PSYC_2016_FINAL_STUDY_GUIDE_

Purpose● Compares means of two independent groups.Formula● t=M1−M2s12n1+s22n2t=n1s12+n2s22M1−M2.Steps1. Compute means (M1,M2M1,M2) and variances (s12,s22s12,s22).2. Calculate the pooled standard error.3. Use the formula to compute tt.4. Compare tt to the critical value.12. Related Samples t-TestPurpose● Compares means from related groups (e.g., pre-test vs. post-test).Formula● t=Mean DifferenceSE Differencet=SE DifferenceMean Difference.Steps1. Compute difference scores (D=X1−X2D=X1−X2).2. Calculate the mean and SD of DD.3. Compute SE=snSE=ns.4. Substitute into tt-formula and compare to critical value.13. One-Way ANOVAPurpose● Compares means across three or more groups.Formula● F=MS BetweenMS WithinF=MS WithinMS Between.Steps

1. Compute SS Between and SS Within.2. Divide by their respective dfdf to find MS values.3. Calculate FF-statistic: F=MS BetweenMS WithinF=MS WithinMS Between.4. Compare FF to the critical value in the F-table.When to Use:● More than two groups to compare.1. Picking the Right Test● When to Use What:○ Descriptive Statistics: Summarizing data (mean, median, mode, SD).○ Correlation: Assessing relationships between variables.○ Regression: Predicting values of one variable based on another.○ t-Tests:■ One-sample: Compare sample mean to a known value.■ Independent samples: Compare two unrelated groups.■ Paired samples: Compare related groups (pre/post-test).○ ANOVA:■ One-way: Compare means across 3+ independent groups.■ Repeated measures: Compare means across 3+ related groups.2. Completing the ANOVA Table● Key Components:○ Sum of Squares (SS):■ SS Total=SS Between+SS WithinSS Total=SS Between+SS Within.○ Degrees of Freedom (df):■ df Between=k−1df Between=k−1 (k = number of groups).■ df Within=N−kdf Within=N−k (N = total observations).■ df Total=N−1df Total=N−1.○ Mean Squares (MS):■ MS Between=SS Betweendf BetweenMS Between=df BetweenSSBetween.■ MS Within=SS Withindf WithinMS Within=df WithinSS Within.○ F-statistic:■ F=MS BetweenMS WithinF=MS WithinMS Between.Example Calculation:Given:● SSBetween=40SSBetween=40, SSWithin=120SSWithin=120, N=30N=30, k=3k=3:1. Calculate dfBetween=k−1=2dfBetween=k−1=2.

2. Calculate dfWithin=N−k=27dfWithin=N−k=27.3. CalculateMSBetween=SSBetweendfBetween=20MSBetween=dfBetweenSSBetween=20.4. Calculate MSWithin=SSWithindfWithin=4.44MSWithin=dfWithinSSWithin=4.44.5. Compute F=MSBetweenMSWithin=4.50F=MSWithinMSBetween=4.50.3. Writing APA Results for One-Way ANOVA● Template:○ "A one-way ANOVA revealed a significant/non-significant effect of [IV] on [DV],F(dfBetween,dfWithin)=Fobtained,p=p-value,η2=effectsizeF(dfBetween,dfWithin)=Fobtained,p=p-value,η2=effect size."● Example:○ "A one-way ANOVA revealed a significant effect of teaching method on testscores, F(2,27)=4.50,p<.05,η2=.25F(2,27)=4.50,p<.05,η2=.25. Post hoc analysesshowed that [Group 1] scored significantly higher than [Group 2]."4. Z-Transformation● Formula:○ z=X−μ/σ where:■ X: Raw score.■ μ: Mean of the population.■ σ: Standard deviation.○● Steps:○ Subtract the mean from the raw score (X−μ).○ Divide by the population standard deviation (σ).● Example:○ For X=85X=85, μ=80μ=80, σ=5σ=5:■ z=85−805=1.0z=585−80=1.0.■ Interpretation: The score is 1 SD above the mean.○5. Calculating t-Obtained● Formula:○ t=M−μSEt=SEM−μ, where SE=snSE=ns.● Steps:

○ Calculate SESE: Find the standard error using ss (sample SD) and nn (samplesize).○ Subtract the population mean (μμ) from the sample mean (MM).○ Divide the result by SESE.● Example:○ M=50,μ=45,s=10,n=25M=50,μ=45,s=10,n=25:■ SE=1025=2SE=2510=2.■ t=50−452=2.5t=250−45=2.5.○6. Determining Sphericity● What is Sphericity?○ Assumption that variances of differences between all possible pairs of groups areequal.● Testing:○ Mauchly’s test: Significant pp-value (p<.05p<.05) indicates violation of sphericity.● Correction Methods (if violated):○ Use Greenhouse-Geisser or Huynh-Feldt corrections to adjust dfdf.7. Interpreting Frequency Tables● Key Steps:○ Identify the variable and its categories.○ Analyze the frequencies to find the mode or the most common value.○ Calculate percentages if relative frequencies are needed.○ Look for patterns or outliers.Picking the Right Test Guide1. Z-Test● When to Use: Compare a sample mean to a known population mean when thepopulation SD (σσ) is known.● Example: Determining if a class's average IQ significantly differs from the populationmean of 100 (σ=15σ=15).2. T-Tests● Types:

1. One-Sample T-Test:■ When to Use: Compare a sample mean to a known population meanwhen σσ is unknown.■ Example: Testing whether students' scores on a test differ from a nationalaverage.2. Independent Samples T-Test:■ When to Use: Compare means of two independent groups.■ Example: Comparing male vs. female test scores.3. Related Samples T-Test:■ When to Use: Compare means of the same group under two conditions(pre-test/post-test) or paired groups.■ Example: Evaluating the effect of a training program on participants.3. Correlation Tests● Pearson Correlation:○ When to Use: Measure the strength and direction of a linear relationshipbetween two continuous variables.○ Example: Relationship between study hours and exam scores.● Spearman Correlation:○ When to Use: Measure monotonic relationships between two ordinal variables ornon-linear continuous data.○ Example: Relationship between rank in class and participation rate.● Point-Biserial:○ When to Use: Measure the relationship between one continuous variable andone dichotomous variable.○ Example: Relationship between pass/fail status and test scores.● Phi Correlation:○ When to Use: Measure the relationship between two dichotomous variables.○ Example: Relationship between gender (male/female) and voting preference(yes/no).4. F-Test● When to Use: Compare variances between groups to test equality of variances.● Example: Determining if two populations have equal variability.5. Regression● When to Use: Predict one variable (Y) based on another (X).● Example: Predicting income based on years of education.6. ANOVA Tests● 1-Way Between Subjects ANOVA:○ When to Use: Compare means of three or more independent groups.

○ Example: Comparing the test scores of students in three teaching methods.● 1-Way Within Subjects ANOVA:○ When to Use: Compare means of three or more related groups (e.g., repeatedmeasures).○ Example: Comparing individuals' stress levels across three different time points.● 2-Way ANOVA (Factorial):○ When to Use: Examine the effect of two independent variables on a dependentvariable, including their interaction.○ Example: Studying the effects of gender and study technique on exam