Wilk test. A significant p-value (< 0.05) indicates a violation of normality.

Corrections for Violations

• If sphericity is violated, apply corrections like Greenhouse-Geisser or Huynh-Feldt.

• Degrees of Freedom: Report with decimal points when corrections are applied.

Variance Analysis Structure

1. SS Total: Total variability in data.

2. Between Subjects Variance: Variance between participants.

3. Within Subjects Variance: Variance within participant responses across different conditions.

Calculation Steps

1. SS Total: Calculate the squares of the differences between each data point and grand mean.

2. SS Between: Calculate based on the differences between participant means and grand mean.

3. SS Effect: Based on the differences between condition means and grand mean.

4. SS Error: Remaining variance calculated by rearranging total variance equation.

Degrees of Freedom Calculation

• Between: N - 1

• Effect: K - 1

• Error: (N - 1)(K - 1)

• Total: (N \times K) - 1

Final Reporting

• Compute mean squares for error and effect.

• Determine the F statistic from mean squares.

Repeated Measures ANOVA Recap:

• Used when one group of participants completes every condition, providing repeated measures of the dependent variable.

• Assumptions include normality, interval or ratio level dependent variable, and sphericity.

  • Normality: Assessed via descriptives and Shapiro-Wilk statistic.

  • Sphericity: Assessed via Mauchly's test; if violated, Greenhouse-Geisser or Huynh-Feldt correction is applied.

ANOVA Details:

• Total variance (SS total) is broken into between-subjects (SS between) and within-subjects (SS within) variance.

• Repeated measures ANOVA focuses on variance within participants (SS within), further partitioned into SS effect and SS error.

• Calculations involve determining the sums of squares, degrees of freedom, mean squares, and the F ratio to assess the significance of the experimental effect.

Follow-Up Tests for Repeated Measures ANOVA:

• Selection depends on specific hypotheses and whether comparisons are orthogonal.

• Types include complex contrasts (a priori) and pairwise comparisons (a priori or post hoc).

  • A priori tests: Complex contrasts (orthogonal or non-orthogonal) and Bonferroni pairwise comparisons.

  • Post hoc tests: Tukey's HSD (for equal group sizes) or Bonferroni (if group sizes vary).

Correlational Research:

• Measures the relationship between two naturally occurring variables (no manipulation).

• Establishes a relationship when two variables covary.

Forms of Correlation:

• No correlation: No relationship between variables.

• Positive correlation: As one variable increases, the other increases (incline upwards).

• Negative correlation: As one variable increases, the other decreases (decline downwards).

Covariation:

• Positive covariance: High scores on variable X are met with high scores on variable Y, and vice versa.

• Negative covariance: High scores on X are met with low scores on Y, and vice versa.

Pearson’s Correlation Coefficient (r):

• Value between -1 and 1 indicating the strength of the correlation.

  • Close to 1 (positive) or -1 (negative) indicates a strong relationship.

Correlation Strength Guidelines:

• 0 to ±0.29: Weak correlation.

• ±0.30 to ±0.49: Moderate correlation.

• ±0.50 to ±1: Strong correlation.

APA Reporting:

• No leading zeros (report 0.30 as .30).

• Indicate direction with a negative symbol or no symbol for positive.

Visual Assessment of Correlations:

• Closer data points indicate a stronger correlation.

• No correlation: Randomly scattered points.

• Positive correlation: Gathering in a positive direction.

• Negative correlation: Gathering in a negative direction.

Outliers:

• Data points that don't fit the trend can affect the correlation value.

• Outliers weaken the correlation between variables.

Causation:

• Correlational research cannot explain the relationship between variables due to no strict manipulation.

• Correlation does not equal causation.

Possible Meanings of Significant Correlation:

• Variable A causes variable B.

• Variable B causes variable A.

• A third variable causes the relationship between A and B.

Coefficient of Determination (R²):

• R squared is the squared version of R.

• Indicates how much variability in one variable is explained by the other.

• Interpretation:

  • 0.01 to 0.09: Small effect size.

  • 0.09 to 0.25: Medium effect size.

  • Above 0.25: Large effect size.

