Psychology 301 Statistical Tests Flashcards

Fundamentals of Hypothesis Testing and APA Reporting

• Hypothesis Testing Logic  

  • Testing begins with the assumption that the null hypothesis ($H_0$) is correct. This assumes there is no difference between the sample values and the population values.   

  • The alternative hypothesis ($H_1$) posits that there is a difference between the sample value(s) and the population value(s).  

  • The statistical test functions by comparing the sample value (test statistic) with the population value (critical value) to determine the likelihood of observing the current sample's difference.   

• Significance Thresholds:    

  • If the probability ($p$) of observing the difference is greater than $5\%$ ($1.0 > p > 0.051$), the null hypothesis is retained.  

  • If the probability ($p$) is less than $5\%$ ($p < .05$), a difference is concluded to exist; the null hypothesis is rejected, and the alternative hypothesis is accepted.

• APA-Style Reporting Conventions   

  • Standard format: type of test (degrees of freedom) = test statistic, p-value (effect size).

  • Report exact p-values to $3$ decimal places.  

  • Use a leading $0$ before decimal values only if the value has the potential to exceed $1.0$.

One-Sample Comparison Tests

• One-Sample z-Test  

  • Purpose: To compare a sample mean to a population mean when the population variance is known.

  • Distribution: $z$   

  • SAS Procedure: None (rarely used).   

  • Post-Hoc: No.

• One-Sample t-Test   

  • Purpose: To compare a sample mean to a population mean when the population variance must be estimated.  

  • Distribution: $t$   

  • Post-Hoc: No.   

  • SAS Syntax:     - PROC TTEST H0 = [VALUE OF POPULATION MEAN];  VAR [DEPENDENT VARIABLE]; RUN;    

  • Example: PROC TTEST H0=83; VAR DREAM; RUN;   

  • Example Results: $t(19) = -2.85, p = .010$. (Significant difference; reject null).

Tests for Comparing Two Sample Means

• Independent Samples t-Test  

  • Purpose: Used for one independent variable with two levels to compare two different sample means.   

  • Distribution: $t$  

  • Post-Hoc: No.  

  • SAS Syntax: PROC TTEST; CLASS [INDEPENDENT VARIABLE]; VAR [DEPENDENT VARIABLE];   

  • Example: PROC TTEST; CLASS ANXIETY; VAR MATH;  

  • Example Results: $t(18) = 1.14, p = .269$. (Not significant; retain null).

• Related Samples t-Test  

  • Purpose: Used for one independent variable with two levels to compare two sample means where the samples consist of the same or matched participants.

  • Distribution: $t$   

  • Post-Hoc: No.  

  • SAS Syntax: PROC TTEST; PAIRED [INDEPENDENT VARIABLE LEVEL1]*[INDEPENDENT VARIABLE LEVEL2];   

  • Example: PROC TTEST; PAIRED PRETEST*POSTTEST;  

  • Example Results: $t(9) = -3.32, p = .009$. (Significant difference; reject null).

Analysis of Variance (ANOVA)

• One-Way Between-Subjects ANOVA  

  • Purpose: One independent variable with more than two levels.

  • Distribution: $F$  

  • Post-Hoc: Tukey HSD.  

  • SAS Syntax: PROC ANOVA; CLASS [INDEPENDENT VARIABLE]; MODEL [DEPENDENT VARIABLE] = [INDEPENDENT VARIABLE]; MEANS [INDEPENDENT VARIABLE] / [POST-HOC];   

  • Example: PROC ANOVA; CLASS BP_STATUS; MODEL WEIGHT = BP_STATUS; MEANS BP_STATUS / TUKEY;  

  • Example Results: $F(2, 5200) = 242.59, p < .001 (R^2 = .085)$.

• One-Way Repeated Measures ANOVA  

  • Purpose: One independent variable with more than two levels where participants are exposed to all levels.  

  • Distribution: $F$

  • Post-Hoc: Bonferroni Procedure.  

