Chapter 3 Displaying Data

2 Major Points Plotting data: Why bother? Plotting data: Why bother? Histograms Histograms Frequency polygon Frequency polygon Describing distributions Describing distributions Review questions Review questions

3 Displaying Data 8 Statistical Methods: Describing Score Distributions When we collect a large amount of data it is very difficult to make sense out of these data without plots and descriptive statistics which use score distributions.When we collect a large amount of data it is very difficult to make sense out of these data without plots and descriptive statistics which use score distributions. X Example: Test scores from 50 people Hum...

4 Displaying Data 9 Statistical Methods: Example 50 Scores; page 25 Walsh & Betz (1995) Scores in this presentation are not very interpretable.

5 Displaying Data 10 Statistical Methods: Example Grouped Frequency Distribution _____________________________________________ TEST SCORESFREQUENCY OF IN INTERVALSOCCURRENCE _____________________________________________ N=50

6 Displaying Data Plotting Data Histograms Histograms Values on X axis Values on X axis Group the values in a way that is sensible Group the values in a way that is sensible Frequency on Y axis Frequency on Y axis Histogram example Histogram example

7 Displaying Data 11 Bar Graph of Frequency Distribution Walsh & Betz (1995), page 27 N=50

8 Displaying Data Describing Distributions Symmetry: same shape on both sides Symmetry: same shape on both sides Modality Modality Unimodal: one peak Unimodal: one peak Bimodal: two peaks Bimodal: two peaks Skewness Skewness Positively skewed: trails to right, test too hard Positively skewed: trails to right, test too hard Negatively skewed: trails to left, test too easy Negatively skewed: trails to left, test too easy Kurtosis Kurtosis Leptokurtic:leaps up Leptokurtic:leaps up Platykurtic: flat like a plate Platykurtic: flat like a plate Mesokurtic: Normal Mesokurtic: Normal

9 Displaying Data Describe each of the following based on the criteria listed on the previous slide.

10 Displaying Data Review Questions What is a frequency distribution? What is a frequency distribution? How does a histogram differ from a bar graph? How does a histogram differ from a bar graph? List 4 types of terms we use to describe distributions. List 4 types of terms we use to describe distributions.

Stem and Leaf Plots Chapter 3 Displaying Data

12 Chapter 3 Displaying Data Stem and leaf displays Conceptually they can be interpreted like a histogram BUT you also retain the individual values and freq. Of those values. Conceptually they can be interpreted like a histogram BUT you also retain the individual values and freq. Of those values. Stem: vertical axis, will indicate the range of values Stem: vertical axis, will indicate the range of values Leaves: horizontal axis, indicates the frequency of individual values Leaves: horizontal axis, indicates the frequency of individual values You can completely regenerate the data (ex a frequency distribution) from a stem and leaf display You can completely regenerate the data (ex a frequency distribution) from a stem and leaf display

13 Chapter 3 Displaying Data Stem-and-Leaf Display Stem-and-leaf of RxTime N = 300 Leaf Unit =

14 Chapter 3 Displaying Data Review Questions How does a stem-and-leaf display differ from a histogram? How does a stem-and-leaf display differ from a histogram?