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Summary of Statistics for BA1 Business Economics at the VUB.
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Statistics for Business Economics II. Outline of Statistics
Different types of statistics:
- Descriptive statistics (Summarizing & Displaying).
- Probability statistics.
- Inferential statistics.
II. Displaying and Describing Categorical Data
You display to see:
- Patterns
- Relationships
- Exceptions
A) Summarizing and displaying a categorical variable
A categorical variable can be categories or qualitative variables.
Example: Data table containing all 226 925 visits to KEENS website in February 2013.
IP Number Time Source
xxx.xxx.xxx xx/xx/xxxx, xx:xx:xx GOOGLE, DIRECT
Variable source: how customers found their way to the website.
A Data Table answers the “Five W’s”: who, what, when, where, and (if possible) why. In
general, rows of a data table correspond to individual cases about which we’ve recorded
some characteristics called variables. Actual data includes who and what (content), while
metadata includes where, when and how (context).
Frequency Table (counts):
Source Count
Direct X
Google X
Total: 226 925
+ Percentage (visits as %). Known as Relative Frequency.
, ↳ Proportion: 130 000 » 0.5736 x 100 = 57%
Percentage = Proportion x 100
Bar chart (%):
ð Categorical (keep spaces, it means you
can change the order of the bars).
ð Respect the area principle (width and
height).
Final Frequency Table:
Classic frequency table (with percentages).
Combined frequency (counts) and relative frequency table (percentages).
An alternative is the pie chart (%):
, ð From the biggest to the smallest + add percentages.
ð Bar charts are better.
If you have two categorical values, you use a contingency table (counts), which is like a freq.
table but with more variables:
Contingency table of Social Networking and Country
Relative frequency table: PERCENTAGE, frequency distribution of either one of the variables.
Contingency table: COUNTS, shows how individuals are distributed along a variable
depending on the value of the other variable. In a contingency table, when the distribution of
one variable is the same for all categories of another variable, we say that the two variables
are independent.
Independence: Random phenomena are independent when the outcome of one trial does
not influence the outcome of another.
e.g.: “roll a die twice”.
Conditional distribution table: a table that shows the distribution of one variable for just
those cases that satisfy a condition on another.
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Marginal distribution shows percentage.
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Frequency table for variable “Social Networking”.
=> Answers the question: “Do you use social network sites ?”.
, Contingency table for social networking from country to country.
=> Answers the question: “Does social networking differ from country to country?”.
ð The “300” means: “There are 300 respondents who are from Egypt that have
access and use social-networking sites”. (OR “and answered yes to the survey
question”).
For every cell we can compute three percentages:
"##
ð Total percentage = $#"% . 100% » 6.0%
"##
ð Row percentage = ,-.$ . 100% » 13.8%
"##
ð Column percentage = -### . 100% » 30%
ð The “13.8%” means: “13.8% of all respondents who answered YES are from
Egypt”.
ð The “30.0%” means: “30% of respondents living in Egypt answered YES”.
è Compare social networking country by country:
↳ Column percentages: conditional distribution of the variable social-networking
conditional on the variable country. (Which condition did we impose ? Countries).
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