Statistics

# Statistics - Statistics1:ManagingData...

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Click to edit Master subtitle style   Statistics 1: Managing Data,  Frequency Counts, Measures of  KIN 3502

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Summary of today’s lecture How do we measure variables? How do we ‘summarize’ scores using statistics?
Statistical Tools in Evaluation Allows you to:  Summarize a group of scores Look for patterns in scores Provide information about group and individual  performance relative to the group

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Sample vs Population Big Bucket and Little Buckets
Distributions How are the scores ‘spread out’ (distributed) Smooth curve? Either or? Two bumps?  Where is the middle? How spread out are they?  Minimum and maximum?

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Types of Scores Discrete (Categorical) Limited to specific values Usually whole numbers e.g. scores hitting a target Continuous Potentially infinite number of values Continuous scores exist between values
Levels of Data Nominal Category, no order Ordinal Ranks: do not assume equal interval Interval Common unit of measurement Equal distance between units Ratio Common unit of measurement

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What some of the symbols mean x = an individual’s score x (x-bar) = the mean   (sigma) = sum of; add up all the numbers  n = the sample size s or sd = standard deviation
Organizing and  Graphing Scores Simple Frequency  Distribution Grouping Scores for  Graphing 89-91 2 86-88 0 83-85 3 80-82 1 77-79 4 74-76 6 71-73 4 68-70 7 65-67 6 62-64 4 59-61 2 56-58 5 53-55 2 50-52 0 47-49 3 44-46 1

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Frequency graph
Cumulative Frequency X F cf 10 6 5 4 3 0 1 4 10 6 3 1 25 24 20 10 4 1 Mode Median [Position = (n +1)/2]=13th score

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Measures of Central Tendency Mode Score that occurs most frequently “Calculate” from frequency distribution Median Midpoint Rank scores high to low Position of the Median = (n +1)/2 10 scores: (10+1)/2 = 11/2=5.5 Median = (5th score + 6th score)/2 Mean
Descriptive Statistics:  Measures of Central Tendency Mean Usually the most appropriate measure of CT Sum of the scores divided by the number of scores Arithmetic average Must have interval or ratio data  Advantage: includes every score Disadvantage: affected by extreme scores (especially  with small samples)

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The Normal Curve
The Normal Curve Mathematically defined, symmetrical curve Centered around a point 50th percentile Mean, median, and mode are the same Measurement issue: role in probability

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Descriptive Statistics:  Measures of  Range Easiest to compute Difference between the highest and lowest scores Depends on only two scores Standard Deviation
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Statistics - Statistics1:ManagingData...

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