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Reasoning in Psychology Using Statistics

Reasoning in Psychology Using Statistics. Psychology 138 2017. Let ’ s collect set of data I ’ ll pass out some pairs of dice Collect n=36 data points 12 people roll a pair of dice three times. Type numbers here:. Rolling the dice. Distribution

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Reasoning in Psychology Using Statistics

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  1. Reasoning in PsychologyUsing Statistics Psychology 138 2017

  2. Let’s collect set of data • I’ll pass out some pairs of dice • Collect n=36 data points • 12 people roll a pair of dice three times Type numbers here: Rolling the dice

  3. Distribution • The distribution of a variable is a summary of all the different values of a variable • The set of all of the outcomes of rolling the dice • Both type (each value) and token (each instance) • Un-organized, the overall pattern and properties of the distribution are difficult to see • A “picture” of the distribution is usually helpful Type numbers here: Distributions David McCandless: The beauty of data visualization

  4. Descriptive statistics • Statistical tools/procedures to help organize, summarize, and simplify large sets of data (distributions) • Important descriptive properties of distribution • Center • Where most of the data in the distribution are • Spread (variability) • How similar/dissimilar are the scores in the distribution? • Shape • Symmetric vs. asymmetric (skew) • Unimodal vs. multimodal Describing Distributions

  5. Today’s focus Describing Distributions

  6. A “picture” of the distribution is usually helpful • Gives a good sense of the properties of the distribution • Many different ways to display distribution • Table • Frequency distribution table • Stem and leaf plot • Graphs Describing Distributions

  7. A “picture” of the distribution is usually helpful • Gives a good sense of the properties of the distribution • Many different ways to display distribution • Table • Frequency distribution table • Stem and leaf plot • Graphs Describing Distributions

  8. The values of the variable The proportion of tokens at each value The percentage of tokens at each value The number of tokens of each variable Cumulative percentage p = f/N N=total Frequency distribution table

  9. 10% got a 1 or worse Quiz: “What % got this score or worse?” 10 Cumulative percent

  10. 15% got a 2 & 10% got a 1 25% got a 2 or worse Quiz: “What % got this score or worse?” 25 10 Cumulative percent

  11. 10% got a 3 & 15% got a 2 & 10% got a 1 35% got a 3 or worse Quiz: “What % got this score or worse?” 35 25 10 Cumulative percent

  12. 35% got a 4 & 10% got a 3 & 15% got a 2 & 10% got a 1 70% got a 4 or worse Quiz: “What % got this score or worse?” 70 35 25 10 Cumulative percent

  13. 20% got a 5 & 35% got a 4 & 10% got a 3 & 15% got a 2 & 10% got a 1 90% got a 5 or worse Quiz: “What % got this score or worse?” 90 70 35 25 10 Cumulative percent

  14. 10% got a 6 & 20% got a 5 & 35% got a 4 & 10% got a 3 & 15% got a 2 & 10% got a 1 100% got a 6 or worse Quiz: “What % got this score or worse?” 100 90 70 35 25 10 Cumulative percent

  15. Fill in numbers from our class: Sample distribution n = 36 Frequency distribution: sum of 2 dice

  16. Value D1+D2 Value D1+D2 Value D1+D2 D2 D2 D2 D1 D1 D1 frequency frequency frequency 1 1 4 12 7 4 11 7 2 2 11 4 7 6 10 3 7 3 3 10 3 7 2 10 7 9 6 9 4 6 9 5 6 9 6 8 6 8 5 5 8 5 4 8 5 8 5 Total outcomes = 62 = 36 = 1+2+3+4+5+6+5+4+3+2+1 = 36 Theoretical Frequency distribution: sum of 2 dice

  17. p = probability when predicting p = proportion when describing what you observed Think of this as defining our population distribution of the outcome of tossing two dice Total outcomes = 62 = 36 = 1+2+3+4+5+6+5+4+3+2+1 = 36 Theoretical Frequency distribution: sum of 2 dice

  18. population sample Sampling error Theoretical frequency distribution & class sample(Actual fs are from a previous term.)

  19. Important properties of distribution • Center • Where most of the data in the distribution are • Spread (variability) • How similar/dissimilar are the scores in the distribution? • Shape • Symmetric vs. asymmetric (skew) • Unimodal vs. multimodal Distributions

  20. 7 What is the most frequent score? Describing the distribution

  21. Two-thirds of the data are here What is the most frequent score? Where do most of the scores lie? Describing the distribution

  22. Maximum score: 12 Minimum score: 2 What is the most frequent score? Where do most of the scores lie? What was the range of scores? Describing the distribution

  23. A “picture” of the distribution is usually helpful • Gives a good sense of the properties of the distribution • Many different ways to display distribution • Table • Frequency distribution table • Stem and leaf plot • Graphs Distributions

  24. 10 9 8 7 6 5 4 • Distribution of exam scores (section 01): • 67, 90, 92, 58, 76, 75, 84, 92, 78, 93, 89, 74, 62, 98, 75, 73, 75, 89, 89, 76, 65, 49 0 2 2 3 8 4 9 9 9 6 5 8 4 5 3 5 6 7 2 5 8 9 Stem and Leaf Plots

  25. 0 10 5 3 0 9 0 2 2 3 8 9 4 3 8 4 9 9 9 5 4 3 3 2 2 1 1 0 7 3 4 5 5 5 6 6 8 6 5 5 2 2 6 2 5 7 8 5 8 2 4 9 • Distribution of exam scores (section 01): • 67, 90, 92, 58, 76, 75, 84, 92, 78, 93, 89, 74, 62, 98, 75, 73, 75, 89, 89, 76, 65, 49 • Distribution of exam scores (section 03): • 72, 90, 83, 58, 66, 65, 84, 95, 72, 93, 89, 70, 42, 100, 71, 73, 75, 62, 62, 74, 65 Stem and Leaf Plots

  26. A “picture” of the distribution is usually helpful • Gives a good sense of the properties of the distribution • Many different ways to display distribution • Table • Frequency distribution table • Stem and leaf plot • Graphs • Graphs types • Continuous variable: • histogram, line graph (frequency polygons) • Categorical (discrete) variable: • pie chart, bar chart Distributions

  27. Histogram • Line graph Graphs for continuous variables

  28. Bar chart • Pie chart Graphs for categorical variables

  29. Important properties of distribution • Center • Where most of the data in the distribution are • Spread (variability) • How similar/dissimilar are the scores in the distribution? • Shape • Symmetric vs. asymmetric (skew) • Unimodal vs. multimodal Distributions

  30. tail tail • Symmetric • Asymmetric Positive Skew Negative Skew Shape

  31. Major mode Minor mode • Unimodal (one mode) • Multimodal • Bimodal examples Shape

  32. Coming up in future lectures: • In addition to pictures of the distribution, numerical summaries are also presented. • Numeric Descriptive Statistics • Shape • Skew (symmetry) & Kurtosis (shape) • Number of modes • Measures of Center • Measures of Variability (Spread) • In lab, create basic tables and graphs both by hand and using SPSS • If time in lecture there are some SPSS show and tell slides Descriptive statistics

  33. Drag & drop Drag & drop SPSS: Bar graph

  34. SPSS: Bar graph

  35. Drag & drop Drag & drop SPSS: Cluster bar graph

  36. Legend SPSS: Cluster bar graph

  37. Drag & drop Drag & drop SPSS: Histogram

  38. SPSS Graphing

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