Introduction
1. Descriptive statistics and inferential statistics
1.1. Subareas of statistics
1.2. Descriptive statistics
1.3. Inferential statistics
2. Level of measurement
2.1. Nominal variables
2.2. Ordinal variables
2.3. Categorical variables
2.4. Metric variables
2.5. Ratio scale and interval scale
3. Sampling
3.1. Full or total survey vs. random sample
3.2. Population and sample
3.3. Types of sampling?
3.4. Probability selection
3.5. Deliberate selection
3.6. Arbitrary selection
3.7. Sample selection in online surveys
3.8. Sample description in bachelor or master thesis
4. Location parameter
4.1. Mean value (arithmetic mean)
4.2. Geometric mean and quadratic mean
4.3. Median
4.4. Mean and median in comparison
4.5. Mode (modal value)
4.6. Advantage and disadvantage of the mean, median and mode
5. Dispersion parameter
5.1. Standard deviation
5.2. Variance
5.3. Difference between variance and standard deviation
5.4. Range
5.5 Quartile
5.6. Interquartil range
5.7. Example dispersion parameter
6. Frequency table
6.1. Absolute and relative frequencies
6.2. Valid percent
6.3. Frequency table in statistics
6.4. Example frequency table
6.5. Frequency table in APA style
7. Contingency table (Crosstab)
7.1. Crosstabs in statistics
7.2. Interpretation of crosstabs
7.3. Example crosstab
7.4. Testing a crosstab for significance
8. Charts
8.1. Bar chart
8.2. Bar chart for frequencies
8.3. Grouped bar charts
8.4. Bar chart for mean values
8.5. Error bar
8.6. Example bar chart
8.7. Histogram
8.8. Histogram example
8.9. Bar chart vs. Histogram
8.10. Scatter plot
8.11. Line charts
8.12. Boxplot
8.13. Bland-Altman plot
8.14. Create charts online with DATAtab
9. Inferential Statistics
9.1. Hypotheses
9.2. Null and alternative hypothesis
9.3. Difference and correlation hypotheses
9.4. Directional and undirectional hypotheses
9.5. Hypothesis Testing
9.5.1. Hypothesis testing and the null hypothesis
9.5.2. The uncertainty in hypothesis testing
9.5.3. Level of significance or probability of error
9.5.4. Example significance level and p-value
9.5.5. Types of errors
9.5.6. Significance vs effect size
9.5.7. Choosing the appropiate hypothesis test
9.5.8. Examples for hypothesis tests
9.6. The p-value
9.6.1. Defining the p-value
9.6.2. Using the p-value
9.6.3. Significance level
9.6.4. One-tailed p-values
9.6.5. Calculate p-value
9.6.6. Statistical tests and the p-value
9.6.7. Specify the p-value
10. Checking assumptions of statistical tests
10.1. Levene test of variance homogeneity
10.2. Levene test example
10.3. Interpreting the Levene Test
10.4. Normality test
10.4.1. Statistical test for normal distribution
10.4.2. Disadvantage of analytical tests for normal distribution
10.4.3. Graphical test for normal distribution
10.5. Multicollinearity test
10.5.1. How to avoid multicollinearity?
10.5.2. Multicollinearity test
10.5.3. Tolerance value
10.5.4. VIF Multicollinearity
11. Statistical tests for differences
11.1. One sample t-test
11.1.1. Basics of the one sample t-test
11.1.2. Examples of a t-test for one sample
11.1.3. Assumptions of the one-sample t-test
11.1.4. Hypotheses for the one-sample t-test
11.1.5. Calculation of the one-sample t-test
11.1.6. One sample t-test with example
11.1.7. APA format | One sample t-test
11.2. T-test for independent samples (unpaired t-test)
11.2.1 Using and independent t-test
11.2.2. Purpose of the independent/unpaired t-test
11.2.3. Examples for the unpaired t-test
11.2.4. Research question and hypotheses for the unpaired t-test
11.2.5. Assumptions unpaired/independent t-test
11.2.6. Calculate t-test for independent samples
11.2.7. Confidence interval for the true mean difference
11.2.8. One-sided and two-sided unpaired t-test
11.2.9. Effectsize unpaired t-test
11.2.10. Example t-test for independent samples
11.2.11. Interpretation t-test for independent samples
11.2.12. Report a t-test for independent samples
11.3. Paired-samples t-test
11.3.1. Why do you need the dependent t-test?
11.3.2. What is the advantage of a dependent t-test over an independent t-test?
11.3.3. Examples of the t-test for paired samples
11.3.4. Research question and hypotheses of the paired t-test
11.3.5. Assumptions paired t-test
11.3.6. Calculating a paired t-test
11.3.7. Example t-test for dependence samples with DATAtab
11.3.8. Interpretation of a t-test for dependent samples
