Statistics!

Statistics

• Purpose for today and wednesday– Familiarize you with statistical terms and concepts– Help you get a general sense of statistics• What are they?• Why do we use them?• What are some basic statistics?

What are they

• Statistics are numbers that describe a sample• Parameters are numbers that describe a

population

What are statistics for?

• We use them to describe our variables– Descriptive statistics

• We use them to make inferences from samples to populations– Inferential statistics

• This is why sampling and bias are so very important

Basic descriptive statistics-frequencies

• Frequencies• Remember: variables are divided into

categories• Frequencies tell us how many are in each type

of category– Frequencies can refer to the raw number, or the

percent

Frequency--exampleScores Frequency (raw Percent

1 3 30%

1

1

3 2 20%

3

4 4 40%

4

4

4

Types of variables

• Nominal• Ordinal• Interval• Ratio

Nominal

• “named” variables • Can be represented with numbers but have no

numerical qualities– There is no rank order

• E.g. Red, blue, green cars• Male/female gender

Nominal

blue

red

green

Ordinal

• Variables that have “order”• We assign them a rank, and may use numbers• We don’t actually know how much the ranks

differ• E.g. bad, worse, worst• Some of the time, most of the time, all of the

time

Ordinal

1 2

3

Ordinal

• We should not manipulate ordinal variables numerically– Add, subtract, multiply

• Because we don’t know if the categories are exact

• But in practice ordinal variables are numerically manipulated all the time

Interval

• Interval data is rank ordered• We know that the space from one to the next is

“equal”• E.g. temperature• But interval data has “no true zero”– There can’t be a true absence of the thing being

measured• Like temperature, zero is “arbitrary”• We decide what zero is

Interval

Even more

less than 0

Less than 0 “0” 1 2 3 4

“heat”

Ratio Data

• Like interval data• It is ordered• We know that the space from one rating to

the next is “equal”• It has a “true zero”• There CAN be an absence of it• E.g. length, weight– You can have “zero” weight

Ratio

0 1 2 3 4

“Weight”

Useful terms

• Univariate—referring to a single variable• Bivariate—two variables• Multivariate—more than two variables• Proportion—a percent