Experimental Design Experiments Observational Studies Random assignment Observational Studies Random sampling Equal chance of group assignment/ selection from population for each person/observation

Frequency Distributions & Graphs

Descriptive Statistics The goal of descriptive statistics is to summarize a collection of data in a clear and understandable way. What is the pattern of scores over the range of possible values? Where, on the scale of possible scores, is a point that best represents the set of scores? Do the scores cluster about their central point or do they spread out around it?

What is the pattern of scores? Create a Frequency Distribution Frequency distributions organize raw data or observations that have been collected. Ungrouped Data Listing all possible scores that occur in a distribution and then indicating how often each score occurs. Grouped Data Combining all possible scores into classes and then indicating how often each score occurs within each class. Easier to see patterns in the data, but lose information about individual scores.

Las Vegas Hotel Rates

Las Vegas Hotel Rates

An Example: Grouped Frequency Distribution Las Vegas Hotel Rates An Example: Grouped Frequency Distribution Find the lowest and highest score (order scores from lowest to highest). 891 is highest score. 52 is lowest score. Find the range by subtracting the lowest score from the highest score. 891-52 = 839 Divide range by 10. 839/10 = 83.9 Round off to the nearest convenient width. 100 Determine the scores at which the lowest interval should begin (an interval of the class width).

An Example: Grouped Frequency Distribution Record the limits of all class intervals, placing the interval containing the highest score value at the top. Count up the number of scores in each interval. Hotel Rates Frequency 800-899 1 700-799 4 Las Vegas Hotel Rates 600-699 2 500-599 400-499 6 300-399 8 200-299 8 100-199 4 0-99 2

Frequency Table Guidelines Intervals should not overlap, so no score can belong to more than one interval. Make all intervals the same width. Make the intervals continuous throughout the distribution (even if an interval is empty). Place the interval with the highest score at the top. For most work, use 10 class intervals. Choose a convenient interval width. When possible, make the lower score limit a multiple of the interval width. Sum to N

An Example: Grouped Frequency Distribution Proportion (Relative Frequency) Divide frequency of each class by total frequency. Hotel Rates Frequency Proportion 1/35=.03 800-899 1 .03 700-799 4 .11 600-699 2 .06 500-599 400-499 6 .17 300-399 8 .23 200-299 8 .23 100-199 4 .11 0-99 2 .06 N = 35 Σ = 1.0

An Example: Grouped Frequency Distribution Cumulative Frequency: sum of each frequency and all below it Cumulative Proportion (Cumulative Relative Frequency): Divide Cumulative Frequency by Total Frequency Percentile Rank Cumulative Proportion * 100 35/35= 34/35=

What is the pattern of scores? Graphs often make it easier to see certain characteristics and trends in a set of data. Graphs for quantitative data. Stem and Leaf Display Histogram Frequency Polygon Graphs for qualitative data. Bar Chart Pie Chart number/count class/category

14 24 36 73 52 35 15 24 35 33 34 66 11 14 54 56 24 35 75 43 17 67 26 31 40 29 10 43 27 49 16 9 35 77 28 34 19 64 10 56 Raw data Stem Leaf 1 2 3 4 5 6 7 9 001445679 4446789 134455556 0339 2466 467 357

36 59 65 70 74 78 83 88 38 79 41 84 42 60 75 89 44 66 45 71 90 61 91 48 67 72 49 62 76 92 50 80 85 93 63 51 73 54 81 94 86 56 77 95 64 68 82 87 96 57 58 69 99

Range Frequency 35-39 2 40-44 3 45-49 4 50-54 7 55-59 12 60-64 19 65-69 25 70-74 31 75-79 80-84 26 85-89 20 90-94 95-99 8

Histogram Consists of a number of bars placed side by side. The width of each bar indicates the interval size. The height of each bar indicates the frequency of the interval. There are no gaps between adjacent bars. Continuous nature of quantitative data. Include a descriptive title for the graph. Label each axis.The independent variable is on the X axis The dependent variable (or frequency) is on the Y axis. The numbers along the Y axis indicate the measurement increments.

Histogram

Shapes of Histograms

Frequency Polygons Uses a single point rather than a bar

Bar Graph A graphical representation of qualitative data.Unlike in a histogram, the bars do not touch. Discontinuous nature of qualitative data.

Pie Graph

Misleading Graphs

Homework CANDY BARS EATEN THIS MONTH: 16 8 23 7 31 18 12 19 15 20 28 27 9 18 49 11 14 5 18 17 3 6 25 1 1. Create grouped, relative, & cumulative relative frequency distributions of the data. 2. Create a stem-leaf plot and a histogram of the data. 3. Describe the shape of the distribution. Any outliers? 4. What would you consider an typical value, based on this sample? What number would you guess for the next person? 5. Create a bar graph or pie chart to compare how many ate a candy bar on more than half the days. 6. Create a misleading graph to exaggerate # candy bars eaten. 7. Create a misleading graph to minimize the # candy bars eaten.