  • SAS Syntax: PROC ANOVA; MODEL [IV LEVEL1] [IV LEVEL2] [IV LEVEL3] = ; REPEATED [CREATE IV NAME] [# OF LEVELS] ([LABELS]);    

  • Example: PROC ANOVA; MODEL F1 F2 F3 = ; REPEATED FOOD 3 (1 2 3);   

  • Example Results: $F(2, 8) = 5.58, p = .030$.

• Two-Way ANOVA   

  • Purpose: Two independent variables with one dependent variable.

  • Tests: Three hypotheses are tested: the Main Effect for IV1, the Main Effect for IV2, and the Interaction Effect.  

  • Distribution: $F$  

  • Post-Hoc: Main effects use Tukey HSD; Interaction uses simple main effects tests.

  • SAS Syntax: PROC ANOVA; CLASS [IV 1] [IV 2]; MODEL [DV] = [IV1] [IV2] [IV1]*[IV2]; MEANS [IV1] [IV2] [IV1]*[IV2] / [POST-HOC];  

  • Example Reporting:     

    • Main effect for caffeine: $F(2, 18) = 0.70, p = .510$     

    • Main effect for coffee: $F(1, 18) = 129.60, p < .001$     

    • Interaction effect: $F(2, 18) = 39.90, p < .001$

Advanced Post-Hoc Procedures

• Tukey HSD Post-Hoc Test   

  • Performs all possible pairwise comparisons to identify specifically which levels differ.   

  • SAS Visual Interpretation: Comparisons covered by the same bar (e.g., a blue bar over Delay2 and Delay3) do not differ significantly.  

  • Statistically significant comparisons in table formats are often indicated by an asterisk ($*$ ).

• Bonferroni Procedure  

  • Used for Repeated Measures ANOVA.  

  • Involves performing multiple related samples t-tests with an adjusted alpha level ($.05$ divided by the number of comparisons).

• Simple Main Effects Procedure   

  • Used to analyze significant interactions by splitting the dataset based on one independent variable.   

  • SAS Implementation steps:   

    • 1. Use PROC SORT by the selected IV: PROC SORT; BY [selected IV];   

    • 2. Run a standard ANOVA with a BY statement: PROC ANOVA; BY [selected IV]; CLASS [other IV]; MODEL [DV] = [other IV]; MEANS [other IV] / TUKEY;

Degree of Relationship and Prediction

• Correlation  

  • Purpose: Examines the relationship between two variables, usually continuous.  

  • Distribution: $r$   

  • SAS Syntax: PROC CORR; VAR [VARIABLE 1] [VARIABLE 2];   

  • APA Reporting: $r(sample\,size) = correlation, p = value$.  

  • Example: For Mindset & Social Support, $r(289) = .053, p = .366$.

• Linear Regression  

  • Purpose: One continuous predictor variable used to predict one criterion variable.  

  • Distribution: $F$   

  • SAS Syntax: PROC REG; MODEL [CRITERION] = [PREDICTOR];

  • Reporting: Focused on the Regression Equation: $y' = ax + b$.

  • Example: $BMI = -0.20965x + 34.91834$.

• Multiple Regression  

  • Purpose: Two or more continuous predictor variables are used to predict one criterion variable.  

  • Distribution: $F$   - SAS Syntax: PROC REG; MODEL [CRITERION] = [PREDICTOR 1] [PREDICTOR 2];  

  • Reporting: Regression Equation: $y' = ax_1 + ax_2 + b$.  

  • Example: $BMI = 1.66965x_1 + -0.01749x_2 + 16.8894$.

Chi-Square Tests for Categorical Variables

• Chi-Square Test for Goodness-of-Fit  

  • Purpose: Compare expected versus observed frequencies for one categorical variable.   

  • Distribution: $\chi^2$  

  • SAS Syntax: PROC FREQ; TABLES [VARIABLE] / CHISQ;   

  • APA Reporting: $\chi^2(2) = 763.4356, p < .001$.

• Chi-Square Test for Independence  

  • Purpose: Compare expected versus observed frequencies for two or more categorical variables.  

  • Distribution: $\chi^2$  

  • SAS Syntax: PROC FREQ; TABLES [VARIABLE]*[VARIABLE] / CHISQ;  

  • APA Reporting: $\chi^2(2) = 40.5063, p < .001$.