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1. 1. Introducing Communication Research 2e © 2014 SAGE Publications Chapter Seven Generalizing From Research Results: Inferential Statistics
2. 2. Key Concepts • Statistical significance. • Normal distribution. • Random sampling. • Confidence level & confidence interval. • Parametric vs. non-parametric. • t-test, ANOVA & correlation. • Type I and Type II error. Introducing Communication Research 2e © 2014 SAGE Publications
3. 3. Inferential Statistics Inferential statistics help us – • Estimate the probability that a sample represents the population it came from. • Decide whether groups differ significantly on a variable. • Decide whether there are significant relationships among or between variables. Introducing Communication Research 2e © 2014 SAGE Publications
4. 4. Inferential Statistics and the Normal Curve • Inferential statistics assume that the values of a variable in a population are normally distributed. • Assuming a normal distribution of values in a population, we can calculate the probability that a sample of that population has captured its characteristics. Introducing Communication Research 2e © 2014 SAGE Publications
5. 5. The Normal Curve and Standard Deviation In a normal distribution – • 68% of values occur plus or minus one standard deviation (SD) from the mean. • 95% of its values occur plus or minus two SDs from the mean. • 99.7% of its values occur plus or minus three SDs from the mean. Introducing Communication Research 2e © 2014 SAGE Publications
6. 6. Statistical Significance • Significance means that there is a better than random chance that a relationship exists. Introducing Communication Research 2e © 2014 SAGE Publications
7. 7. Confidence Interval and Confidence Level • Confidence Interval The possible range of values for a variable in a population, calculated from a sample of the population. • Confidence Level The probability of a calculated value occurring. • Example – There is a 95% probability that the mean lies between 0.98 and 10.42. Introducing Communication Research 2e © 2014 SAGE Publications
8. 8. For a Sample • The distribution of the sample results is called the sampling distribution. • The standard deviation is called the standard error. • Standard error decreases as sample size increases. Introducing Communication Research 2e © 2014 SAGE Publications
9. 9. Parametric vs Non-parametric Statistics • Parametric Statistics Used where we can assume a normal distribution of values in the population. • Non-Parametric Statistics Used where we cannot assume a normal distribution of values in the population. Introducing Communication Research 2e © 2014 SAGE Publications
10. 10. Standard Deviation • A measure of the extent to which a set of scores vary on either side of their mean value. • The square root of variance. • For a sample, standard deviation is referred to as the standard error. Introducing Communication Research 2e © 2014 SAGE Publications
11. 11. t-Test Compares mean scores from two groups to determine the probability the groups are different. • t-test for independent samples - Used where the groups are different. • t-test for dependent samples - Used where the groups are the same. • The higher the t-value, the lower the probability it will occur. Introducing Communication Research 2e © 2014 SAGE Publications
12. 12. Degrees of Freedom • A measure of “room to move.” ▫ How many ways could our data be combined and still produce the same values for a statistic? Introducing Communication Research 2e © 2014 SAGE Publications
13. 13. One and Two-tailed Tests • One-tailed Test Presupposes that a difference between groups will be directional for example, that a value for group A will be higher than for group B. • Two-tailed Test Presupposes that the difference will be non- directional for example, group A and group B simply differ; either group could score higher or lower. Introducing Communication Research 2e © 2014 SAGE Publications
14. 14. Analysis of Variance (ANOVA) • Assesses the probability of difference among two or more groups. • Compares the variance within groups with the variance between groups. • One-way ANOVA compares one variable across more two or more groups. • Multiple Analysis of Variance (MANOVA) assesses relationships among multiple variables across two or more groups. Introducing Communication Research 2e © 2014 SAGE Publications
15. 15. Correlation and Regression Correlation – a measure of the strength of association among and between variables. Correlation coefficient - expresses the strength of association between variables. Regression - predicts a value for one variable given a value for another variable. • Relationships between variables may plot out as linear or curvilinear Introducing Communication Research 2e © 2014 SAGE Publications
16. 16. Type I and Type II Error Accept null hypothesis Reject null hypothesis Null hypothesis is true in the wider population. No problem. Type I Error. Decided wrongly that there was a significant result. Null hypothesis is false in the wider population. Type II Error. Decided wrongly that there was no significant result. No problem. Introducing Communication Research 2e © 2014 SAGE Publications
17. 17. Chapter Summary • Inferential statistics assess – ▫ the probability that a sample represents a population ▫ the strength of relationships among variables ▫ the strength of differences among groups. • t-test – compares values of a continuous variable for two groups. • Correlation - assesses the strength of association between variables. • Regression - computes the values of one variable, given the values of another. • ANOVA compares values of a variable across multiple groups. Introducing Communication Research 2e © 2014 SAGE Publications
18. 18. Vocabulary Review Introducing Communication Research 2e © 2014 SAGE Publications
19. 19. Web Resources t- test Calculators • http://www.physics.csbsju.edu/stats/t-test_NROW_form.htm • http://graphpad.com/quickcalcs/ttest1.cfm Introducing Communication Research 2e © 2014 SAGE Publications