Political Science 3N06 Semester II 2014 Lecture 2a: Frequency distributions: Tables and Graphs
- Identify and understand the kind of variable involved; Mechanism where by you can transform the variable
and what is associated with it.
- FREQUENCY DISTRIBUTION
- Some basic math to get things started
- A) Proportion and Percentage
o Comparisons between different sized groups possible
o Controlling for sample size
- B) Ratios and Rates
Ratio = f1 / f2
f1 - number of cases in first category
f2 - number of cases in second category
- Compare the size of one group against the size of another group
- Provides meaningful information in certain context,
o E.G 2006 survey, it asked question about federal sponsorship scandal;
o f1 = 3351
o f2 = 630
o f1 / f2
- In the case of ratios, we are interested in the relative size of two categories with respect to one another
- How many men are in this class compared to women?
- How many are satisfied with the performance of the Conservatives compared to how many who are
dissatisfied?
- A Rate (think unemployment rate, birth rate, murder rate) is calculated by dividing the number of actual
occurrences of an event (over a given period of time), by the number of possible occurrences
- The answer is often multiplied by some unit of 10 to shift the decimal point, and make the number easier to
interpret
o MURDER RATES
o 2010 = 554 people were murdered
o How many people were murdered compared to how many could have been murdered?
o 554 / 34,349,200 = 0.0000161:1
1.61 / 100,000 (allows us to compare two differently sized populations)
- Rates are useful for making comparisons between two groups of different size
**** Frequency Distributions
- The first step in moving from a huge collection of raw data into a summary statistic is to construct a
frequency distribution table
1 - Taking raw data and breaking it down into the first form of order;
- The type of frequency distribution will depend upon the level of measurement of VARIABLE (Nominal,
Ordinal… etc.)
o (Note that some of the charts below differ somewhat from the Charts in the Healey and Prus,
Second edition):
o Sex = Nominal (for nominal level variables it does not matter)
o Marital Status = Nominal
o Satisfaction with Services = Ordinal (have to list in order)
o Age = Interval-ration level
- From this
- To this:
- A) For Nominal Variables (does not matter if it’s not listed in order)
- B) For Ordinal Variables (have to be listed in order)
- The listing of the categories of the variable should reflect their rank – from low to high or from high to low
2 - C) For Interval-Ratio Variables
- Follow the same pattern as is the case for ORDINAL (ranking, etc.) real complication when it comes down
to doing frequency tables, many interval ratio levels have LARGE ranges.
o Have to group together different attributes to simplify it.
o 0-10,000 Group A
o 10,001 - 20,000 Group B… etc.
- The listing of the categories of the variable should also reflect the rank – from low to high or from high to
low
- The real complication here is that interval-ratio level variables (like income) often have a large range of
possible scores
- Like Income – from 0 to 2,000,000,000, and everything in between
- This can make a

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