11.3.9. Effect size dependent t-test
11.4. Mann-Whitney U test
11.4.1. Assumptions Mann-Whitney U test
11.4.2. Hypotheses Mann-Whitney U test
11.4.3. Calculate Mann-Whitney U test
11.4.4. Calculate Mann-Whitney U test with tied ranks
11.4.5. Mann-Whitney U test Example with DATAtab
11.4.6. Interpret Mann-Whitney U test
11.4.7. Mann-Whitney U test and effect size
11.5. Wilcoxon test
11.5.1. Assumptions of the Wilcoxon test
11.5.2. Hypotheses in the Wilcoxon test
11.5.3. Wilcoxon test and test power
11.5.4. Calculate Wilcoxon test
11.5.5. Calculate Wilcoxon signed-rank test with tied ranks
11.5.6. Effect size in the Wilcoxon signed-rank test
11.5.7. Example Wilcoxon test with DATAtab
12. Frequency analysis
12.1. Binomial test
12.1.1. Hypotheses in binomial test
12.1.2. Binomial test calculation
12.1.3. Binomial test example
12.1.4. Interpretation of a Binomial Test
12.2. Chi-square test
12.2.1. Applications of the Chi-Square Test
12.2.2. Calculation of Chi-Square test
12.2.3. Chi-Square Test of Independence
12.2.4. Chi-square distribution test
12.2.5. Chi-square homogeneity test
12.2.6. Effect size for Chi-square test
12.2.7. Effect size vs. p-value
12.2.8. Example: Chi-square test with DATAtab
13. Statistical tests to test for differences in more than two groups
13.1. Analysis of Variance (ANOVA)
13.1.1. Why not calculate multiple t-tests?
13.1.2. Difference between one-way and two-way ANOVA
13.1.3. Analysis of variance with and without repeated measures
13.2. One-factor ANOVA
13.3. One-factor ANOVA example
13.4. Analysis of variance hypotheses
13.5. Assumptions of one-way analysis of variance
13.6. Welch's ANOVA
13.7. Effect size Eta squared (n2)
13.8. Two factor analysis of variance
13.9. Calculate example with DATAtab
13.10. Repeated Measures ANOVA
13.10.1. What are dependent samples?
13.10.2. Difference of analysis of variance with and without repeated measurements
13.10.3. Example of repeated measures ANOVA
13.10.4. Research question and hypotheses
13.10.5. Assumptions ANOVA with repeated measures
13.10.6. Results of the one-factor analysis of variance with repeated measures
13.10.7. Effect size for repeated measures ANOVA
13.10.8. Bonferroni Post-hoc-Test
13.10.9. Calculate ANOVA with measurement repetitions with DATAtab
13.10.10. Calculate a repeated measures ANOVA by hand
13.11. Two-way ANOVA (without repeated measures)
13.11.1. What is a factor?
13.11.2. Two factors
13.11.3. Example Two-Way ANOVA
13.11.4. Hypotheses
13.11.5. Assumptions
13.11.6. Calculation of a two-way ANOVA
13.11.7. Calculating two-way ANOVA with DATAtab
13.11.8. Interpreting two-way ANOVA
13.11.9. Interaction effect
13.12. Two-way ANOVA with measurement repetition
13.12.1. Sample with measurement repetition
13.12.2. Example two-way ANOVA with repeated measures
13.12.3. Hypotheses
13.12.4. Assumptions of the two-way analysis of variance with repeated measures
13.13. Kruskal-Wallis test
13.13.1. Examples for the Kruskal-Wallis test
13.13.2. Research question and hypotheses in the Kruskal-Wallis test
13.13.3. Assumptions of the Kruskal-Wallis test
13.13.4. Calculate Kruskal-Wallis test
13.13.5. Kruskal-Wallis test example
14. Correlation
14.1.1. Correlation and causality
14.1.2. Correlation and causality example
14.1.3. Correlation interpretation
14.1.4. Direction of correlation
14.1.5. Strenght of correlation
14.1.6. Scatter plot and correlation
14.1.7. Test correlation for significance
14.1.8. Directional and non-directional hypotheses
14.2. Pearson correlation analysis
14.2.1. Pearson Correlation assumptions
14.3. Spearman rank correlation
14.4. Point biserial correlation
14.5. Partial correlation
14.5.1. Calculation of the partial correlation
14.5.2. Partial correlation example
14.5.3. Partial correlation 2nd order
14.5.4. Example: Pearson correlation
14.5.5. Directional (one-sided) correlation hypothesis
15. Regression analysis
15.1. Basic of regression
15.1.1. Using a regression analysis
15.1.2. Types of regression analysis
15.1.3. Dummy variables and Reference category
15.1.4. Examples of regression:
15.2. Linear regression
15.2.1. Simple Linear Regression
15.2.2. Multiple Linear Regression
15.2.2.1. Multiple Regression vs. Multivariate Regression
15.2.2.2. Coefficient of determination
15.2.2.3. Adjusted R2
15.2.2.4. Standard estimation error
15.2.2.5. Standardized and unstandardized regression coefficient
