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Mean

interval, the most common type of average, sensitive to extreme scores

Median

Ordinal, defined as the midpoint

Mode

Nominal, the value that occurs most frequently

Nominal measurement

defined by the characteristics of an outcome that fit into one and only one class or category.

Ordinal Measurement

stands for order, and the characteristic of things being measured here is that they are ordered

Interval measurement

test or an assessment tool is based on some underlying continuum such that we can talk about how much more a higher performance is than a lesser one

Ratio level of measurement

characterized by the presence of an absolute zero on the scale

A measure of central tendency for qualitative, categorical, or nominal data

Mode

The median and the mean are best used

with Quantitative data, Examples: height, income, age, test score

A correlation coefficient

a single number, ranging from -1.0 to 1.0, that indicates the strength and direction of an association between two variables, abbreviated r

Linear correlation

relation between two variables that shows up on a scatter diagram as the dots roughly following a straight line

Eyeball Method

Possibly the easiest (but not the most informative) way to interpret the value of a correlation coefficient is by eyeballing it and using the information

The coefficient of determination

r^2, measures the proportion of variability in one variable that can be determined from the relationship with the other variable

Coefficient of alienation

The amount of variance in one variable that is not accounted for by the variance in another variable

Correlations Limitations

Outliers, Range Restriction, Only good for linear relationships

Correlation Matrix

a table showing a simple way to report all relevant correlations at once

Reverse causation

the causal direction could be the opposite from what has been hypothesized

Reciprocal Causation

two variables cause each other, "Spiral effect"

Common Causation

x and y are affected by a third variable, For example, ice cream sales and drowning deaths are caused by a third variable, temperature

Variability

the spread or dispersion of data, Range, Standard Deviation, and Variance

Range

most basic measure of variability, r = highest - lowest

Range Issues

Ignoring values in the middle, overemphasizing extreme scores

Interquartile Range (IQR)

Q3 - Q1

Standard deviation

reflects how much scores differ from one another, How far from the mean on average?

High SD means

values farther from the mean on average

Low SD means

the data point is close to the mean!

Variance

standard deviation squared, s^2

Standard deviation is susceptible to outliers

outliers are two SD from the mean

X-bar ± (c * s)

c = cutoff scores, s = standard deviation