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Describing Scatterplots

Learn how to describe the shape, trend, and strength of scatterplots for both univariate and bivariate data. Understand the 6-step process to analyze scatterplots and identify any outliers or clusters.

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Describing Scatterplots

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  1. Describing Scatterplots Section 3.1

  2. Data Univariate data:

  3. Data Univariate data: data that involve a single variable per case This is the type of data we have been working with so far.

  4. Data Bivariate data:

  5. Data Bivariate data: data that involve two variables per case

  6. Data Bivariate data: data that involve two variables per case For quantitative variables, often displayed as a scatterplot.

  7. Scatterplot Scatterplot shows relationship between two quantitative variables.

  8. Scatterplot Scatterplot shows relationship between two quantitative variables. y vs x

  9. Describing Scatterplots Recall, for univariate data we use shape, center, and spread to summarize data.

  10. Describing Scatterplots Recall, for univariate data we use shape, center, and spread to summarize data. For bivariate data, we use shape, trend, and strength.

  11. Describing Scatterplots Describing scatterplots is a 6-step process.

  12. 6-Step Process • Identify cases and variables

  13. 6-Step Process • Identify cases and variables • Describe overall shape

  14. 6-Step Process • Identify cases and variables • Describe overall shape • Describe trend

  15. 6-Step Process • Identify cases and variables • Describe overall shape • Describe trend • Describe strength

  16. 6-Step Process • Identify cases and variables • Describe overall shape • Describe trend • Describe strength • Does pattern generalize to other cases?

  17. 6-Step Process • Identify cases and variables • Describe overall shape • Describe trend • Describe strength • Does pattern generalize to other cases? • Plausible explanation for pattern – or is there a lurking variable

  18. 1. Identify Cases and Variables

  19. 1. Identify Cases and Variables Need these to put the data in context; otherwise, data are meaningless

  20. Cases and Variables Scatterplot: each point represents one case

  21. Cases and Variables Scatterplot: each point represents one case x-coordinate equal to value of one variable and y-coordinate equal to value of the other variable Describe scale (units of measurement) and range of each variable

  22. 2. Describe Overall Shape

  23. 2. Describe Overall Shape • Linearity: is pattern linear, curved, or none at all?

  24. 2. Describe Overall Shape • Linearity: is pattern linear, curved, or none at all? • Clusters: is there just one cluster or more than one?

  25. 2. Describe Overall Shape • Linearity: is pattern linear, curved, or none at all? • Clusters: is there just one cluster or more than one? • Outliers: any striking exceptions to the pattern?

  26. Shape : Linear Points do not have to form a line to have a linear pattern!

  27. Shape : Linear

  28. Shape: Curved

  29. Shape: Curved

  30. Shape: Curved

  31. Shape: None

  32. Shape: None

  33. Outliers : Extreme x-value

  34. Outliers : Extreme x-value

  35. Outlier: Extreme y-value

  36. Outlier: Extreme y-value

  37. Outliers: Not Follow General Trend

  38. Outliers: Not Follow General Trend

  39. Clusters Is there just one cluster or is there more than one?

  40. 3. Describe Trend If as x gets larger, y tends to get larger, there is a positive trend.

  41. Trend

  42. Trend Think of slope!

  43. Trend If as x gets larger, y tends to get smaller, there is a negative trend.

  44. Trend

  45. Trend If there is no shape, then there is no trend.

  46. Trend

  47. 4. Describe Strength If the points cluster closely around an imaginary line or curve, the strength is strong.

  48. Strength

  49. 4. Describe Strength If the points are scattered farther away from an imaginary line or curve, the strengthdecreases.

  50. Strength

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