Which statistical tests to choose?
Inhoudsopgave
Choosing a statistical test? ............................................................................................................................... 6
Variable types .................................................................................................................................................. 6
Numeric or metric variables ............................................................................................................................... 6
Categorical variables .......................................................................................................................................... 6
Hypothesis ....................................................................................................................................................... 8
Types of hypothesis ............................................................................................................................................ 8
Alternative hypothesis ................................................................................................................................... 8
Null hypothesis .............................................................................................................................................. 8
Research methods .......................................................................................................................................... 10
Correlational research methods ....................................................................................................................... 10
Experimental research method ........................................................................................................................ 10
Measurement error: ......................................................................................................................................... 10
Validity and reliability .................................................................................................................................. 10
Objectivity.................................................................................................................................................... 11
Actuality ....................................................................................................................................................... 11
Data collection.................................................................................................................................................. 11
Variation ........................................................................................................................................................... 12
Randomization ................................................................................................................................................. 12
Analyzing data ................................................................................................................................................ 13
Frequency distributions or histogram ............................................................................................................... 13
Normal distribution ..................................................................................................................................... 13
The center of a distribution ......................................................................................................................... 14
The dispersion in a distribution ................................................................................................................... 16
Using a frequency distribution to go beyond the data ................................................................................ 18
Probability density functions (PDF .......................................................................................................... 18
The normal probability distribution ........................................................................................................ 19
Z-scores ................................................................................................................................................... 20
Statistical models ........................................................................................................................................... 21
Statistical models ............................................................................................................................................. 21
Populations and samples ............................................................................................................................. 21
SPINE ................................................................................................................................................................ 21
S is for standard error .................................................................................................................................. 21
Mean ....................................................................................................................................................... 22
Sampling variation .................................................................................................................................. 22
Sampling distribution .............................................................................................................................. 22
Standard error of the mean (SE)/ Standard Error ................................................................................... 22
Central limit theorem ............................................................................................................................. 22
P is for parameters ...................................................................................................................................... 22
Symbols parameters ............................................................................................................................... 23
1
, The mean as a statistical model .............................................................................................................. 23
Assessing the fit of a model .................................................................................................................... 24
I is for interval .............................................................................................................................................. 25
N is for null hypothesis significance testing................................................................................................. 26
Test statistics .......................................................................................................................................... 27
Type I and Type II errors ......................................................................................................................... 28
Sample size and statistical significance ................................................................................................... 28
E is for estimating parameters..................................................................................................................... 28
Bias and outliers ............................................................................................................................................. 29
Bias ................................................................................................................................................................... 29
Reducing Bias ............................................................................................................................................... 29
Outliers ............................................................................................................................................................. 32
Spotting outliers in SPSS .............................................................................................................................. 32
Overview of assumptions ............................................................................................................................... 34
Violations of assumptions ................................................................................................................................ 34
Additivity and linearity: ............................................................................................................................... 34
Spotting linearity and heteroscedasticity/ heterogeneity of variance ................................................... 34
Normally distributed something or other: .................................................................................................. 35
Spotting normality .................................................................................................................................. 36
Homoscedasticity/ homogeneity of variance .............................................................................................. 40
Spotting homogeneity of variances/ homoscedasticity ......................................................................... 40
Independence .............................................................................................................................................. 41
SPSS: basic functions ...................................................................................................................................... 43
Getting started ................................................................................................................................................. 43
The data editor ............................................................................................................................................ 43
Other windows ................................................................................................................................................. 43
Menu options ................................................................................................................................................... 43
Data view ..................................................................................................................................................... 44
Transform .................................................................................................................................................... 44
Split file ................................................................................................................................................... 44
Select cases ............................................................................................................................................. 45
Compute variable.................................................................................................................................... 45
Recode .................................................................................................................................................... 46
Analyze ........................................................................................................................................................ 46
