Overview Statistics Course - Fall 2020
Table of content
Levels of variables........................................................................................................................................... 3
Recoding and Computing variables ................................................................................................................. 3
Graphs ............................................................................................................................................................ 3
Histogram and PP/QQ plots ............................................................................................................................... 3
Boxplot................................................................................................................................................................ 4
Bar chart ............................................................................................................................................................. 4
Scatterplot .......................................................................................................................................................... 4
Exploring data................................................................................................................................................. 4
Normality testing ................................................................................................................................................ 4
Homogeneity (Variance Ratio) ........................................................................................................................... 4
Outliers ............................................................................................................................................................... 5
Cronbach’s alpha ................................................................................................................................................ 5
Kind of tests.................................................................................................................................................... 5
Testing the effect on a variable .......................................................................................................................... 5
Testing the association between variables ......................................................................................................... 5
T-Test ............................................................................................................................................................. 6
Independent-Samples T-Test .............................................................................................................................. 6
1. Explore data ......................................................................................................................................... 6
2. Run the t-test ....................................................................................................................................... 6
3. Calculate effect size .............................................................................................................................. 6
4. Reporting the outcomes....................................................................................................................... 6
Paired-Samples T-Test (dependent) .................................................................................................................... 6
1. Explore data ......................................................................................................................................... 7
2. Run the t-test ....................................................................................................................................... 7
3. Calculate effect size .............................................................................................................................. 7
4. Report the outcomes ........................................................................................................................... 7
One-Sample T-Test.............................................................................................................................................. 7
1. Run the t-test ....................................................................................................................................... 7
2. Calculate effect size .............................................................................................................................. 8
3. Report the outcomes ........................................................................................................................... 8
Calculate the effect size ...................................................................................................................................... 8
One-Sample T-test ......................................................................................................................................... 8
Independent- and Paired-Samples T-test ...................................................................................................... 8
Outcomes effect size ..................................................................................................................................... 8
Reporting the outcomes of a t-test ..................................................................................................................... 8
, 2
ANOVA ........................................................................................................................................................... 9
One-way ANOVA................................................................................................................................................. 9
1. Prepare data ....................................................................................................................................... 10
2. Explore data ....................................................................................................................................... 10
3. Run the test ........................................................................................................................................ 10
4. Follow-up tests ................................................................................................................................... 10
5. Calculate effect size ............................................................................................................................ 10
6. Report the outcomes ......................................................................................................................... 11
Factorial ANOVA ............................................................................................................................................... 12
1. Prepare data ....................................................................................................................................... 12
2. Explore data ....................................................................................................................................... 12
3. Run the test ........................................................................................................................................ 13
4. Understanding the test outcomes...................................................................................................... 13
5. Follow-up analysis .............................................................................................................................. 13
6. Calculate effect size ............................................................................................................................ 16
7. Report the outcomes ......................................................................................................................... 17
8. Splitting and merging independent variables .................................................................................... 17
Chi-Square Test ............................................................................................................................................. 20
Chi-Square test of Association .......................................................................................................................... 20
Chi-Square test of Association in SPSS ......................................................................................................... 21
Calculate effect size ..................................................................................................................................... 21
Reporting Chi-Square test of Association .................................................................................................... 22
Chi-Square Goodness-of-fit ............................................................................................................................... 22
Chi-Square Goodness-of-fit in SPSS ............................................................................................................. 22
Reporting Chi-Square Goodness-of-fit ......................................................................................................... 22
Correlation Coefficient .................................................................................................................................. 23
Outcome correlation coefficient ....................................................................................................................... 23
Positive correlation ...................................................................................................................................... 23
Negative correlation .................................................................................................................................... 23
Zero correlation ........................................................................................................................................... 23
Strength of the correlation .......................................................................................................................... 23
Correlation in SPSS ............................................................................................................................................ 24
1. Explore data ....................................................................................................................................... 24
2. Run the test ........................................................................................................................................ 24
3. Visualizing correlation ........................................................................................................................ 24
4. Effect size ........................................................................................................................................... 25
5. Report the outcome ........................................................................................................................... 25
Partial correlation ............................................................................................................................................. 25
1. Run the test ........................................................................................................................................ 25
Simple Linear Regression .............................................................................................................................. 26
Regression analysis in SPSS............................................................................................................................... 27
1. Assumptions ....................................................................................................................................... 28
2. Running the regression analysis ......................................................................................................... 30
3. Reporting the outcome ...................................................................................................................... 30
, 3
Levels of variables
Categorial variable: it is a variable of one kind, so either human or animal for example.
