Statistics: Descriptive Statistics and Data
Visualisation
Video 1: Exploring data
Introduction
Population is the people you are interested in in your study, however, you
can’t interview all of them thus you have to select a sample.
Population: Set of units that we are interested in studying
Sample: Subset unit of population
What you want to see is if there is a significant difference and whether it’s
based on the population or chance.
Types of variables
Dependent and independent variables
Variables: things that can change between people, time and products.
Independent variable (IV): a variable that influences another variable
Dependent variable (DV) a variable that is influenced by another variable
Measurement levels: Nominal, Ordinal and Scale
Nominal variables (categorical): non-ordered categories gender
Ordinal variable (categorical): categories with a ranking high school,
BSc, MSc (the order makes sense, but not the difference between the
numbers)
Scale (aka metric) variables (continuous): measured on a numerical scale
age, income. The are several scales: Likert scale, semantic differential.
Measurement levels are important because you can perform different
types of analyses depending on the measurement level.
Representing Variables: Graphs
Pie chart: presentation of categorical variables (nominal or ordinal)
Bar chart: presentation of categorical variables (preferred for ordinal)
Histogram: presentation of scale variables
There are common errors you can make:
- Wrong type of graph
- Missing text
- Inconsistent scales
- Misplaced (or missing) zero point
, - Poor chart effects (no 3D)
Hypothesis testing
H0 and Ha
H0: there is no effect or difference
Ha: there is an effect or difference Research question
SPSS calculates the probability p (often indicated in SPSS as Sig.) that the
null hypothesis H0 is true.
Types of errors
Type 1 error: your H0 is zero (no
effect) while your study shows that
there is an effect
Type 2 error: your H0 is non zero
(yes effect) while your study shows
that there is no effect
2 sided vs 1 sided tests
Hypothesis has no direction 2 sided test.
Hypothesis has a direction 1 sided test.
Steps for statistical testing
1. Formulate a research question
2. Formulate H0
3. Choose an appropriate statistical analysis
4. Perform analysis using SPSS
5. Compare significance level with alfa
6. Draw conclusions
Descriptive statistics
Frequency
Mean is only one value to summarize data. There is no information about
the spread or dispersion.
Measures for central tendency (Mean, Median and Mode)
Mode: the most frequently occurring set in a set of data
Median: the middle score of a set of ordered observation
Mean:
, Measures for Dispersion (Sum of square, Variance, Standard deviation)
Sum of Squares = SS This one only works for scale (metric) variables.
Normal distribution
Most scale variables follow the normal
distribution. Important assumption for
many statistical tests.
Testing methods for normal
distribution
You want to check the normality of the test.
Outliers
Why detecting them?
An outlier is an observation that strongly deviates from the other
observations.
They are important to detect because:
- Potential error in dataset
- May influence the result, e.g. mean
Methods to detect outliers: z-scores and boxplot
z-score: number of standard deviations that the
original score deviates from the mean.
For z-scores: Mean = 0 and std. dev. =1.
Testing method 2: boxplot.
1. Check score
2. “Throw him out”
3. Replace the data point by mean
Visualisation
Video 1: Exploring data
Introduction
Population is the people you are interested in in your study, however, you
can’t interview all of them thus you have to select a sample.
Population: Set of units that we are interested in studying
Sample: Subset unit of population
What you want to see is if there is a significant difference and whether it’s
based on the population or chance.
Types of variables
Dependent and independent variables
Variables: things that can change between people, time and products.
Independent variable (IV): a variable that influences another variable
Dependent variable (DV) a variable that is influenced by another variable
Measurement levels: Nominal, Ordinal and Scale
Nominal variables (categorical): non-ordered categories gender
Ordinal variable (categorical): categories with a ranking high school,
BSc, MSc (the order makes sense, but not the difference between the
numbers)
Scale (aka metric) variables (continuous): measured on a numerical scale
age, income. The are several scales: Likert scale, semantic differential.
Measurement levels are important because you can perform different
types of analyses depending on the measurement level.
Representing Variables: Graphs
Pie chart: presentation of categorical variables (nominal or ordinal)
Bar chart: presentation of categorical variables (preferred for ordinal)
Histogram: presentation of scale variables
There are common errors you can make:
- Wrong type of graph
- Missing text
- Inconsistent scales
- Misplaced (or missing) zero point
, - Poor chart effects (no 3D)
Hypothesis testing
H0 and Ha
H0: there is no effect or difference
Ha: there is an effect or difference Research question
SPSS calculates the probability p (often indicated in SPSS as Sig.) that the
null hypothesis H0 is true.
Types of errors
Type 1 error: your H0 is zero (no
effect) while your study shows that
there is an effect
Type 2 error: your H0 is non zero
(yes effect) while your study shows
that there is no effect
2 sided vs 1 sided tests
Hypothesis has no direction 2 sided test.
Hypothesis has a direction 1 sided test.
Steps for statistical testing
1. Formulate a research question
2. Formulate H0
3. Choose an appropriate statistical analysis
4. Perform analysis using SPSS
5. Compare significance level with alfa
6. Draw conclusions
Descriptive statistics
Frequency
Mean is only one value to summarize data. There is no information about
the spread or dispersion.
Measures for central tendency (Mean, Median and Mode)
Mode: the most frequently occurring set in a set of data
Median: the middle score of a set of ordered observation
Mean:
, Measures for Dispersion (Sum of square, Variance, Standard deviation)
Sum of Squares = SS This one only works for scale (metric) variables.
Normal distribution
Most scale variables follow the normal
distribution. Important assumption for
many statistical tests.
Testing methods for normal
distribution
You want to check the normality of the test.
Outliers
Why detecting them?
An outlier is an observation that strongly deviates from the other
observations.
They are important to detect because:
- Potential error in dataset
- May influence the result, e.g. mean
Methods to detect outliers: z-scores and boxplot
z-score: number of standard deviations that the
original score deviates from the mean.
For z-scores: Mean = 0 and std. dev. =1.
Testing method 2: boxplot.
1. Check score
2. “Throw him out”
3. Replace the data point by mean