Chart builder ................................................................................................................................................ 46
Graphs ........................................................................................................................................................... 47
Graphs in SPSS .................................................................................................................................................. 52
Histogram in SPSS ........................................................................................................................................ 52
Boxplot in SPSS ............................................................................................................................................ 53
Bar chart in SPSS .......................................................................................................................................... 53
Line chart in SPSS ......................................................................................................................................... 55
Scatterplot in SPSS ....................................................................................................................................... 55
Which statistical test to choose? .................................................................................................................... 56
Statistical tests ............................................................................................................................................... 59
1 Descriptive statistics ...................................................................................................................................... 59
Descriptive statistics .................................................................................................................................... 59
Descriptive statistics in SPSS ................................................................................................................... 59
2
, Frequencies ................................................................................................................................................. 59
Frequencies in SPSS ................................................................................................................................ 59
2 Correlation analysis (relationship between variables/ predicting variables) ................................................ 61
Correlation ................................................................................................................................................... 61
Associations ................................................................................................................................................. 61
Covariance ................................................................................................................................................... 62
The correlation coefficient .......................................................................................................................... 63
Types of correlation ................................................................................................................................ 65
Assumptions in correlation ..................................................................................................................... 66
Correlation analysis in SPSS= .................................................................................................................. 67
Interpreting output correlation analysis ................................................................................................. 68
Reporting correlation analysis ................................................................................................................ 68
3 Regression analysis (relationship between variables/ predicting variables) ................................................. 70
Regression analysis ...................................................................................................................................... 70
Linear model ................................................................................................................................................ 70
Bias in linear models ............................................................................................................................... 73
Assumptions of the linear model ............................................................................................................ 75
Simple (linear) regression ............................................................................................................................ 79
Simple (linear) regression in SPSS ........................................................................................................... 79
Interpreting output simple (linear) regression ....................................................................................... 80
Reporting simple (linear) regression ....................................................................................................... 81
Multiple (linear) regression ......................................................................................................................... 82
Multiple (linear) regression in SPSS ........................................................................................................ 83
Interpreting output multiple (linear) regression .................................................................................... 85
Reporting multiple (linear) regression .................................................................................................... 88
Logistic regression ....................................................................................................................................... 89
The Wald statistic ................................................................................................................................... 93
The odds ratio ......................................................................................................................................... 93
Assumptions of logistic regression ......................................................................................................... 94
Building a model ..................................................................................................................................... 96
Logistic regression in SPSS ...................................................................................................................... 96
Interpreting output logistic regression ................................................................................................... 99
Reporting logistic regression ................................................................................................................ 102
Binary logistic regression ........................................................................................................................... 103
Multinomial logit ....................................................................................................................................... 103
Conditional logit ........................................................................................................................................ 103
Chi-square test........................................................................................................................................... 104
Assumptions of Chi-square test ............................................................................................................ 107
Other measures of associations ............................................................................................................ 108
Chi-square test in SPSS ......................................................................................................................... 109
Interpreting output chi-square ............................................................................................................. 110
Reporting chi-square ............................................................................................................................ 114
Log-linear regression ................................................................................................................................. 115
Assumptions of log-linear analysis........................................................................................................ 115
Loglinear regression in SPSS ................................................................................................................. 116
Interpreting loglinear regression in SPSS .............................................................................................. 116
4 T-test............................................................................................................................................................ 117
T-test.......................................................................................................................................................... 117
Assumptions of the t-test ..................................................................................................................... 119
Independent t-test..................................................................................................................................... 121
Independent t-test in SPSS ................................................................................................................... 123
Interpreting output independent t-test ................................................................................................ 124
Reporting independent t-test ............................................................................................................... 125
Paired-sample t-test .................................................................................................................................. 126
Paired-sample t-test in SPSS ................................................................................................................. 127
3
, Interpreting output paired-sample t-test ............................................................................................. 128
Reporting paired-sample t-test............................................................................................................. 129
5 AN(C)OVA .................................................................................................................................................... 130
ANOVA ....................................................................................................................................................... 130
Two-way ANOVA ....................................................................................................................................... 130
Assumptions of ANOVA ........................................................................................................................ 136
Planned contrast ................................................................................................................................... 137
Post-hoc tests ....................................................................................................................................... 140