Assumptions of Correlations:

• Related pairs: Both X and Y scores for each participant.

• Interval or ratio scale: Continuous data.

• Normality: Scores for each variable should be normally distributed.

• Linearity and homoscedasticity: Assessed via scatter plot.

  • Curvilinear relationships violate linearity.

  • Fanning or coning violates homoscedasticity.

Non-Parametric Tests (for violated assumptions):

• Spearman’s rho correlation: Ranks data and conducts Pearson’s correlation on rankings.

• Kendall’s tau: For small data sets with tied scores.

Restricted Range:

• Be cautious when interpreting correlations based on a restricted data range.

• Cannot generalize the correlation beyond the assessed data subset.

Simple Linear Regression:

• Predicts one variable from another.

• Linear model (straight line) to predict outcome variable values based on a predictor variable.

Terminology:

• Outcome variable: Dependent variable.

• Predictor variable: Independent variable.

Regression Line Equation:

• Equation: Y = B0 + B1X

  • Y: Predicted score on the outcome variable.

  • X: Score on the predictor variable.

  • B*0: Intercept (where the predicted value of Y intercepts the Y-axis when X is 0).

• B*1: Slope (incline of the regression line; positive or negative).

Model Fit Measures:

• R value: Same as Pearson’s r in simple linear regression.

• R-squared value: Coefficient of determination (how much variance in the outcome is accounted for by the predictor).

• Adjusted R-squared: Predicted R-squared for the population.

ANOVA Test:

• Tests whether the model is significantly better at predicting the outcome than using the mean.

Model Coefficients Table:

• Intercept: Value of Y when X is 0.

• Predictor: Assesses significance; significant predictor if the variable is significant.

Interpreting Regression Lines:

• Uphill: Positive regression (positive slope).

• Downward: Negative regression (negative slope).

Method of Least Squares:

• Aims to find the line that minimizes deviations between the line and data points.

• Finds the line of best fit by minimizing the sum of the squares of the differences (residuals) between predicted and observed values.

Goodness of Fit:

• Assessed using R-squared and the significance of the ANOVA statistic.

Calculations:

• Total Sum of Squares (SST): Total variability in the data set.

• Model Sum of Squares (SSM): Variation between the mean and the regression line.

• Sum of Squares Residual (SSR): Error of the regression as a model.

• The formulas regarding calculating R, and degrees of freedom, T value, are all listed above.

Standardised Estimate:

• With multiple predictors, we can look to our standardised estimate to be able to compare the relative contribution of each predictor.

Simple Linear Regression

• Predicts one variable from another (outcome from predictor).

• Builds upon correlation analysis by predicting outcomes.

• Uses a linear model (straight line) to predict values of the outcome variable from one or more predictor variables.

• Regression Equation: Y = B0 + B1X

  • Y: Calculated

• B*0: Y intercept.

• B*1: Slope.

• X: Predictor variable.

• Method of Least Squares: Calculates the regression equation, providing the line of best fit.

• Line of Best Fit: A line as close as possible to data points (residuals) in a scatter plot.

Determining Significance

• Assess if the line of best fit is significantly better than using the mean score.

• Coefficient of Determination (R^2):

  • Indicates how much variance in the outcome is accounted for by the predictor variable.

  • Higher R^2 means a better fit.

  • Example: R^2 = 0.82 means 82% of the variance in exam scores is accounted for by time spent

• ANOVA Statistic (F statistic):

  • Tests if the regression model is significantly better at predicting the outcome than having no model at all.

  • A significant F statistic indicates a significant line of best fit.

Interpreting Regression Output

• Coefficient of Determination:

  • Found under model fit measures.

  • R: Pearson's correlation between variables.

  • R^2: Coefficient of determination (percentage of variance in the outcome accounted for by the

• Omnibus ANOVA Test:

  • F statistic.

  • Indicates whether the model is significantly better than no model.

  • Write-up: F(df1, df2) = F value, p < 0.001.

• Model Coefficients Table:

  • Y intercept (B*0): Value of the outcome when the predictor is zero.

  • Slope (B*1): Direction and significance of the predictor.

  • Positive slope: Positive predictor.

  • Negative slope: Negative predictor.

