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 11th graders at CCHS, little difference

–Sizes of shoes of all 11th 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 68-95-99.7 Rule

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SAT Scores

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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