ANOVA in SPSS ...................................................................................................................................... 142
Interpreting output ANOVA .................................................................................................................. 144
Reporting ANOVA ................................................................................................................................. 147
ANCOVA ..................................................................................................................................................... 147
Assumptions in ANCOVA=..................................................................................................................... 150
ANCOVA in SPSS .................................................................................................................................... 153
Interpreting output ANCOVA ................................................................................................................ 155
Reporting ANCOVA ............................................................................................................................... 157
Repeated-measures design or one-way Repeated-Measures ANOVA ...................................................... 158
Assumptions of repeated-measures design or repeated-measures ANOVA ........................................ 161
Repeated-measures design or repeated-measured ANOVA in SPSS .................................................... 164
Interpreting output repeated-measures design or repeated-measured ANOVA ................................. 166
Reporting repeated-measures design or repeated-measured ANOVA ................................................ 170
Factorial ANOVA ........................................................................................................................................ 171
Independent factorial design or Factorial ANOVA .................................................................................... 171
Assumptions in independent factorial designs or factorial ANOVA ..................................................... 177
Independent factorial design or Factorial ANOVA in SPSS ................................................................... 177
Interpreting output independent factorial design or factorial ANOVA ................................................ 178
Reporting independent factorial design or factorial ANOVA ................................................................ 183
Repeated-measures factorial design or Repeated-measures factorial ANOVA ........................................ 185
Assumptions in factorial repeated-measures design or factorial repeated-measures ANOVA............ 185
Factorial repeated-measures design or factorial repeated-measures ANOVA in SPSS ........................ 188
Interpreting output factorial repeated-measures designs or factorial repeated-measures ANOVA ... 190
Reporting the results from factorial repeated-measures designs ........................................................ 194
Mixed design ............................................................................................................................................. 195
- Where you have measured a dependent variable (e.g. back pain or salary) over two or more points or
when all subjects have undergone two or more conditions (time and conditions are the within-subject
factors) but also when your subject have been assigned into two or more separate groups. ....................... 195
- Mixed-model ANOVA= tests whether each of the three effects – the two main effects and the
interaction effect – is statistically significant. ................................................................................................ 195
- Mix of independent factorial design and repeated-measured factorial design. ................................... 195
6 Factor analysis ............................................................................................................................................. 196
Factor analysis ........................................................................................................................................... 196
Exploratory factor analysis= purpose is to reduce many individual items into fewer number of dimensions.
........................................................................................................................................................................ 196
- When you need to develop a hypothesis about the relationship between variables, but you do not know
what the exact variables or sub-variables are or reducing the number of variables in regression models. .. 196
Confirmatory factor analysis= used to test a hypothesis about the relationship between variables............ 196
- Allows the researcher to test the hypothesis that a relationship between observed variables and their
underlying latent constructs exist. ................................................................................................................. 196
- If you carry out the confirmatory facto analysis but the goodness of fit is low, then the exploratory
factor analysis also needs to be performed. ................................................................................................... 196
Steps involved in factor analysis ........................................................................................................... 199
Overview of the process in Factor analysis........................................................................................... 203
4
Inhoudsopgave
Choosing a statistical test? ............................................................................................................................... 6
Variable types .................................................................................................................................................. 6
Numeric or metric variables ............................................................................................................................... 6
Categorical variables .......................................................................................................................................... 6
Hypothesis ....................................................................................................................................................... 8
Types of hypothesis ............................................................................................................................................ 8
Alternative hypothesis ................................................................................................................................... 8
Null hypothesis .............................................................................................................................................. 8
Research methods .......................................................................................................................................... 10
Correlational research methods ....................................................................................................................... 10
Experimental research method ........................................................................................................................ 10
Measurement error: ......................................................................................................................................... 10
Validity and reliability .................................................................................................................................. 10
Objectivity.................................................................................................................................................... 11
Actuality ....................................................................................................................................................... 11
Data collection.................................................................................................................................................. 11
Variation ........................................................................................................................................................... 12
Randomization ................................................................................................................................................. 12
Analyzing data ................................................................................................................................................ 13
Frequency distributions or histogram ............................................................................................................... 13
Normal distribution ..................................................................................................................................... 13
The center of a distribution ......................................................................................................................... 14
The dispersion in a distribution ................................................................................................................... 16
Using a frequency distribution to go beyond the data ................................................................................ 18
Probability density functions (PDF .......................................................................................................... 18
The normal probability distribution ........................................................................................................ 19
Z-scores ................................................................................................................................................... 20
Statistical models ........................................................................................................................................... 21
Statistical models ............................................................................................................................................. 21
Populations and samples ............................................................................................................................. 21
SPINE ................................................................................................................................................................ 21
S is for standard error .................................................................................................................................. 21
Mean ....................................................................................................................................................... 22
Sampling variation .................................................................................................................................. 22
Sampling distribution .............................................................................................................................. 22
Standard error of the mean (SE)/ Standard Error ................................................................................... 22