15.2.2.6. Assumptions of Linear Regression
15.2.2.7. Linearity
15.2.2.8. Homoscedasticity
15.2.2.9. Normal distribution of the erro
15.2.2.10. Multicollinearity
15.2.2.11. Significance test and Regression
15.2.2.12. Example linear regression
15.2.2.13. Interpretation of the results
15.2.2.14. Presenting the results of the regression
15.2.3. Logistic regression
15.2.3.1. What is logistic regression?
15.2.3.2. Logistic regression and probabilities
15.2.3.3. Calculate logistic regression
15.2.3.4. Logistic function
15.2.4. Maximum Likelihood Method
15.2.4.1. The Likelihood Function
15.2.4.2. Maximum Likelihood Estimator
15.2.5. Multinomial logistic regression
15.2.6. Interpretation of the results
15.2.7. Pseudo-R squared
15.2.8. Null Model
15.2.9. Cox and Snell R-square
15.2.10. Nagelkerkes R-square
15.2.11. McFadden's R-square
15.2.12. Chi2 Test and Logistic Regression
15.2.13. Example logistic regression
15.2.14. Calculating logistic regression with DATAtab
16. Factor analysis
16.1. What is a factor?
16.2. Example factor analysis
16.3. Research questions factor analysis
16.4. Factor load, eigenvalue, communalities
16.5. Correlation Matrix
16.6. Factor Analysis and dimensionality
16.6.1. Eigenvalue criterion (Kaiser criterion)
16.6.2. Scree-Test
16.6.3. Communalities
16.6.4. Component matrix
16.6.5. Rotation Matrix
16.6.6. Varimax Rotation
17. Cluster analysis
17.1. Example Hierarchical Cluster Analysis
17.1.1. Calculating a Hierarchical Cluster Analysis
17.1.2. Distance between two points
17.1.3. Euclidean Distance
17.1.4. Manhattan Distance
17.1.5. Maximum Distance
17.1.6. Linking methods
17.1.6.1. Single-linkage
17.1.6.2. Complete-linkage
17.1.6.3. Average-linkage
17.1.7. Example Hierarchical Cluster Analysis
17.1.7.1. Calculate hierarchical cluster analysis with DATAtab
17.2. K-means cluster analysis
17.2.1. Optimal cluster number
17.2.2. Elbow curve
17.2.3. Scaling data for k-means clustering
17.2.4. K-means clustering calculator
17.2.5. Key Features
18. What does association analysis do?
18.2. Market Basket Analysis Example
18.3. Interpreting the results of a Market basket analysis
18.3.1. Frequency
18.3.2. Support
18.3.3. Confidence
18.3.4. Lift
18.3.5. Market basket analysis and data mining
18.3.6. Critical note on the market basket analysis
19. Cronbach's Alpha
19.1. Latent variables
19.2. Assumptions for Cronbach's Alpha
19.3. Calculate Cronbach's Alpha
19.4. Example Cronbach's Alpha
19.5. Interpret Cronbach's Alpha
20. Cohen's Kappa
20.1. Cohen's Kappa Example
20.2. Inter-rater reliability
20.3. Use cases for Cohen's Kappa
20.4. Cohen's Kappa reliability and validity
20.5. Calculate Cohen's Kappa
20.6. Cohen's Kappa Interpretation
20.7. Cohen's Kappa Standard Error (SE)
20.8. Calculating Standard Error of Cohen's Kappa
20.9. Interpreting Standard Error
20.10. Calculate Cohen's Kappa with DATAtab
21. Weighted Cohen's Kappa
21.1. Reliability and validity
21.2. Calculating weighted Cohen's Kappa
21.3. Calculate expected frequency
21.4. Calculate weighting matrix
21.5. Linear and quadratic weighting
21.6. Calculate weighted Kappa
21.7. Calculating Cohen's weighted kappa with DATAtab
22. Fleiss Kappa
22.1. Fleiss Kappa Example
22.2. Fleiss Kappa with repeated measurement
22.3. Fleiss Kappa reliability and validity
22.4. Calculate Fleiss Kappa
22.5. Fleiss Kappa interpretation
22.6. Calculate Fleiss Kappa with DATAtab
23. Survival time analysis
23.1. Basics of survival time analysis
23.2. Use cases for survival time analysis
23.3. Example of survival time analysis
23.4. Censored data
23.5. Methods of survival time analysis
23.6. Kaplan-Meier Curve
23.6.1. Survival rate
23.6.2. Interpreting the Kaplan-Meier curve
23.6.3. Calculating the Kaplan-Meier curve
23.6.4. Draw Kaplan Meier curve
23.6.5. Censored data
23.6.6. Comparing different groups
23.6.7. Kaplan-Meier curve assumptions
23.6.8. Create Kaplan Meier curve with DATAtab
23.7. Log Rank Test
23.7.1. Hypotheses in the Log Rank Test
23.7.2. Assumptions for the LOg Rank Test
23.7.3. Calculate Log Rank Test
23.7.4. Calculate Log Rank Test with DATAtab
23.8. Cox regression
23.8.1. Survival time analysis
23.8.2. Censoring
23.8.3. Cox Regression Example
13.8.4. Calculate Cox Regression with DATAtab
23.8.5. Interpretation of the Cox Regression
23.8.6. Assumptions of a Cox Regression
23.8.7. Calculate survival time analysis with DATAtab
References