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Statistics Without Fear! AP Ψ

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Page 1: Statistics Without Fear! AP Ψ. An Introduction Statistics-means of organizing/analyzing data Descriptive-organize to communicate Inferential-Determine

Statistics Without Fear!

AP Ψ

Page 2: Statistics Without Fear! AP Ψ. An Introduction Statistics-means of organizing/analyzing data Descriptive-organize to communicate Inferential-Determine

An Introduction

• Statistics-means of organizing/analyzing data

• Descriptive-organize to communicate

• Inferential-Determine if data can be generalized.

Page 3: Statistics Without Fear! AP Ψ. An Introduction Statistics-means of organizing/analyzing data Descriptive-organize to communicate Inferential-Determine

Measurement Scales

• Nominal • Ordinal • Interval

• Ratio

Page 4: Statistics Without Fear! AP Ψ. An Introduction Statistics-means of organizing/analyzing data Descriptive-organize to communicate Inferential-Determine

Nominal Scale

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

Page 5: Statistics Without Fear! AP Ψ. An Introduction Statistics-means of organizing/analyzing data Descriptive-organize to communicate Inferential-Determine

Ordinal Scale

• Numbers represent serial position–Class Rank–Age–Baseball Standings

Page 6: Statistics Without Fear! AP Ψ. An Introduction Statistics-means of organizing/analyzing data Descriptive-organize to communicate Inferential-Determine

Interval Scale

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

Page 7: Statistics Without Fear! AP Ψ. An Introduction Statistics-means of organizing/analyzing data Descriptive-organize to communicate Inferential-Determine

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

Page 8: Statistics Without Fear! AP Ψ. An Introduction Statistics-means of organizing/analyzing data Descriptive-organize to communicate Inferential-Determine

Frequency Distribution

• Allows a meaningful way to look at a list of numbers

• List in ascending or descending order

• Allows for grouping

Page 9: Statistics Without Fear! AP Ψ. An Introduction Statistics-means of organizing/analyzing data Descriptive-organize to communicate Inferential-Determine

Graphs

• Pie• Frequency Histogram • Frequency Polygon • Line Graph

Page 10: Statistics Without Fear! AP Ψ. An Introduction Statistics-means of organizing/analyzing data Descriptive-organize to communicate Inferential-Determine

Measures of Central Tendency

• Describe a typical score around which the others fall–Mean –Median –Mode

Page 11: Statistics Without Fear! AP Ψ. An Introduction Statistics-means of organizing/analyzing data Descriptive-organize to communicate Inferential-Determine

Measures of Variability

• Refers to the amount of difference among data collected within a group or between groups

• Examples:–Ages of all 11th graders at CCHS, little difference

–Sizes of shoes of all 11th Graders, variability

Page 12: Statistics Without Fear! AP Ψ. An Introduction Statistics-means of organizing/analyzing data Descriptive-organize to communicate Inferential-Determine

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

Page 13: Statistics Without Fear! AP Ψ. An Introduction Statistics-means of organizing/analyzing data Descriptive-organize to communicate Inferential-Determine

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)

Page 14: Statistics Without Fear! AP Ψ. An Introduction Statistics-means of organizing/analyzing data Descriptive-organize to communicate Inferential-Determine

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

Page 15: Statistics Without Fear! AP Ψ. An Introduction Statistics-means of organizing/analyzing data Descriptive-organize to communicate Inferential-Determine

The 68-95-99.7 Rule

Page 16: Statistics Without Fear! AP Ψ. An Introduction Statistics-means of organizing/analyzing data Descriptive-organize to communicate Inferential-Determine

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

0.004

0.0045

200 300 400 500 600 700 800

SAT Scores

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A Normal Frequency Curve for the Population of SAT scores

Page 17: Statistics Without Fear! AP Ψ. An Introduction Statistics-means of organizing/analyzing data Descriptive-organize to communicate Inferential-Determine

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

Page 18: Statistics Without Fear! AP Ψ. An Introduction Statistics-means of organizing/analyzing data Descriptive-organize to communicate Inferential-Determine

Positively Skewed

• Positive skewed distribution is pulled to the right, tail pointing towards the positive numbers

• Mean is higher than the median

Page 19: Statistics Without Fear! AP Ψ. An Introduction Statistics-means of organizing/analyzing data Descriptive-organize to communicate Inferential-Determine

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

Page 20: Statistics Without Fear! AP Ψ. An Introduction Statistics-means of organizing/analyzing data Descriptive-organize to communicate Inferential-Determine

A Skewed Distribution

Page 21: Statistics Without Fear! AP Ψ. An Introduction Statistics-means of organizing/analyzing data Descriptive-organize to communicate Inferential-Determine

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

Page 22: Statistics Without Fear! AP Ψ. An Introduction Statistics-means of organizing/analyzing data Descriptive-organize to communicate Inferential-Determine

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