Statistics 1
Lecture 1
Measurement levels
A qualitative variable places each case into one of several groups (or categories)
o Label: no rank order, an identifier for each case
Participant/case number, name
o Nominal: no rank order
Hair colour, eye colour, bachelor programme
o Ordinal: rank order, distance between values is not the same
Socio economics status, 2nd person to enter lecture hall
A quantitative variable takes numerical values for which arithmetic operations, such
as adding and averaging make sense
o Interval: arbitrary zero, distance between values is the same, adding and
subtracting make sense
temperature
o Ratio: non-arbitrary zero, multiplication and division make sense
Weight, length, age
Rare in social sciences
Looking at data
Qualitative variables
o Graphical representations for categorical variables (nominal or ordinal)
Pie chart
Bar chart
Quantitative variables
o Graphical representations for qualitative variables
Stem and leaf plot
Histogram
Describing distributions with numbers
We can use a number to describe the “typical” score within a set of cases
Measures of central tendency
o Mean: add up all values and divide by the number of cases
o Median: the value in the middle (when values are sorted low to high)
o Mode: the value that occurs most frequently
Quartiles
o First quartile: value in the middle between the minimum and q2
o Median (q2): value un the middle
o Third quartile: value in the middle between q2 and the maximum
Five number summary
o Minimum, q3, median (q2), q3, maximum
o Accompanied by a box plot
, Distributions
Median
Mean
Variance
2
o s2= Σ(xi−x ̅ )
n−1
Standard deviation
√
2
o σ = Σ ( xi−μ )
N
Normal distributions
o Symmetric, single peaked, bell-shaped
Standard normal distributions
o μ=0
o σ =1
o N (0 ; 1)
o To standardize a value, we use Z-scores
x−μ
z=
σ
o 68, 95, 99.7 rule
Lecture 1
Measurement levels
A qualitative variable places each case into one of several groups (or categories)
o Label: no rank order, an identifier for each case
Participant/case number, name
o Nominal: no rank order
Hair colour, eye colour, bachelor programme
o Ordinal: rank order, distance between values is not the same
Socio economics status, 2nd person to enter lecture hall
A quantitative variable takes numerical values for which arithmetic operations, such
as adding and averaging make sense
o Interval: arbitrary zero, distance between values is the same, adding and
subtracting make sense
temperature
o Ratio: non-arbitrary zero, multiplication and division make sense
Weight, length, age
Rare in social sciences
Looking at data
Qualitative variables
o Graphical representations for categorical variables (nominal or ordinal)
Pie chart
Bar chart
Quantitative variables
o Graphical representations for qualitative variables
Stem and leaf plot
Histogram
Describing distributions with numbers
We can use a number to describe the “typical” score within a set of cases
Measures of central tendency
o Mean: add up all values and divide by the number of cases
o Median: the value in the middle (when values are sorted low to high)
o Mode: the value that occurs most frequently
Quartiles
o First quartile: value in the middle between the minimum and q2
o Median (q2): value un the middle
o Third quartile: value in the middle between q2 and the maximum
Five number summary
o Minimum, q3, median (q2), q3, maximum
o Accompanied by a box plot
, Distributions
Median
Mean
Variance
2
o s2= Σ(xi−x ̅ )
n−1
Standard deviation
√
2
o σ = Σ ( xi−μ )
N
Normal distributions
o Symmetric, single peaked, bell-shaped
Standard normal distributions
o μ=0
o σ =1
o N (0 ; 1)
o To standardize a value, we use Z-scores
x−μ
z=
σ
o 68, 95, 99.7 rule
