1 Review Definitions of Statistics, Population, Sample, Experimental Unit, Inference, Parameter, Statistic, Variable, Reliability. Observational versus defined experiment studies Sampling and Bias Classification of Variables (qualitative, quantitative, discrete and continuous)

2 Key Elements of a Statistical Problem Describe the population Describe the variable/s of interest Describe the sample Describe the inference Describe sources of possible errors/bias

3 Example Michael Gray and Jessica Sauerbeck researchers at Northern Kentucky University designed and tested a speed training program for a junior-varsity and varsity high school football players Each participant was timed in a 40-yard sprint prior to the start of the training program and timed again after completing the program. Based on these sprint times, each participant was classified as having an “improved” time, “no change” in time, or a “decrease” in time. In a sample of 15 players selected from different schools in the area, 13 had an “improved” time. The results show that nearly 87% of players who participated in this speed training program improved their sprint times.

4 Chapter 2: Descriptive Statistics

5 Two types of variables –Qualitative –Quantitative

6 Chapter 2: Descriptive Statistics Two types of variables –Qualitative –Quantitative There are different ways to represent each type of Data, but we will find there are more techniques for describing Quantitative data.

7 Qualitative Data To describe Qualitative data we must place the data into a certain classes.

8 Qualitative Data To describe Qualitative data we must place the data into a certain classes. Each class has an associated class frequency and relative frequency and class percentage.

9 Qualitative Data To describe Qualitative data we must place the data into a certain classes. Each class has an associated class frequency and relative frequency and class percentage. Sometimes we keep track of these cumulatively.

10 Example A total of 22 StFX students were tested and found to have the following blood types:

11 Example A total of 22 StFX students were tested and found to have the following blood types: Frequency is how often each class occurs Blood TypeFrequency 02 A11 B5 AB4

12 Example A total of 22 StFX students were tested and found to have the following blood types: Frequency is how often each class occurs Blood TypeFrequencyCumulative Frequency 022 A1113 B518 AB422

13 Example A total of 22 StFX students were tested and found to have the following blood types: Blood TypeFrequency Relative Frequency 022/22 A1111/22 B55/22 AB44/22

14 Example A total of 22 StFX students were tested and found to have the following blood types: Blood TypeFrequency Percentage % A % B522.73% AB418.18%

15 Example A total of 22 StFX students were tested and found to have the following blood types: Blood Type FrequencyRelative Frequency Percentage 022/ A1111/ B55/ AB44/

16 Example A total of 22 StFX students were tested and found to have the following blood types: Blood Type FrequencyPercentageCumulative Percentage A B AB

17 Qualitative Data With qualitative data (and any other data we wish to separate into certain classes), tables, charts and diagrams are often the best way to present the data. It gives us a visual feel for the data and pictures can be more easily understood quickly and information can be passed on without technical jargon.

18 Example A total of 22 StFX students were tested and found to have the following blood types: Blood Type FrequencyPercentageCumulative Percentage A B AB

19 Example Pie Chart

20 Example Bar Graph

21 Example We may also ask you to draw a histogram where the height of each bar is the class percentage or class frequency.

22 Example Pareto Graph – bar graph arranged from highest to lowest.

Use of “side-by-side” charts Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Physicians studied 114 coronary bipass patients 57 given a drug to reduce blood-loss Concerns raised about side-effects Variables surveyed:  Did or did not receive drug  Type of complications: 1. Redo surgery 2. Post-op infection 3. Both 1 and 2 4. None Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure 2.5 SAS summary tables for DRUG and COMP

Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 2.6 MINITAB side-by-side bar graphs for COMP by value of DRUG

Copyright © 2013 Pearson Education, Inc.. All rights reserved. SPSS summary tables for COMP by value of drug (used to produce preceding slide)