Statistics Without Fear! AP Ψ. An Introduction Statisticsmeans of organizing/analyzing data...

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Transcript of Statistics Without Fear! AP Ψ. An Introduction Statisticsmeans of organizing/analyzing data...
Statistics Without Fear!
AP Ψ
An Introduction
• Statisticsmeans of organizing/analyzing data
• Descriptiveorganize to communicate
• InferentialDetermine if data can be generalized.
Measurement Scales
• Nominal • Ordinal • Interval
• Ratio
Nominal Scale
• Numbers used to categorize or name:–Driver’s License –Gender (#1female, #2male)–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
–Rangedifference 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 689599.7 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
Hei
gh
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f C
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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