Quantitative methods
Lecture 1 videoclips
Orders of operations: follow BODMAS brackets orders (powers/indices or roots), division,
multiplication, addition, subtraction.
Pie = represents a proportion in this course, so not the 3,14…
Σ (sigma) = sum of all the values that come after that
Population ‘big world’
Sample ‘small world’ group of people drawn from the population.
- It is never a perfect representation of the big world / population
- Random samples are the goal every person has the same chance of getting ‘chosen’
- Convenience sample certain respondents that are easier to reach
Descriptive statistics summarize the data from a sample. There is no uncertainty of the sample
Inferential statistics always a little bit of uncertainty, as we are making a guess of the population
based on the sample. A sample is never hundred percent representative of the population, we
always have a sampling error.
Cases: units in your sample = can be individuals, companies, countries.
Variables: ages, gender, happiness etc.
Mnemonic device: NOIR: Nominal, Ordinal, Interval, Ratio
Categorical (discrete) variables: different cases can belong to one or several categories. These are
discrete, which means there is no overlapping into the other.
- Nominal: there is no order/ranking (like gender)
- Ordinal: there is an order/ranking to the categories
Continuous variables: can take any numerical value, like temperature can go to infinite. Same
with age. They can fall in between ‘categories’.
- Interval: distance between two points on a scale are meaningful, it has the same distance
between the points. There is NO zero point/no true zero point. You can have 0 degrees (in
temperature), but it doesn’t mean that temperature does not exist at 0, but that water
starts to freeze.
- Ratio: has a true zero. For example, income, if there is zero income, they will not get any
money. If someone is zero cm, you ‘don’t exist’. If someone is 100 cm and someone is
200cm, the 200cm is twice as tall.
Population: µ
Mean: average. Five numbers: 3, 5, 7, 9, 11 = = 7 = mean = M or X̄
Weighted mean: adding the mean of each of the groups and multiplying by the
number of people in that group. Then divide by the total number of people. Helpful in descriptive
statistics where we group the different groups together.
Median: the middle value of a series of numbers. 3, 5, 7, 9, 11 = median is 7
Mode: the most common value. 3, 5, 7, 9, 11 = no mode. 3, 5, 5, 9, 11 = mode = 5.
1
,Lecture 1
Aims for this course
- Give you an appreciation of the increasingly important role of quantitative methods in
empirical research
- To provide some useful quantitative methods that you could use in empirical research
o Test hypotheses
o Answer research questions
o Make predictions about an outcome of relevance
- To convince you that quantitative methods are not the devil’s work
The role of statistics in research
Descriptive vs. inferential statistics
Small world vs. big world
The percentage we calculated via Menti exactly describes the percentage of respondents who
identify as woman in the ‘small world’ of Menti poll. There is no uncertainty about this this is a
descriptive statistic
This percentage is also our best guess about the percentage of
people who identify as women in the ‘big world’ of this zoom
call (or the students taking 1.4 QM).
But when we use small world statistics to make guesses about
the big world, there is always some uncertainty now we’re
doing inferential statistics (we are inferring something about
the population based on a sample).
2
,Random sampling
The best way to minimize sampling error (uncertainty), is to have a random sample, where every
individual in the population has an equal chance to be included
- Was our initial Menti sample random? convenience sample
- Could there be differences between people who answered on Menti that bias our estimate
of the 1% women on the Zoom call?
Noir level of measurement
Categorical: nominal, ordinal
Continuous: interval, ratio
Nominal: separate categories without any ranking
- Gender
- Study
- Living situation
- Car
Ordinal: categories with a rank
- Birthyear (if transformed into categories, if not it’s interval)
- Study interest
Ratio: has a true zero (the absence of the ‘thing’)
- Travel time (if you have zero, you live on the campus)
- Height
Interval: does not have a true zero
- Birth year (if not in categories) (zero years of birth does not mean the absence of something,
therefore not ratio)
Why is this important?
- Selecting the best ways to describe them (e.g., measures of central tendency)
- What kinds of analyses we can do… (week 3)?
Summarizing data (1)
You will be able to:
- Describe your data with tables and graphs and select an appropriate visualization based on
the level of measurement of the variable
- Select an appropriate measure of central tendency based on the level of measurement and
shape of your data
- Describe the shape of your data based on graphical presentations of data and measures of
central tendency
Graphs and level of measurement
Rule of thumb: if you have an interval or ratio level of measurement, use a histogram.
Histograms:
- Continuous data
- With unequal intervals, are represents counts (remember to use frequency density on y-axis)
- Bars touch
Rule of thumb: if you have a nominal or ordinal level of measurement, use a bar chart.
3
, Bar charts:
- Categorical data
- Height represents & of counts
- Bars do not touch
Describing distributes
1. Central tendency
- Mean
- Median
- Mode
Rule of thumb: if you have an interval or ratio level of measurement, use mean or median.
Mean or median, which one? this depends on if there are any outliers.
We need to know more about distributions of data before choosing a measure.
Mean vs. mean:
- Mean is influenced by outliers because it accounts for all values
o Beware in small datasets
- Median is just the middle number, so not influenced by outliers
Sample of 9 students (exercise hours per week): 0, 2, 2, 3, 3, 4, 5, 5, 6
- Mean: 3.33
- Median: 3
Sample of 10 students (exercise hours per week): 0, 2, 2, 3, 3, 4, 5, 5, 6, 90 (error?!)
- Mean: 12
- Median: 3,5*
o If you have an even number of observations, so no middle values. To find the
median, take the mean of the two middle values (for example 3+4/2)
Rule of thumb: if you have a nominal level of measurement,
use the mode
Rule of thumb: if you
have an ordinal level of measurement, it’s possible to use
mean, median or mode
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