Statistics

Nominal Data

Data that names or labels categories without any order

Ex: fav food, eye color, types of blood

Ordinal Data

Categories that have a meaningful order or ranking but no differences between them

Ex: Ranking in a competition (1st, 2nd, 3rd, 4th,…..)

Interval Data

Data with an order and the differences between the values are equal!

Ex: temperature 10C + 20C + 30C + 40C (difference is 10 degrees btwn each)

Ratio Data

Data that has an order, a true zero (meaning none), and equal intervals btwn numbers

Ex: 0lbs= no weight, 100lbs + 150lbs + 200lbs

Mean

The average score calculated by adding all numbers together and dividing by how many numbers there are.

Median

Center score that is calculated by listing all numbers in order and finding the middle one.

*If there are two medians, add together and divide by 2.

Mode

The most frequent score in a distribution.

Range

Calculated by subtracting the lowest from the highest score. (Highest-Lowest).

Variance

Calculated by:

• find the mean

• Subtract the mean from every number

• Square each number

• Add the squared numbers

• Divide (N-1)

Standard Deviation

Calculated by:

• find the mean

• Subtract mean from every number

• Square each number

• Add squared numbers

• Divide (N-1)

• Take the square root!

Correlation

Two things are related or change together.

Positive correlation

As one variable increases the other does too

Ex: The more you study the better your test scores are

Negative Correlation

One variable increases and the other decreases

Ex: The more absences, the lower your grades

No correlation

No clear relationship between two variables

Ex: A persons favorite color and their shoe size

Causation

One variable actually causes a change in another

Bivariate

A study or analysis that looks at the relationship between TWO variables.

Symbol r

Represents the correlation coefficient number used to describe the relationship between 2 variables

Pearson Product Moment Correlation

The full name of a common statistical method used to measure correlation

Irrelevant Signs

Ignore the signs and look at the absolute value

Ex: -0.56 is greater than +0.29

Method to identify correlations

1) find variables

2) determine direction (-), (+) or none

3) write conclusion

How to interpret coefficient

1) identify variable

2) determine relationship: “as ___ variable increases, ___ variable decreases”

3) write interpretation

Correlation Matrix

Correlations can involve multiple variables

Ex: relationship satisfaction includes several variables

Coefficient of Determination (r²)

Calculated by:

Ex: if r=70

• Square .70 x .70= .49

• Convert to percent .49 × 100= 49%

Coefficient of non-determination (1- r²)

Tells the percentage of variance that is NOT shared btwn two variables

Calculated by:

1. Square the correlation

2. Subtract 1

3. Convert to percentage

Pearson Correlation Coefficient (r)

Finds r from the coefficient of determination

Calculated by:

• take the square root

• Either plus or minus

Interval Data

There is an order and difference between variables