Continuous variable: one that can give scores for each person and can take on any value of
measurement scale that is used.
Nominal: scales are used for labeling variables, without any quantitative data.
Ordinal: the order of the values is what’s important and significant, but the differences
between each other are not really known. ‘On a scale of 1 to 10’, we know what is better but
not how much.
Interval: numeric scales in which we know the order and the exact differences between the
values, however, there is no absolute zero.
Ratio: they tell us about the order, the exact value between units and they also have an
absolute zero. We can also calculate with it.
Recoding and Computing variables
Recoding to different variables is used when the meaning of the value labels for related
variables are not the same. E.g. within a survey, different questions about happiness are asked
but some in a negative way and some in a positive way but on the same kind of scale. In this
case, the positive OR negative variables need to be recoded, so they have the same meaning
on the scale.
Computing a new variable is used when for example a MEAN score has to be calculated for
multiple existing variables. E.g. a MEAN_Happiness can be created by adding up all the
different variables (after recoding them!) so there is a mean for the happiness variables.
Steps: statistical – mean. Also, computing a new variable can be created to measure the
difference between happiness and sadness. Name: Diff_Happ_Sad and the formula would be
MEAN_Happiness-MEAN_Sadness.
Graphs
Histogram and PP/QQ plots
These are useful to explore how a continuous variable is distributed. You can explore the
skewness and kurtosis of the distribution, see whether it is normally distributed (normal
curve) and whether it has outliers. When you use plots to present the distribution, the data
should be on the line.
Table of content
Levels of variables........................................................................................................................................... 3
Recoding and Computing variables ................................................................................................................. 3
Graphs ............................................................................................................................................................ 3
Histogram and PP/QQ plots ............................................................................................................................... 3
Boxplot................................................................................................................................................................ 4
Bar chart ............................................................................................................................................................. 4
Scatterplot .......................................................................................................................................................... 4
Exploring data................................................................................................................................................. 4
Normality testing ................................................................................................................................................ 4
Homogeneity (Variance Ratio) ........................................................................................................................... 4
Outliers ............................................................................................................................................................... 5
Cronbach’s alpha ................................................................................................................................................ 5
Kind of tests.................................................................................................................................................... 5
Testing the effect on a variable .......................................................................................................................... 5
Testing the association between variables ......................................................................................................... 5
T-Test ............................................................................................................................................................. 6
Independent-Samples T-Test .............................................................................................................................. 6
1. Explore data ......................................................................................................................................... 6
2. Run the t-test ....................................................................................................................................... 6
3. Calculate effect size .............................................................................................................................. 6
4. Reporting the outcomes....................................................................................................................... 6
Paired-Samples T-Test (dependent) .................................................................................................................... 6
1. Explore data ......................................................................................................................................... 7
2. Run the t-test ....................................................................................................................................... 7
3. Calculate effect size .............................................................................................................................. 7
4. Report the outcomes ........................................................................................................................... 7
One-Sample T-Test.............................................................................................................................................. 7
1. Run the t-test ....................................................................................................................................... 7
2. Calculate effect size .............................................................................................................................. 8
3. Report the outcomes ........................................................................................................................... 8
Calculate the effect size ...................................................................................................................................... 8
One-Sample T-test ......................................................................................................................................... 8
Independent- and Paired-Samples T-test ...................................................................................................... 8
Outcomes effect size ..................................................................................................................................... 8
Reporting the outcomes of a t-test ..................................................................................................................... 8
, 2
ANOVA ........................................................................................................................................................... 9
One-way ANOVA................................................................................................................................................. 9
1. Prepare data ....................................................................................................................................... 10
2. Explore data ....................................................................................................................................... 10
