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Statistics Without Fear! AP Ψ

erick-harrell
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### Transcript of Statistics Without Fear! AP Ψ. An Introduction Statistics-means of organizing/analyzing data... 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 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 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