Statistics Without Fear! AP Ψ

An Introduction Statistics-means of organizing/analyzing data Descriptive-organize to communicate Inferential-Determine if data can be generalized.

Measurement Scales Nominal Ordinal Interval Ratio

Nominal Scale Numbers used to categorize or name: –Driver’s License –Gender (#1-female, #2-male) –Car Color (denote #’s to represent color)

Ordinal Scale Numbers represent serial position –Class Rank –Age –Baseball Standings

Interval Scale Consistent units of measurement, equal spacing between measurement units –Fahrenheit temperature (because there is no true zero point)

Ratio Scale Same consistent units of measurement as in the interval scale, added property of a true zero point. –Four pounds is twice as heavy as two pounds –Time –Length

Frequency Distribution Allows a meaningful way to look at a list of numbers List in ascending or descending order Allows for grouping

Graphs Pie Frequency Histogram Frequency Polygon Line Graph

Measures of Central Tendency Describe a typical score around which the others fall –Mean –Median –Mode

Measures of Variability Refers to the amount of difference among data collected within a group or between groups Examples: –Ages of all 11 th graders at CCHS, little difference –Sizes of shoes of all 11 th Graders, variability

Calculations of Variability –Range-difference between the highest and lowest scores –An single outlying score can make a big difference –See Test Scores example on the resource sheet

Standard Deviation Measure of variance to determine how different the scores are from each other Can be reported as standardized scores or z scores. Allows for comparisons of scores designed on differing measures (see SAT/IQ example)

The Normal Distribution Curve Normal curve is hypothetical, bell shaped curve Allows us to see what percent of a population would fall in the “normal” range 68% of scores fall within +1 and -1 standard deviation

The Rule

A Normal Frequency Curve for the Population of SAT scores

Skewed Distributions Distributions where most of the scores are squeezed into one end A few scores stretch out away from the group like a tail Skew is named for the direction of the tail

Positively Skewed Positive skewed distribution is pulled to the right, tail pointing towards the positive numbers Mean is higher than the median

Negatively Skewed A negatively skewed distribution moves the graph to the left with the tail pointing towards the negative numbers The mean pulls to the tail, so it is lower than the median

A Skewed Distribution

Inferential Statistics Allows us to make conclusions about the data gathered Determine if there is a meaningful or significant difference between groups when an independent variable is manipulated

Statistical Significance Determined by the degree of difference between the performance of the two groups Set at 5%, if we did the experiment 100 different times using a different sample group from the same population, we would expect to see significant differences between experimental and control groups at least 95 of those times