Statistical Analysis Chapter 1-6

Nominal

• Only Categories including dichotomous/binary variables

• Not graded/ranked – simply labeled

• E.g., Political Party {Republican, Democrat}, Race

Ordinal

• Have “order” , but are not informative of magnitude of differences

• E.g., Level of education (Bachelors, Masters, PhD)

• E.g., How often do you vote (Never, Seldom, Sometimes, Almost always)

Interval/Ratio

• Standard unit of measurement (interval “distances” make sense)

• e.g., temperature, wage, weight

If there are a lot of observations

then frequency distributions are almost essential

If there are a lot of different score values

then grouped frequency distributions are needed

Percentiles

divide a distribution into 100 equal portions

Deciles

divide a distribution into 10 equal portions

Quartiles

divide a distribution into 4 equal portions

When to use row percents

if the independent variable is on the rows

When to use column percents

if the independent variable is on the columns

Calculating weighted mean

add up the averages of each group then divide by the number of groups

Symmetrical unimodal distribution

Mean=Median=Mode

Skewed distribution

The mean is influenced by other outlier values (median is not and falls below mean and mode). Reporting the median makes the most sense.

Bimodal distributions

Report both modes instead of just reporting the mean or median

The Converse Rule of Probability

P ( not A ) = 1 − P ( A )

The probability of an event NOT occuring is 1 minus the probability the event occurring

The Addition Rule

P (A or B) = P(A) + P(B)

This assumes Events A and B are mutually exclusive (no two outcomes can occur simultaneously

The Multiplication Rule

P (A and B) = P(A)*P(B)

Probability of obtaining two or more outcomes in combination. This assumes Events A and B are independent (they do not affect the likelihood of each other)