# Interpreting and Using Statistics in Psychological Research

- Andrew N. Christopher - Albion College, USA

Statistical Thinking and Everyday Life |

Failing to Use Information About Probability |

Availability heuristic |

Representativeness heuristic |

Misunderstanding Connections Between Events |

Illusory correlations |

Gambler’s fallacy |

Goals of Research |

Goal: To Describe |

Goal: To Predict |

Goal: To Explain |

Goal: To Apply |

Statistical Thinking: Some Basic Concepts |

Parameters Versus Statistics |

Descriptive Statistics Versus Inferential Statistics |

Sampling Error |

Chapter Application Questions |

Questions for Class Discussion |

The Study |

Variables |

Operational Definitions |

Measurement Reliability and Validity |

Scales of Measurement: How We Measure Variables |

Nominal Data |

Ordinal Data |

Interval and Ratio (Scale) Data |

Discrete Versus Continuous Variables |

The Basics of SPSS |

Variable View |

Data View |

Chapter Application Questions |

Questions for Class Discussion |

The Study |

Frequency Distributions |

Frequency Distribution Tables |

Frequency Distribution Graphs |

Common Visual Displays of Data in Research |

Bar Graphs |

Scatterplots |

Line Graphs |

Using SPSS to Make Visual Displays of Data |

Making a Bar Graph |

Making a Scatterplot |

Making a Line Graph |

Chapter Application Questions |

Questions for Class Discussion |

Measures of Central Tendency |

Three Measures of Central Tendency |

Mean |

Median |

Mode |

Reporting the measures of central tendency in research |

Choosing a Measure of Central Tendency |

Consideration 1: Outliers in the data |

Consideration 2: Skewed data distributions |

Consideration 3: A variable’s scale of measurement |

Consideration 4: Open-ended response ranges |

Measures of Central Tendency and SPSS |

Measures of Variability |

What Is Variability? Why Should We Care About Variability? |

Three Measures of Variability |

Range |

Variance |

Standard deviation |

Reporting variability in research |

Measures of Variability and SPSS |

Chapter Application Questions |

Questions for Class Discussion |

Types of Distributions |

Normal Distributions |

Skewed Distributions |

Standardized Scores (z Scores) |

z Scores, the Normal Distribution, and Percentile Ranks |

Locating Scores Under the Normal Distribution |

Percentile Ranks |

z Scores and SPSS |

Chapter Application Questions |

Questions for Class Discussion |

Basics of Null Hypothesis Testing |

Null Hypotheses and Research Hypotheses |

Alpha Level and the Region of Null Hypothesis Rejection |

Gathering Data and Testing the Null Hypothesis |

Making a Decision About the Null Hypothesis |

Type I Errors, Type II Errors, and Uncertainty in Hypothesis Testing |

The z Test |

A Real-World Example of the z Test |

Ingredients for the z Test |

Using the z Test for a Directional (One-Tailed) Hypothesis |

Using the z Test for a Nondirectional (Two-Tailed) Hypothesis |

One-Sample t Test |

A Real-Word Example of the One-Sample t Test |

Ingredients for the One-Sample t Test |

Using the One-Sample t Test for a Directional (One-Tailed) Hypothesis |

Using the One-Sample t Test for a Nondirectional (Two-Tailed) Hypothesis |

One-Sample t Test and SPSS |

Statistical Power and Hypothesis Testing |

Chapter Application Questions |

Questions for Class Discussion |

Conceptual Understanding of the Statistical Tool |

The Study |

The Tool |

Ingredients |

Hypothesis from Kasser and Sheldon (2000) |

Interpreting the Tool |

Assumptions of the tool |

Testing the null hypothesis |

Extending our null hypothesis test |

Using Your New Statistical Tool |

Hand-Calculating the Independent Samples t Test |

Step 1: State hypotheses |

Step 2: Calculate the mean for each of the two groups |

Step 3: Calculate the standard error of the difference between the means |

Step 4: Calculate the t test statistic |

Step 5: Determine degrees of freedom (dfs) |

Step 6: Locate the critical value |

Step 7: Make a decision about the null hypothesis |

Step 8: Calculate an effect size |

Step 9: Determine the confidence interval |

Independent Samples t Test and SPSS |

Establishing your spreadsheet |

Running your analyses |

What am I looking at? Interpreting your SPSS output |

Chapter Application Questions |

Questions for Class Discussion |

Conceptual Understanding of the Tool |

The Study |

The Tool |

Ingredients |

Hypothesis from Stirling et al. (2014) |

Interpreting the Tool |

Testing the null hypothesis |

Extending our null hypothesis test |

Assumptions of the tool |

Using Your New Statistical Tool |

Hand-Calculating the Paired Samples t Test |

Step 1: State hypotheses |

Step 2: Calculate the mean difference score |

Step 3: Calculate the standard error of the difference scores |

Step 4: Calculate the t test statistic |

Step 5: Determine degrees of freedom (dfs) |

Step 6: Locate the critical value |

Step 7: Make a decision about the null hypothesis |

Step 8: Calculate an effect size |

Step 9: Determine the confidence interval |

Paired Samples t Test and SPSS |