  • Significance (p-value): Indicates if the slope is significantly different from zero.

  • Magnitude of Coefficient: For every one unit increase in the predictor variable, the outcome variable changes by this value.

Regression Equation

• Y = B0 + B1X

  • Y:

• X: Score on the predictive variable.

• B*0: Y intercept (estimate of the intercept).

• B*1: Estimate of the slope (from the predictive variable).

Simple Linear Regression Example (Self-Compassion)

• Outcome Variable: Self-compassion (understanding and patient towards oneself).

• Predictors:

  • Insomnia (how much sleep interferes with daily functioning).

  • Well-being (daily life filled with positive interests).

Bivariate Correlations

• Self-compassion and Well-being: Significant, moderate, positive correlation.

  • As self-compassion increases, well-being increases.

  • Variance shared: 16%.

• Self-compassion and Insomnia: Significant, moderate, negative correlation.

  • As insomnia increases, self-compassion decreases.

  • Variance shared: 9.6%.

Regression Output Interpretation

• Model Fit Measures:

  • Correlation (R) and R-squared (R^2).

• ANOVA Test:

  • Tests if the model is significant.

  • Write up: F(df1, df2) = F value, p < 0.001.

• Model Coefficients:

  • Predictor significance (p < 0.001).

  • Estimate: Positive or negative slope.

  • T statistic: T(df) = T value, p < 0.001.

  • Interpretation of Estimates:

  • Intercept: When X is zero, Y is the intercept value.

  • Slope: For every one unit increase in X, Y increases/decreases by the slope value.

Regression Equations (Examples)

• Predicting compassion based on well-being: Compassion = B0 + B1 * WellBeing

• Predicting compassion based on insomnia: Compassion = B0 - B1 * Insomnia

• Important: Regression predictions do not equal causation.

Assumptions of Regression

1. Normally Distributed Errors:

   • Assessed via QQ plot of residuals.

   • Assumption met when residuals fall on the solid black line.

   • Snaking indicates non-normality.

2. Linearity:

   • Assessed using residual plot.

   • Want an equal distribution of residuals above and below the zero line.

3. Homoscedasticity:

• Equal variance of residuals across the graph.

• No major fanning or conning.

  4. Independent Errors:

• Durbin-Watson statistic between 1 and 3.

Jamovi Implementation

• Analysis -> Regression -> Linear Regression.

• Dependent Variable: Outcome.

• Covariates: Predictors.

• Model Fit: R, R^2, Adjusted R^2.

• Model Coefficients: Confidence intervals, standardized estimates, ANOVA test.

• Assumption Checks: Autocorrelation (Durbin-Watson), QQ plot of residuals, residual plots.

Chi-Squared Analysis

• Used to determine the relationship between categorical variables.

• Analyzes differences between frequencies.

Categorical Data Analysis

• Previously: Categorical IVs and continuous DVs (t-tests, ANOVAs).

• Continuous variables: correlations and regressions.

• Now: Relationship between two categorical variables.

Frequencies

• Assess frequency as numbers in categories.

• Example: Pet Ownership and Survival

  • Organized in a frequency table.

Chi-Squared Statistic

• Compared to critical table of distributions.

• Determines if differences between categories are significant.

Research Question

• Is there a relationship between having a dog and survival after a heart attack?

• Variables:

  • Dog ownership (yes/no).

  • Survival status (survived/did not survive).

• No specific dependent variable here.

Chi-Square Test

• Tests for a relationship between two categorical variables.

• Pearson's chi-squared test.

• Compares observed frequencies to expected frequencies.

Null Hypothesis

• Variables have no relationship.

• Rejecting the null: there are differences between the two variables.

Assumptions of Chi-Square

1. Independence:

   • Each person falls into only one category.

2. Expected Frequencies:

   • Should be greater than 5 for each cell.

• Must be assessed when expected frequencies are calculated.

Calculating Expected Frequencies

• Also called model frequency.

• Equation: (Row Total * Column Total) / Total Number of Scores (N).