3. Run the test ........................................................................................................................................ 10
4. Follow-up tests ................................................................................................................................... 10
5. Calculate effect size ............................................................................................................................ 10
6. Report the outcomes ......................................................................................................................... 11
Factorial ANOVA ............................................................................................................................................... 12
1. Prepare data ....................................................................................................................................... 12
2. Explore data ....................................................................................................................................... 12
3. Run the test ........................................................................................................................................ 13
4. Understanding the test outcomes...................................................................................................... 13
5. Follow-up analysis .............................................................................................................................. 13
6. Calculate effect size ............................................................................................................................ 16
7. Report the outcomes ......................................................................................................................... 17
8. Splitting and merging independent variables .................................................................................... 17
Chi-Square Test ............................................................................................................................................. 20
Chi-Square test of Association .......................................................................................................................... 20
Chi-Square test of Association in SPSS ......................................................................................................... 21
Calculate effect size ..................................................................................................................................... 21
Reporting Chi-Square test of Association .................................................................................................... 22
Chi-Square Goodness-of-fit ............................................................................................................................... 22
Chi-Square Goodness-of-fit in SPSS ............................................................................................................. 22
Reporting Chi-Square Goodness-of-fit ......................................................................................................... 22
Correlation Coefficient .................................................................................................................................. 23
Outcome correlation coefficient ....................................................................................................................... 23
Positive correlation ...................................................................................................................................... 23
Negative correlation .................................................................................................................................... 23
Zero correlation ........................................................................................................................................... 23
Strength of the correlation .......................................................................................................................... 23
Correlation in SPSS ............................................................................................................................................ 24
1. Explore data ....................................................................................................................................... 24
2. Run the test ........................................................................................................................................ 24
3. Visualizing correlation ........................................................................................................................ 24
4. Effect size ........................................................................................................................................... 25
5. Report the outcome ........................................................................................................................... 25
Partial correlation ............................................................................................................................................. 25
1. Run the test ........................................................................................................................................ 25
Simple Linear Regression .............................................................................................................................. 26
Regression analysis in SPSS............................................................................................................................... 27
1. Assumptions ....................................................................................................................................... 28
2. Running the regression analysis ......................................................................................................... 30
3. Reporting the outcome ...................................................................................................................... 30
, 3
Levels of variables
Categorial variable: it is a variable of one kind, so either human or animal for example.
Continuous variable: one that can give scores for each person and can take on any value of
measurement scale that is used.
Nominal: scales are used for labeling variables, without any quantitative data.
Ordinal: the order of the values is what’s important and significant, but the differences
between each other are not really known. ‘On a scale of 1 to 10’, we know what is better but
not how much.
Interval: numeric scales in which we know the order and the exact differences between the
values, however, there is no absolute zero.
Ratio: they tell us about the order, the exact value between units and they also have an
absolute zero. We can also calculate with it.
Recoding and Computing variables
Recoding to different variables is used when the meaning of the value labels for related
variables are not the same. E.g. within a survey, different questions about happiness are asked
but some in a negative way and some in a positive way but on the same kind of scale. In this
case, the positive OR negative variables need to be recoded, so they have the same meaning
on the scale.
Computing a new variable is used when for example a MEAN score has to be calculated for
multiple existing variables. E.g. a MEAN_Happiness can be created by adding up all the
different variables (after recoding them!) so there is a mean for the happiness variables.
Steps: statistical – mean. Also, computing a new variable can be created to measure the
difference between happiness and sadness. Name: Diff_Happ_Sad and the formula would be
MEAN_Happiness-MEAN_Sadness.
Graphs
Histogram and PP/QQ plots
These are useful to explore how a continuous variable is distributed. You can explore the
skewness and kurtosis of the distribution, see whether it is normally distributed (normal
curve) and whether it has outliers. When you use plots to present the distribution, the data
should be on the line.