Establishing your spreadsheet |

Running your analyses |

What am I looking at? Interpreting your SPSS output |

Chapter Application Questions |

Questions for Class Discussion |

Conceptual Understanding of the Tool |

The Study |

The Tool |

Ingredients |

Assumptions of the tool |

Hypothesis from Eskine (2012) |

Interpreting the Tool |

Testing the null hypothesis |

Extending our null hypothesis test |

Going beyond the F ratio: Post hoc tests |

Using Your New Statistical Tool |

Hand-Calculating the One-Way, Between-Subjects ANOVA |

Step 1: State hypotheses |

Step 2: Calculate the mean for each group |

Step 3: Calculate the sums of squares (SSs) |

Total Sums of Squares (SStotal) |

Within-Groups Sums of Squares (SSwithin-groups) |

Between-Groups Sums of Squares (SSbetween-groups) |

Step 4: Determine degrees of freedom (dfs) |

Total Degrees of Freedom (dftotal) |

Within-Groups Degrees of Freedom (dfwithin-groups) |

Between-Groups Degrees of Freedom (dfbetween-groups) |

Step 5: Calculate the mean squares (MSs) |

Step 6: Calculate your F ratio test statistic |

Step 7: Locate the critical value |

Step 8: Make a decision about the null hypothesis |

Step 9: Calculate an effect size |

Step 10: Perform post hoc tests |

One-Way Between-Subjects ANOVA and SPSS |

Establishing your spreadsheet |

Running your analysis |

What am I looking at? Interpreting your SPSS output |

Chapter Application Questions |

Questions for Class Discussion |

Conceptual Understanding of the Tool |

The Study |

The Tool |

Between-subjects versus repeated-measures ANOVAs |

Assumptions of the tool |

Hypothesis from Bernard et al. (2014) |

Interpreting the Tool |

Testing the null hypothesis |

Extending our null hypothesis test |

Going beyond the F ratio: Post hoc tests |

Using Your New Statistical Tool |

Hand-Calculating the One-Way, Repeated-Measures ANOVA |

Step 1: State the hypothesis |

Step 2: Calculate the mean for each group |

Step 3: Calculate the sums of squares (SSs) |

Total Sums of Squares (SStotal) |

Between Sums of Squares (SSbetween) |

Error Sums of Squares (SSerror) |

Step 4: Determine degrees of freedom (dfs) |

Total Degrees of Freedom (dftotal) |

Between Degrees of Freedom (dfbetween) |

Error Degrees of Freedom (dferror) |

Step 5: Calculate the mean squares (MSs) |

Step 6: Calculate your F ratio test statistic |

Step 7: Locate the critical value |

Step 8: Make a decision about the null hypothesis |

Step 9: Calculate an effect size |

Step 10: Perform post hoc tests |

One-Way, Repeated-Measures ANOVA and SPSS |

Establishing your spreadsheet |

Running your analysis |

What am I looking at? Interpreting your SPSS output |

Chapter Application Questions |

Questions for Class Discussion |

Conceptual Understanding of the Tool |

The Study |

The Tool |

Factorial notation |

Main effects and interactions |

Hypothesis from Troisi and Gabriel (2011) |

Interpreting the Tool |

Testing the null hypothesis |

Extending the null hypothesis tests |

Dissecting a statistically significant interaction |

Using Your New Statistical Tool |

Hand-Calculating the Two-Way, Between-Subjects ANOVA |

Step 1: State the hypotheses |

Step 2: Calculate the mean for each group and the marginal means |

Step 3: Calculate the sums of squares (SSs) |

Total Sums of Squares (SStotal) |

Within-Groups Sums of Squares (SSwithin-groups) |

Between-Groups Sums of Squares (SSbetween-groups) |

Step 4: Determine degrees of freedom (dfs) |

Total Degrees of Freedom (dftotal) |

Within-Groups Degrees of Freedom (dfwithin-groups) |

Between-Groups Degrees of Freedom (dfbetween-groups) |

Step 5: Calculate the mean squares (MSs) |

Step 6: Calculate your F ratio test statistics |

Step 7: Locate the critical values |

Step 8: Make a decision about each null hypothesis |

Step 9: Calculate the effect sizes |

Step 10: Perform follow-up tests |

Two-Way, Between-Subjects ANOVA and SPSS |

Establishing your spreadsheet |

Running your analysis |

What am I looking at? Interpreting your SPSS output |

Dissecting interactions in SPSS |

Chapter Application Questions |

Questions for Class Discussion |

Conceptual Understanding of the Tool |

The Study |

The Tool |

Types (directions) of correlations |

Strength of correlations |

Assumptions of the Pearson correlation |

Uses for correlations |

Use 1: Studying naturally occurring relationships |

Use 2: Basis for predictions |

Use 3: Establishing measurement reliability and validity |

Hypotheses from Clayton et al. (2013) |

Interpreting the Tool |

Testing the null hypothesis |

Cautions in interpreting correlations |

Caution 1: Don’t confuse type (direction) and strength of a correlation |

Caution 2: Range restriction |

Caution 3: “Person-who” thinking |

Caution 4: Curvilinear relationships |

Caution 5: Spurious correlations |

Using Your New Statistical Tool |

Hand-Calculating the Person Correlation Coefficient (r) |

Step 1: State hypotheses |

Step 2: For both variables, find each participant’s deviation score and then multiply them together |