• Steps:

  1. Calculate totals for rows and columns using observed frequencies.

  2. Calculate N (add row totals or column totals).

  3. Calculate expected values for each cell using the equation.

Calculating Chi-Squared Statistic

• Calculate the squared deviation between observed and expected frequencies for each category.

• Divide by the expected frequency.

• Sum all of the calculations to obtain a single chi-squared statistic.

• Equation: Sum of \frac{(Observed - Expected)^2}{Expected}

Comparing Chi-Squared to Critical Value

• Degrees of freedom = (number of rows - 1) * (number of columns - 1)

• For 2x2 table, degrees of freedom = 1.

• Compare obtained X^2 to critical value (e.g., 3.84 for alpha = 0.05).

• If obtained X^2 > critical value, reject the null hypothesis.

Jamovi Implementation

• Analyses -> Frequencies -> Independent Samples (Chi-Square Test of Association).

• Rows: One variable (e.g., Ownership).

• Columns: Other variable (e.g., Survival).

• Counts: Include frequency count.

• Cells: Click on observed and expected.

• Output: Provides observed/expected frequencies, percentages, chi-square statistic, degrees of freedom, and p-value.

Write-Up

• Significant relationship between categories.

• Chi-squared statement: \chi^2 (df, N = sample size) = chi-squared value, p = p-value.

• Interpret differences using percentage frequencies.

• Example: Dog owners had a better survival rate than those who did not have a dog.

Regression revision:

• Simple Linear Regression Revision: Using screen time as a predictor for depression, anxiety, and stress.

  • Descriptive statistics including bivariate correlations: direction, strength, and significance of

Correlations:

• Example: Significant moderate positive correlation between screen time and stress; weak positive non-significant correlation between screen time and anxiety; moderate, positive, significant relationship between screen time and depression.

Goodness of Fit and Regression Variables:

• R-squared values indicating the proportion of variance in the outcome accounted for by the predictor.

• Model significance assessed to determine if screen time is a significant predictor.

• Exponents in Jamalfi output: Notation for very small or large numbers; converts exponents to decimals by shifting decimal places.

• Regression Equations: Predicting depression, anxiety, and stress based on screen time, interpreting the coefficients and significance

Assumptions of Regression:

• Normally distributed errors, linearity, homoscedasticity, and independent

Errors:

• Assessment methods include QQ plot for normality, scatter plot for linearity and homoscedasticity, and Durbin Watson statistic for independence of errors.

• Note: Testing or reporting assumptions not required for the data analysis report Part B.

Non-Parametric Statistics:

• Used when assumptions of linear models are violated.

• Each parametric test has a non-parametric equivalent (e.g., Kruskal-Wallace test for one-way independent
  between-subjects ANOVA).

• Depends on research question, data collection methods (continuous vs. categorical variables), and what is being compared.

Assumptions for ANOVA:

• Normal distribution of the dependent variable, equality of variance across groups, independence of data points, and continuous dependent variables

• Reason for testing assumptions: to draw accurate inferences from data

What to do if assumptions are violated:

• Accept the robustness of a test

• Transform the data to fit the test

• Change the test to fit the data (Non-Parametric Testing).
  Non-Parametric Testing:
  ranks data instead of testing bassed on distribution - solves issues of non-normal distributions and outliers - loses information about the degree of difficulty
  ranking data examples: ages of 5 people ranked from lowest to highest tied ranks -assign the averages of what ranks could have been. -Underlining theory - assess ranked values rather than the original data

Non-Parametric Tests:

• make fewer assumptions, versions to answer the same questions as metric tests, and non-reality rated or small samples sizes

Rules for Parametric testing:

• between subjects design:

  • Two groups: man-Whitney Test

  • then 3 levels Kruskal-Wallace

• repeated measures designs

  • Two groups: Wilcoxen signed rank test

  • More then 2 levels friedman's ANOVA
    *

SPEAKER 1:

conducts no matric tests to focus on jamovie including examples

Between Subjects Design - Kruskal-Wallace Test:

• Research example: Effectiveness of treatments in treating depression (no treatment, CBT, antidepressants, CBT and AD).

• Violation of normality: Conduct non-parametric ANOVA (Kruskal-Wallace test).

• Step 1: Rank the scores from lowest to highest on the