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THE ROLE OF STATISTICS IN RESEARCH. Reading APPENDIX A: Statistics pp. 673-677.

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Presentation on theme: "THE ROLE OF STATISTICS IN RESEARCH. Reading APPENDIX A: Statistics pp. 673-677."— Presentation transcript:

1 THE ROLE OF STATISTICS IN RESEARCH

2 Reading APPENDIX A: Statistics pp. 673-677

3 Definition A field of mathematics dealing with the analysis, interpretation, and presentation of masses of numerical data (Merriam-Webster’s Collegiate Dictionary). There are three kind of lies: “Lies, damned lies, and statistics.”

4 Types of Statistics Descriptive Statistics - simple quantitative summaries of the data - describe the basic features of the data in a study Inferential Statistics - used for testing hypotheses. - complex calculations based on probabilities - help reach conclusions about the data. eg did these 2 samples come from the same population ?

5 We’ll focus on Descriptive Statistics

6 A summary of the frequency of individual scores on one variable i.e., How many people got each score Nominal (categories) vs. Score (ordered) variables Smooth curve vs. histogram Frequency Distributions

7 Histogram of of Psych 100 grades

8 1.SHAPE: flat, normal, skewed etc 2.CENTRAL TENDENCY: where is the "center" of a distribution? -Mean, median, or mode 3.VARIABILITY: how different are the scores from each other? Three Aspects of Distributions

9 1. Shapes of Distributions The normal distribution (bell-curve) Flat distribution

10 More Shapes Skewed distributions Leans to right Leans to left

11 2. Measures of Central Tendency MEAN - average of the scores - (Sum of scores)/Number of people MEDIAN - the middle score when ordered MODE - most frequent score

12 Shape is important too Multi-modal distributions 0 2

13 They sometimes disagree Mo 50, 60, 60, 99, 100 (Mean = 74) Jo 50, 60, 70, 70, 90 (Mean = 68) Flo 50, 50, 75, 76, 77 (Mean = 66)

14 2. Measures of Variability RANGE: - the highest value minus the lowest value STANDARD DEVIATION: - the average difference among the scores

15 e.g. of Variability Two normal distributions -same mean --differ in variability

16 Normal Curve 170 190 150 130 210 Mean 68% 3% 13%

17 Standard Normal Curve (in terms of standard deviations) 0 +1 - 1 - 2 +2 Mean 68%

18 Measuring associations between variables: The main goal of science

19 Plotting Associations

20 CORRELATION COEFFICIENT (r) -quantifies associations -plug your numbers into the correlation formula (see book) -yields a number between -1 and +1

21 Perfect positive correlation r = + 1.00

22 Perfect negative r = - 1.00

23 r = +.85

24 Zero correlation r = 0

25 SUMMARY One variable: Frequency distributions measures of central tendency measures of variability Two variables: correlations


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