statistics without fear! ap Ψ. an introduction statistics-means of organizing/analyzing data...
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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