1
Introduction to statistical analyses
, 2
Table of contents
1.1 Basics 8
Unit of analysis: 8
Population 8
Sample 8
Variable 8
continuous vs discrete variables 9
inferential statistics vs descriptive statistics 9
1.2 Descriptive: univariate statistics: 10
Measures of central tendency 10
- Mean 10
- Median 10
- Mode 10
Measures of variability 10
- Range 10
- Interquartile range 10
- Variance 11
- Standard Deviation 11
1.3 Descriptive: Bivariate statistics: 11
1. Independent variable 11
2. Dependent variable 11
1.4 Measuring relationships: 11
1. Pearson’s R – Pearson’s correlation coefficient (r) 11
1. Bivariate relationships crosstab 12
2.1 measures of variability 13
Measures of variability 13
Range 13
Interquartile range 13
(IQR) 13
Variance 14
Standard deviation 15
(SD) 15
Overview of Central Tendency and variability 17
2.2 Bivariate statistics 18
bivariate statistics 18
Covariance 18
(step 1 Pearson’s correlation coefficient) 18
Standard deviations x and y 20
, 3
(step 2 Pearson’s correlation coefficient) 20
Pearson’s R (final step for Pearson’s correlation coefficient) 20
3.1 Three preconditions to making causal claims 22
Confounding variables 22
Reverse causality 22
3.2 Assumptions in Pearson’s R 23
Three major assumptions underlying Pearson’s r 23
VIOLATION OF LINEARITY 23
VIOLATION OF HOMOSCEDASTICITY 23
VIOLATION OF NORMALITY 24
3.3 Crosstabs 25
3.4 Inferential statistics 26
3.5 Z Transformation 28
Example: Turning a Normal Distribution into a Standard Normal Distribution 29
3.6 Sampling and sampling means 33
Standard Error (SE), 33
4.1 formulating hypotheses 35
Null hypothesis H0 and alternative hypothesis H1 (step 1 of hypotheses testing) 35
4.2 significance tests 37
level of significance (alpha) (step 2 of hypotheses testing) 37
one sample z-test 37
One independent sample t test 40
Sample standard deviation approximation 40
One sample t test in SPSS 43
4.3 accept or reject the null Hypothesis 44
types of errors in significance testing 44
5.1 Confidence interval estimation 45
significance testing vs interval estimation 45
Interval estimation 45
confidence interval 45
Distribution of sample means 46
Confidence interval 46
confidence interval with z values 47
confidence interval with t value 50
5.2 Two independent samples T test 53
Comparing sample means of two different samples 53
Levene’s test for Equality of Variances 54
SPSS example two sample t test 55
5.3 Significance tests - Chi-square goodness-of-fit test 56
, 4
• These tests are called parametric tests 57
Chi-square goodness-of-fit test 57
The four steps of hypothesis testing 58
Chi-Square Goodness-of-fit-test - an example 59
6.1 Significance testing (Chi-square and ANOVA) 61
assumptions in significance testing 61
chi-square test-for-independence (SPSS) 61
analysis of variance 65
anova (f test) 65
7.1 Regression analysis 68
regression analysis 68
STEP 1 R SQUARED 70
STEP 2 ANOVA 70
STEP 3 COEFFICIENT 71
Multiple regression analysis 72
dichotomous variables 74
Interaction effects 74
Introduction to statistical analyses
, 2
Table of contents
1.1 Basics 8
Unit of analysis: 8
Population 8
Sample 8
Variable 8
continuous vs discrete variables 9
inferential statistics vs descriptive statistics 9
1.2 Descriptive: univariate statistics: 10
Measures of central tendency 10
- Mean 10
- Median 10
- Mode 10
Measures of variability 10
- Range 10
- Interquartile range 10
- Variance 11
- Standard Deviation 11
1.3 Descriptive: Bivariate statistics: 11
1. Independent variable 11
2. Dependent variable 11
1.4 Measuring relationships: 11
1. Pearson’s R – Pearson’s correlation coefficient (r) 11
1. Bivariate relationships crosstab 12
2.1 measures of variability 13
Measures of variability 13
Range 13
Interquartile range 13
(IQR) 13
Variance 14
Standard deviation 15
(SD) 15
Overview of Central Tendency and variability 17
2.2 Bivariate statistics 18
bivariate statistics 18
Covariance 18
(step 1 Pearson’s correlation coefficient) 18
Standard deviations x and y 20
, 3
(step 2 Pearson’s correlation coefficient) 20
Pearson’s R (final step for Pearson’s correlation coefficient) 20
3.1 Three preconditions to making causal claims 22
Confounding variables 22
Reverse causality 22
3.2 Assumptions in Pearson’s R 23
Three major assumptions underlying Pearson’s r 23
VIOLATION OF LINEARITY 23
VIOLATION OF HOMOSCEDASTICITY 23
VIOLATION OF NORMALITY 24
3.3 Crosstabs 25
3.4 Inferential statistics 26
3.5 Z Transformation 28
Example: Turning a Normal Distribution into a Standard Normal Distribution 29
3.6 Sampling and sampling means 33
Standard Error (SE), 33
4.1 formulating hypotheses 35
Null hypothesis H0 and alternative hypothesis H1 (step 1 of hypotheses testing) 35
4.2 significance tests 37
level of significance (alpha) (step 2 of hypotheses testing) 37
one sample z-test 37
One independent sample t test 40
Sample standard deviation approximation 40
One sample t test in SPSS 43
4.3 accept or reject the null Hypothesis 44
types of errors in significance testing 44
5.1 Confidence interval estimation 45
significance testing vs interval estimation 45
Interval estimation 45
confidence interval 45
Distribution of sample means 46
Confidence interval 46
confidence interval with z values 47
confidence interval with t value 50
5.2 Two independent samples T test 53
Comparing sample means of two different samples 53
Levene’s test for Equality of Variances 54
SPSS example two sample t test 55
5.3 Significance tests - Chi-square goodness-of-fit test 56
, 4
• These tests are called parametric tests 57
Chi-square goodness-of-fit test 57
The four steps of hypothesis testing 58
Chi-Square Goodness-of-fit-test - an example 59
6.1 Significance testing (Chi-square and ANOVA) 61
assumptions in significance testing 61
chi-square test-for-independence (SPSS) 61
analysis of variance 65
anova (f test) 65
7.1 Regression analysis 68
regression analysis 68
STEP 1 R SQUARED 70
STEP 2 ANOVA 70
STEP 3 COEFFICIENT 71
Multiple regression analysis 72
dichotomous variables 74
Interaction effects 74