Central limit theorem ............................................................................................................................. 22
P is for parameters ...................................................................................................................................... 22
Symbols parameters ............................................................................................................................... 23
1
, The mean as a statistical model .............................................................................................................. 23
Assessing the fit of a model .................................................................................................................... 24
I is for interval .............................................................................................................................................. 25
N is for null hypothesis significance testing................................................................................................. 26
Test statistics .......................................................................................................................................... 27
Type I and Type II errors ......................................................................................................................... 28
Sample size and statistical significance ................................................................................................... 28
E is for estimating parameters..................................................................................................................... 28
Bias and outliers ............................................................................................................................................. 29
Bias ................................................................................................................................................................... 29
Reducing Bias ............................................................................................................................................... 29
Outliers ............................................................................................................................................................. 32
Spotting outliers in SPSS .............................................................................................................................. 32
Overview of assumptions ............................................................................................................................... 34
Violations of assumptions ................................................................................................................................ 34
Additivity and linearity: ............................................................................................................................... 34
Spotting linearity and heteroscedasticity/ heterogeneity of variance ................................................... 34
Normally distributed something or other: .................................................................................................. 35
Spotting normality .................................................................................................................................. 36
Homoscedasticity/ homogeneity of variance .............................................................................................. 40
Spotting homogeneity of variances/ homoscedasticity ......................................................................... 40
Independence .............................................................................................................................................. 41
SPSS: basic functions ...................................................................................................................................... 43
Getting started ................................................................................................................................................. 43
The data editor ............................................................................................................................................ 43
Other windows ................................................................................................................................................. 43
Menu options ................................................................................................................................................... 43
Data view ..................................................................................................................................................... 44
Transform .................................................................................................................................................... 44
Split file ................................................................................................................................................... 44
Select cases ............................................................................................................................................. 45
Compute variable.................................................................................................................................... 45
Recode .................................................................................................................................................... 46
Analyze ........................................................................................................................................................ 46
Chart builder ................................................................................................................................................ 46
Graphs ........................................................................................................................................................... 47
Graphs in SPSS .................................................................................................................................................. 52
Histogram in SPSS ........................................................................................................................................ 52
Boxplot in SPSS ............................................................................................................................................ 53
Bar chart in SPSS .......................................................................................................................................... 53
Line chart in SPSS ......................................................................................................................................... 55
Scatterplot in SPSS ....................................................................................................................................... 55
Which statistical test to choose? .................................................................................................................... 56
Statistical tests ............................................................................................................................................... 59
1 Descriptive statistics ...................................................................................................................................... 59
Descriptive statistics .................................................................................................................................... 59
Descriptive statistics in SPSS ................................................................................................................... 59
2
, Frequencies ................................................................................................................................................. 59
Frequencies in SPSS ................................................................................................................................ 59
2 Correlation analysis (relationship between variables/ predicting variables) ................................................ 61
Correlation ................................................................................................................................................... 61
Associations ................................................................................................................................................. 61
Covariance ................................................................................................................................................... 62
The correlation coefficient .......................................................................................................................... 63
Types of correlation ................................................................................................................................ 65
Assumptions in correlation ..................................................................................................................... 66
Correlation analysis in SPSS= .................................................................................................................. 67
Interpreting output correlation analysis ................................................................................................. 68
Reporting correlation analysis ................................................................................................................ 68
3 Regression analysis (relationship between variables/ predicting variables) ................................................. 70
Regression analysis ...................................................................................................................................... 70
Linear model ................................................................................................................................................ 70
Bias in linear models ............................................................................................................................... 73
Assumptions of the linear model ............................................................................................................ 75
Simple (linear) regression ............................................................................................................................ 79
Simple (linear) regression in SPSS ........................................................................................................... 79
Interpreting output simple (linear) regression ....................................................................................... 80
Reporting simple (linear) regression ....................................................................................................... 81
Multiple (linear) regression ......................................................................................................................... 82
Multiple (linear) regression in SPSS ........................................................................................................ 83
Interpreting output multiple (linear) regression .................................................................................... 85
Reporting multiple (linear) regression .................................................................................................... 88
