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Lecture3 Graphing & Z-scores

Lecture3 Graphing & Z-scores - Describing Your Data...

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Unformatted text preview: Describing Your Data Part 2 Lecture 3 Overview Graphing Data Distributions of Data Other Descriptive Statistics ZScores Graphing Data Graphs Frequency Polygon Histogram Bar Graph Line Graph Stem & Leaf Plot Boxplot (or Box & Whiskers Plot) Frequency Polygon Frequency distribution of a quantitative variable with frequency points connected by lines 12 10 8 6 4 2 0 86 87 88 89 90 91 92 93 94 Quiz Score Frequency Frequencies on yaxis Histogram Frequency distribution graph of a quantitative variable with frequencies indicated by connected vertical bars. No space between bars Frequencies on yaxis Frequency of Quiz Scores 20 18 16 14 12 10 8 6 4 2 0 86.0 88.0 90.0 92.0 94.0 Std. Dev = 2.17 Mean = 91.1 N = 45.00 QUIZSCR Lower Limit (85) Upper Limit (87) Bar Graph Graph of frequencies of nominal or qualitative data Bars are separated by spaces Counts on Y axis Categories on xaxis Line Graph Graph that shows the relation between two variables with lines Value of the y variable that goes with corresponding x variable Stem & Leaf Plot Tells us the general shape of the data while still showing us what the data is Box & Whiskers Plot Graph that shows a distribution's range, interquartile range, skew, median, & often the mean. Mean Distributions of Data 3 Characteristics 1) Center 2) Spread 3) Shape Where is the middle of the distribution? Are the values close together or spread out? What does the distribution look like? Shape of the distribution Bell Shaped Distributions symmetrical or normal positive (right) negative (left) Skewed Distributions Other Distributions rectangular (uniform) Bimodal Jcurves Normal (symmetrical) Distributions Skewed Distributions Negative (left) Skew Positive (right) Skew Other Distributions Rectangular Bimodal Jcurve Jcurve Guess the Shape # 1 #2 # 3 Guess the Shape Negative Skew Positive Skew Normal The Normal Distribution & Z scores ZScores Combines Two Other Descriptive Stats Reexpresses a raw score in terms of the number of SDs the score is from the center of the distribution What is the score relative to the M and SD? M & SD Allows us to compare scores on different scales ZScore Example 1 You got a 95 on the Exam! But it was out of 200 But the SD was only .5 But the average was only 98 And the 95 was the lowest score on the exam Comparing Apples & Oranges Ted and Harry are both in the middle of the quarter, and they each take a midterm exam in their respective courses. On Ted's biology test, he scores 45 points. On Harry's stats exam, he scores 40 points. Who did better on his exam? ZScore Example Comparing Apples & Oranges ZScore Example Biology Ted's score: 45 40 Class average: 51 SD: 1 Statistics Harry's score: Class average: 36 SD: 1.1 Calculating the Z score Ted: 45 51 = -6 1 Harry: 40 36 1.1 = 3.64 Look for the higher score... so Harry did much better! Normal Distribution If data are normally distributed, we can estimate the proportion of data beyond or before that point... Z 3 2 1 0 +1 +2 +3 p .00125 .02275 .158655 .50 .841345 .97725 .99865 Effect Size How large of an effect is there? Common measures of effect size: How strong is the relationship? How big is the difference? Cohen's d Hedge's g Pearson's r Effect Sizes d & g How many SDs difference does it make? What is a large effect? Ignore the book's conventions... Depends on what you are talking about ...
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