LECTURE NOTES QUANTITATIVE RESEARCH METHODOLOGY AND STATISTICS
WEEK 1
Lecture 1
Quantitative analysis of variables.
Variables must be able to vary – that is must be able to have different values or levels.
- E.g. Gender is a variable since that can be Male, Female.....
- Male is not a variable as that is only the Male level of variable Gender
- Examples of variables: Fruit, Medal colour, Exam grades, Amount of money.
Measurement levels can be..
Nominal: Mere labels for values, no order (sex) Kunt ze niet ranken.
In frequencies or in percentages.
Ordinal: Ordered values with unequal steps (position top 100, educational level). Ranken
In frequencies or in percentages
Interval: Ordered values with equal steps, no natural zero (degrees celsius) exam grades.
Infinitely many options, so infinite categories.
Ratio: ordered values with equal steps and a natural zero (Degrees Kelving, length in cm) Because
there is a natural zero you can compare the numbers.
Infinitely many options, so infinite categories.
- You can always interpret ratio and interval as nominal and interval, but not the other way around.
- For Ratio and interval you create summary measures for central tendency and width of distribution
instead.
Measures of central tendency
- How to best describe the typical or average income in this group?
- The most common (mode)?
- The middle person (median)? not sensitive for outliers
- The mean (aka arithmetical average)? Sensitive for outliers (Extremely high or low number)
Symmetric distribution : Mean + median (bijna) gelijk
Asymmetric distribution: Mean + median verschillen heel erg. → Bevat outliers
Measures of variability:
- Range= maximum – minimum
- Standard deviation = s = Wortel(variance)
Variance= S2 = (1/(n-1) * de som van (Yi – Y)
- Interquartile range (IQR)= Q3-Q1
Q1 = first quartile = 25th percentile = lower quartile
Q3 = third quartile = 75th percentile = upper quartile
Is not sensitive for outliers
Normal distribution:
- a probability density function.
- All central tendency measures the same
- total area under the curve =1
- probabilities → a certain area under the curve.
- symmetrical distribution
- bell-shaped; 1 top. Mote of the distribution, it’s in the middle.
- uni-modal; only one top
,The smaller de standard deviation, the more narrow and more pointed the normal distribution will
be.
Standard deviation (o)
Standard normal distribution
- mean = 0, Standard deviation = 1
,Thumb rule:
,
WEEK 1
Lecture 1
Quantitative analysis of variables.
Variables must be able to vary – that is must be able to have different values or levels.
- E.g. Gender is a variable since that can be Male, Female.....
- Male is not a variable as that is only the Male level of variable Gender
- Examples of variables: Fruit, Medal colour, Exam grades, Amount of money.
Measurement levels can be..
Nominal: Mere labels for values, no order (sex) Kunt ze niet ranken.
In frequencies or in percentages.
Ordinal: Ordered values with unequal steps (position top 100, educational level). Ranken
In frequencies or in percentages
Interval: Ordered values with equal steps, no natural zero (degrees celsius) exam grades.
Infinitely many options, so infinite categories.
Ratio: ordered values with equal steps and a natural zero (Degrees Kelving, length in cm) Because
there is a natural zero you can compare the numbers.
Infinitely many options, so infinite categories.
- You can always interpret ratio and interval as nominal and interval, but not the other way around.
- For Ratio and interval you create summary measures for central tendency and width of distribution
instead.
Measures of central tendency
- How to best describe the typical or average income in this group?
- The most common (mode)?
- The middle person (median)? not sensitive for outliers
- The mean (aka arithmetical average)? Sensitive for outliers (Extremely high or low number)
Symmetric distribution : Mean + median (bijna) gelijk
Asymmetric distribution: Mean + median verschillen heel erg. → Bevat outliers
Measures of variability:
- Range= maximum – minimum
- Standard deviation = s = Wortel(variance)
Variance= S2 = (1/(n-1) * de som van (Yi – Y)
- Interquartile range (IQR)= Q3-Q1
Q1 = first quartile = 25th percentile = lower quartile
Q3 = third quartile = 75th percentile = upper quartile
Is not sensitive for outliers
Normal distribution:
- a probability density function.
- All central tendency measures the same
- total area under the curve =1
- probabilities → a certain area under the curve.
- symmetrical distribution
- bell-shaped; 1 top. Mote of the distribution, it’s in the middle.
- uni-modal; only one top
,The smaller de standard deviation, the more narrow and more pointed the normal distribution will
be.
Standard deviation (o)
Standard normal distribution
- mean = 0, Standard deviation = 1
,Thumb rule:
,
