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THE ROLE OF STATISTICS IN RESEARCH
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Reading APPENDIX A: Statistics pp. 673-677
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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.”
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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 ?
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We’ll focus on Descriptive Statistics
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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
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Histogram of of Psych 100 grades
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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
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1. Shapes of Distributions The normal distribution (bell-curve) Flat distribution
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More Shapes Skewed distributions Leans to right Leans to left
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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
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Shape is important too Multi-modal distributions 0 2
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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)
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2. Measures of Variability RANGE: - the highest value minus the lowest value STANDARD DEVIATION: - the average difference among the scores
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e.g. of Variability Two normal distributions -same mean --differ in variability
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Normal Curve 170 190 150 130 210 Mean 68% 3% 13%
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Standard Normal Curve (in terms of standard deviations) 0 +1 - 1 - 2 +2 Mean 68%
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Measuring associations between variables: The main goal of science
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Plotting Associations
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CORRELATION COEFFICIENT (r) -quantifies associations -plug your numbers into the correlation formula (see book) -yields a number between -1 and +1
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Perfect positive correlation r = + 1.00
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Perfect negative r = - 1.00
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r = +.85
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Zero correlation r = 0
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SUMMARY One variable: Frequency distributions measures of central tendency measures of variability Two variables: correlations
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