Introduction to Statistics

1. Introduction to Statistics Night 1 – Thursday April 5, 2012

2. Statistics - Definition • Statistics describes a set of tools and techniques that is used for describing, organizing, and interpreting information or data.

3. Types of Statistics • Descriptive – to organize and describe the characteristics of a collection of data. • Observation - Data or data set • Measures of Central Tendency • Measures of Dispersion • Inferential – to make inferences from a smaller group of data to a possibly larger one. • Sample • Population • ANOVA, Regression, Correlation, etc. Next

4. Descriptive Statistics Back

5. Types of Sampling Methodology • Probability sampling • Simple Random sampling • Systematic sampling • Stratified sampling • Stratified Random sampling • Nonprobability sampling • Convenience sampling • Judgment sampling • Quota sampling

6. Sampling Methodology Tests • Reliability • Cronbach Alpha • Validity • Measuring what you are supposed to measure • Normality • Normal distribution of data

7. Types of Variables • Qualitative /Categorical variables (categories) • Nominal – outcome or data that can fit into only ONE class or category • Ordinal – outcome or data that is fit in an order or ranks • Quantitative variables (real numbers) • Discrete – outcome or data that is taken from a finite set • Continuous – outcome or data that can assume any value along any underlying continuum

8. Descriptive Statistics • Measures of Central Tendency • Describe the “characteristics” of a distribution • Mean • Median • Mode • Measures of Dispersion • Shows how the “distributions” differ from each other • Range • Standard Deviation • Variance

9. Measures of Central Tendency • Mean • Sum of all values in a group, divided by the number of values in the group • Median • The midpoint in a set of scores • Mode • The value that occurs most frequently Next

10. Mean

11. MHR Students’ Ages 47 48 49 27 47 33 30 44 34 31 28 31 50 33 38 29 40 Back

12. MHR Students’ Ages 27 38 28 40 29 44 30 47 31 47 31 48 33 49 33 50 34 Back

13. When do you use what??? • Qualitative data (categorical, nominal) use = MODE • Quantitative data (discrete, continuous) use = MEAN, MEDIAN • Use MEAN for continuous data (that do not include extreme scores) • Use MEDIAN for data with extreme scores • Use MODE with categorical data (data that fits into only one category)

14. Measures of Dispersion • Is there variability in the data? • Range • Highest number – lowest number • Standard Deviation – Average amount of variability in a set of scores Next

15. Standard Deviation

16. Data Sets • Data set 1 • 7, 6, 3, 3, 1 • Mean = 4 • Data set 2 • 3, 4, 4, 5, 4 • Mean = 4 • Data set • 4, 4, 4, 4, 4 • Mean = 4 Back

17. Quiz scores MHR Systems Management • Data set 1 • 5, 5, 5, 4, 4, 3, 4, 4, 5, 5, 4, 3, 5, 5, 4, 5 • Data set 2 • 5, 1, 3, 1, 4, 5, 3, 2, 1, 1, 2, 5, 4, 5, 3, 1 Back

18. Quiz scores MHR Systems Management • Data set 1 • 5, 5, 5, 4, 4, 3, 4, 4, 5, 5, 4, 3, 5, 5, 4, 5 • 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5 • Data set 2 • 5, 1, 3, 1, 4, 5, 3, 2, 1, 1, 2, 5, 4, 5, 3, 1 • 1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 5 Back

19. Data Distribution • Central Tendency = Average Value or Mean • Variability • Skewness • Positively Skewed • No Skewness • Negatively Skewed Next

20. Mean Distribution

21. Mean Distribution 70 80 90 100 130 110 120 Back

22. So, this explains why the values are not confined to [-1, 1]. It is, however, an interesting fact that 68% of the values are always within one standard deviation of the mean. So, as an interesting test for yourself write a program to draw a large number of values from a normal distribution with mean 0 and variance 1 and count the number that are within one standard deviation of the mean. You should get a number close to 68% (68.2689492137% to be a little more precise). Variability Distribution Back

23. So, this explains why the values are not confined to [-1, 1]. It is, however, an interesting fact that 68% of the values are always within one standard deviation of the mean. So, as an interesting test for yourself write a program to draw a large number of values from a normal distribution with mean 0 and variance 1 and count the number that are within one standard deviation of the mean. You should get a number close to 68% (68.2689492137% to be a little more precise). Skewed Distribution Back

24. Problem 1Dot Diagram

25. Problem 3 Frequency Distributions • Arrange the data in order • Select the number of classes to be used (5-12) • Determine the range • Divide the range by the number of classes and you get the class width • Round it up and then start the frequency with the smallest number and increasing it by the class width

26. Problem 5Histogram

27. Problem 6Pie Chart

28. Project Research Plan Part I OPTION 1 INTERVENTION Your solution DID solve the problem OBJECTIVES OPTION 2 PROPOSED INTERVENTION Your solution WILL solve the problem OBJECTIVES & HYPOTHESES PROBLEM OPTION 3 PROPOSED INTERVENTION Your alternatives WILL solve the problem OBJECTIVES & HYPOTHESES

29. Project Research Plan Part I OPTION 1 INTERVENTION Your solution DID solve the problem OBJECTIVES Intervention (New Process/Training Manual/New Technology) Measurable Objectives (10% reduction in waiting time/50% reduction in errors)

30. Project Research Plan Part I OPTION 2 INTERVENTION Your solution WILL solve the problem OBJECTIVES HYPOTHESIS Intervention (New Process/Training Manual/New Technology) Hypothesis (There is a 25% negative level of patient satisfaction at this office) Measurable Objectives (10% reduction in waiting time/50% reduction in errors)

31. Project Research Plan Part I OPTION 3 INTERVENTION Your solution WILL solve the problem OBJECTIVES HYPOTHESIS (Alternatives) Intervention (New Process/Training Manual/New Technology) Hypothesis (There is a 10% negative level of patient satisfaction at this office/50% of patients feel the waiting times are unreasonable) Measurable Objectives (25% increase in the level of patient satisfaction)