1 / 32

Statistical Evaluation of Data

Statistical Evaluation of Data. Chapter 14 George S. Robinson, Jr., Ph.D. Department of Psychology North Carolina A&T State University. Two General Categories of Statistical Techniques. Descriptive statistics

lassie
Download Presentation

Statistical Evaluation of Data

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Statistical Evaluation of Data Chapter 14 George S. Robinson, Jr., Ph.D. Department of Psychology North Carolina A&T State University

  2. Two General Categories of Statistical Techniques • Descriptive statistics • are methods that help the researchers to organize, summarize, and simplify the results • Inferential statistics • are methods that use the results obtained from samples to help make generalizations about populations

  3. Statistics Terminology • Statistic • a summary value that describes a sample • (e.g., mean of the sample, standard deviation of the sample) • Parameter • a summary value that describes a population • (e.g., mean of the population, standard deviation of the population)

  4. Descriptive Statistics • Frequency distribution • frequency of the number of cases in each category • Frequency distribution table • Frequency distribution graphs • histogram • polygon • bar graph

  5. Frequency distribution table

  6. Frequency distribution graphs - Histogram

  7. Frequency distribution graphs - Bar graph

  8. Frequency distribution graphs - Pie chart

  9. Frequency distribution table - 2

  10. Frequency distribution graphs - Histogram - 2

  11. Frequency distribution graphs - Bar graphs - 2

  12. Frequency distribution graphs - Pie chart

  13. Measures of Central Tendency • Central tendency • a statistical measure that identifies a single score that defines the center of a distribution • mean • median • mode • bimodal • multimodal

  14. Measures of Variability • Variability • a measure of the spread of scores in a distribution • variance • the average squared distance from the mean • standard deviation • the square root of the variance; the average distance from the mean

  15. Selecting a Descriptive Statistical Procedure

  16. Using Graphs to Summarize Data • line graph • bar graph • histogram • pie chart • scatter plot

  17. Stacked Bar Graph

  18. Stacked Bar Graph - 2

  19. Line Graph

  20. Correlation • Correlation • describes the degree of the relationship and direction between two variables • the direction of the relationship • positive • negative • form of the correlation • Pearson r (interval or ratio data) • Spearman r (ordinal data) • strength of the relationship • -1 to +1

  21. Correlation Matrix

  22. Correlation - Scatter Plot

  23. Inferential Statistics • Inferential statistics • Making inferences (generalizations) from a sample to a population • Sampling error • Naturally occurring difference (error) between a sample statistic and the corresponding population parameter

  24. Hypothesis Tests • Hypothesis test • A procedure that determines whether the sample data provide enough evidence to conclude that the original hypothesis is correct

  25. Five Elements of a Hypothesis Test • The Null Hypothesis • States that there is no difference, no effect, or no relationship • The Sample Statistic • Data from the study (e.g., sample means) • The Standard Error • The average difference between a sample statistic and a corresponding population parameter • The Test Statistic • A summary value that measures the degree to which the sample data are in accord with the null hypothesis • Test statistic = sample statistic / standard error  large value (greater than one) leads to rejecting the null hypothesis • The Alpha Level (level of significance) • The maximum probability that the results were due to chance (e.g., alpha level of 0.05 means there is a 0.05 probability the sample results are due to chance; or there is a 95% probability the results are not due to chance

  26. Reporting Results from a Hypothesis Test • Statistically significant (significant results) • Extremely unlikely that the results were due to chance • P-values • p < .05 (less than) • p = .032 (actual value) • Reject the null hypothesis if the p-value is less than the previously specified alpha level • Results are not due to chance • Report the results as significant • Report the actual p-value • Fail to reject the null hypothesis if the p-value is greater than the previously specified alpha level • Results are probably due to chance • Report the results as not significant\ • Report the actual p-value

  27. Errors in Hypothesis Testing • Type I errors • Occurs when the researcher finds a significant result when actually there is no effect in the population • The researcher selected an unusual sample and incorrectly concludes that there is a significant effect • The p-value represents the probability of a Type I error • Type II errors • Occurs when the researcher does not find a significant result when actually there is a real effect in the population • The effect was too small to show up in the sample • 1 – p-value represents the probability of a Type II error

  28. Measures of Effect Size • Simply report the results • Cohen’s d - (used with t-test) = sample mean difference / sample standard deviation • 0 < d < 0.2 small effect (mean difference less than 0.2 standard deviation • 0.2 < d < 0.8 medium effect (mean difference around 0.5 standard deviation) • d > 0.8 large effect (mean difference more than 0.8 standard deviation) • r2 – correlation (correlation squared) • Phi-squared (F2) and Cramer’s V (chi-square) • Eta-squared - ANOVA

  29. Examples of Hypothesis Tests • Tests for mean differences • Two-group between-subjects test • Independent-measures t test • H0 = there is no difference in the number of life-time sexual partners between males and females • H1 = there is a difference between the number of life-time sexual partners between males and females • t(468) = 4.88, p = .000 468 = degrees of freedom (df); 4.88 = t value; .000 = significance level (2-tailed) • Repeated-measures t test • reported the same

  30. Examples of Hypothesis Tests – cont. • More than two groups single-factor analysis of variance (one-way analysis of variance) • One-way ANOVA • H0: there is no difference in the number of hours watching BET between freshmen, sophomores, juniors, seniors, graduate students, or others • H1: there is a difference in the number of hours watching BET between freshmen, sophomores, juniors, seniors, graduate students, or others • F(5, 480) = 2.82, p = .016

  31. Examples of Hypothesis Tests – cont. • Correlation (Spearman) • H0: there is no relationship between the risk of female unprotected oral sex and male unprotected oral sex • H1: there is a relationship between the risk of female unprotected oral sex and male unprotected oral sex • rs = 0.75, N = 469, p = .000 • The same for Pearson correlation except use r

  32. Examples of Hypothesis Tests – cont. • Test for proportions • Chi-square test for independence (Crosstabs) • H0: there is no relationship between gender and music preference • H1: there is a relationship between gender and music preference • X2(8, N = 487) = 78.85, p = .000

More Related