Logistic regression ....................................................................................................................................... 89
The Wald statistic ................................................................................................................................... 93
The odds ratio ......................................................................................................................................... 93
Assumptions of logistic regression ......................................................................................................... 94
Building a model ..................................................................................................................................... 96
Logistic regression in SPSS ...................................................................................................................... 96
Interpreting output logistic regression ................................................................................................... 99
Reporting logistic regression ................................................................................................................ 102
Binary logistic regression ........................................................................................................................... 103
Multinomial logit ....................................................................................................................................... 103
Conditional logit ........................................................................................................................................ 103
Chi-square test........................................................................................................................................... 104
Assumptions of Chi-square test ............................................................................................................ 107
Other measures of associations ............................................................................................................ 108
Chi-square test in SPSS ......................................................................................................................... 109
Interpreting output chi-square ............................................................................................................. 110
Reporting chi-square ............................................................................................................................ 114
Log-linear regression ................................................................................................................................. 115
Assumptions of log-linear analysis........................................................................................................ 115
Loglinear regression in SPSS ................................................................................................................. 116
Interpreting loglinear regression in SPSS .............................................................................................. 116
4 T-test............................................................................................................................................................ 117
T-test.......................................................................................................................................................... 117
Assumptions of the t-test ..................................................................................................................... 119
Independent t-test..................................................................................................................................... 121
Independent t-test in SPSS ................................................................................................................... 123
Interpreting output independent t-test ................................................................................................ 124
Reporting independent t-test ............................................................................................................... 125
Paired-sample t-test .................................................................................................................................. 126
Paired-sample t-test in SPSS ................................................................................................................. 127
3
, Interpreting output paired-sample t-test ............................................................................................. 128
Reporting paired-sample t-test............................................................................................................. 129
5 AN(C)OVA .................................................................................................................................................... 130
ANOVA ....................................................................................................................................................... 130
Two-way ANOVA ....................................................................................................................................... 130
Assumptions of ANOVA ........................................................................................................................ 136
Planned contrast ................................................................................................................................... 137
Post-hoc tests ....................................................................................................................................... 140
ANOVA in SPSS ...................................................................................................................................... 142
Interpreting output ANOVA .................................................................................................................. 144
Reporting ANOVA ................................................................................................................................. 147
ANCOVA ..................................................................................................................................................... 147
Assumptions in ANCOVA=..................................................................................................................... 150
ANCOVA in SPSS .................................................................................................................................... 153
Interpreting output ANCOVA ................................................................................................................ 155
Reporting ANCOVA ............................................................................................................................... 157
Repeated-measures design or one-way Repeated-Measures ANOVA ...................................................... 158
Assumptions of repeated-measures design or repeated-measures ANOVA ........................................ 161
Repeated-measures design or repeated-measured ANOVA in SPSS .................................................... 164
Interpreting output repeated-measures design or repeated-measured ANOVA ................................. 166
Reporting repeated-measures design or repeated-measured ANOVA ................................................ 170
Factorial ANOVA ........................................................................................................................................ 171
Independent factorial design or Factorial ANOVA .................................................................................... 171
Assumptions in independent factorial designs or factorial ANOVA ..................................................... 177
Independent factorial design or Factorial ANOVA in SPSS ................................................................... 177
Interpreting output independent factorial design or factorial ANOVA ................................................ 178
Reporting independent factorial design or factorial ANOVA ................................................................ 183
Repeated-measures factorial design or Repeated-measures factorial ANOVA ........................................ 185
Assumptions in factorial repeated-measures design or factorial repeated-measures ANOVA............ 185
Factorial repeated-measures design or factorial repeated-measures ANOVA in SPSS ........................ 188
Interpreting output factorial repeated-measures designs or factorial repeated-measures ANOVA ... 190
Reporting the results from factorial repeated-measures designs ........................................................ 194
Mixed design ............................................................................................................................................. 195
- Where you have measured a dependent variable (e.g. back pain or salary) over two or more points or
when all subjects have undergone two or more conditions (time and conditions are the within-subject
factors) but also when your subject have been assigned into two or more separate groups. ....................... 195
- Mixed-model ANOVA= tests whether each of the three effects – the two main effects and the
interaction effect – is statistically significant. ................................................................................................ 195
- Mix of independent factorial design and repeated-measured factorial design. ................................... 195
6 Factor analysis ............................................................................................................................................. 196
Factor analysis ........................................................................................................................................... 196
Exploratory factor analysis= purpose is to reduce many individual items into fewer number of dimensions.
........................................................................................................................................................................ 196
- When you need to develop a hypothesis about the relationship between variables, but you do not know
what the exact variables or sub-variables are or reducing the number of variables in regression models. .. 196
Confirmatory factor analysis= used to test a hypothesis about the relationship between variables............ 196
- Allows the researcher to test the hypothesis that a relationship between observed variables and their
underlying latent constructs exist. ................................................................................................................. 196
- If you carry out the confirmatory facto analysis but the goodness of fit is low, then the exploratory
factor analysis also needs to be performed. ................................................................................................... 196
Steps involved in factor analysis ........................................................................................................... 199
Overview of the process in Factor analysis........................................................................................... 203
4