Step 3: Sum the products in step 2 |

Step 4: Calculate the sums of squares for both variables |

Step 5: Multiply the two sums of squares and then take the square root |

Step 6: Calculate the correlation coefficient (r) test statistic |

Step 7: Locate the critical value |

Step 8: Make a decision about the null hypothesis |

The Pearson Correlation (r) and SPSS |

Establishing your spreadsheet |

Running your analysis |

What am I looking at? Interpreting your SPSS output |

Chapter Application Questions |

Questions for Class Discussion |

Univariate Regression |

Ingredients |

Hand-Calculating a Univariate Regression |

Step 1: Calculate the slope of the line (b) |

Step 2: Calculate the y-intercept (a) |

Step 3: Make predictions |

Univariate Regression and SPSS |

Running your analysis |

What am I looking at? Interpreting your SPSS output |

Multiple Regression |

Understanding Multiple Regression in Research |

Multiple Regression and SPSS |

Establishing your spreadsheet |

Running your analysis |

What am I looking at? Interpreting your SPSS output |

Chapter Application Questions |

Questions for Class Discussion |

Chi-Square (x2) Tests |

Chi-Square (x2) Goodness-of-Fit Test |

Hand-calculating the ?2 goodness-of-fit test |

Step 1: State hypotheses |

Step 2: Determine degrees of freedom (dfs) |

Step 3: Calculate the x2 test statistic |

Step 4: Find the critical value and make a decision about the null hypothesis |

x2 goodness-of-fit test and SPSS |

Establishing your spreadsheet |

Running your analysis |

What am I looking at? Interpreting your SPSS output |

Chi-Square (x2) Test of Independence |

Hand-calculating the x2 test of independence |

Step 1: State hypotheses |

Step 2: Determine degrees of freedom (dfs) |

Step 3: Calculate expected frequencies |

Step 4: Calculate the x2 test statistic |

Step 5: Find the critical value and make a decision about the null hypothesis |

Step 6: Calculate an effect size |

x2 test for independence and SPSS |

Establishing your spreadsheet |

Running your analysis |

What am I looking at? Interpreting your SPSS output |

Spearman Rank-Order Correlation Coefficient |

Hand-Calculating the Spearman Rank-Order Correlation |

Step 1: State the hypothesis |

Step 2: Calculate the difference (D) score between each pair of rankings |

Step 3: Square and sum the difference scores in step 2 |

Step 4: Calculate the Spearman correlation coefficient (rs) test statistic |

Step 5: Locate the critical value and make a decision about the null hypothesis |

Spearman’s Rank-Order Correlation and SPSS |

Establishing your spreadsheet |

Running your analysis |

What am I looking at? Interpreting your SPSS output |

Mann-Whitney U Test |

Hand-Calculating the Mann-Whitney U Test |

Step 1: State hypotheses |

Step 2: Calculate the ranks for categories being compared |

Step 3: Sum the ranks for each category |

Step 4: Find the U for each group |

Step 5: Locate the critical value and make a decision about the null hypothesis |

Mann-Whitney U Test and SPSS |

Establishing your spreadsheet |

Running your analysis |

What am I looking at? Interpreting your SPSS output |

Chapter Application Questions |

Questions for Class Discussion |

Deciding on the Appropriate Tool: Six Examples |

Study 1: “Waiting for Merlot: Anticipatory Consumption of Experiential and Material Purchases |

Study 2: “Evaluations of Sexy Women in Low- and High-Status Jobs” |

Study 3: “Evil Genius? How Dishonesty Can Lead to Greater Creativity” |

Study 4: “Differential Effects of a Body Image Exposure Session on Smoking Urge Between Physically Active and Sedentary Female Smokers” |

Study 5: “Texting While Stressed: Implications for Students’ Burnout, Sleep, and Well-Being” |

Study 6: “How Handedness Direction and Consistency Relate to Declarative Memory Task Performance” |

Using Your Toolkit to Identify Appropriate Statistical Tools |

Study 7: “Borderline Personality Disorder: Attitudinal Change Following Training” |

Study 8: “Effects of Gender and Type of Praise on Task Performance Among Undergraduates” |

Study 9: “Please Respond ASAP: Workplace Telepressure and Employee Recovery” |

Answers to Studies 7, 8, and 9 |

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