1. School of Information - The University of Texas at Austin LIS 397.1, Introduction to Research in Library and Information Science LIS 397.1 Introduction to Research in Library and Information Science Student’s t -Test and ANOVA R. E. Wyllys Copyright 2003 by R. E. Wyllys Last revised 2003 Jan 15

2. School of Information - The University of Texas at Austin LIS 397.1, Introduction to Research in Library and Information Science Standardized Tests of Statistical Hypotheses To each type of statistical hypothesis corresponds a particular standardized test procedure or procedures Each test procedure includes a formula, the “test statistic” You –place, into the test statistic, data from observed sample or samples –obtain a number, the observed value of the test statistic

3. School of Information - The University of Texas at Austin LIS 397.1, Introduction to Research in Library and Information Science Standardized Tests of Statistical Hypotheses Traditional Method: Compare absolute value of observed value of test statistic against threshold value from pertinent table –If |test statistic|  tabled threshold Accept H 0 –If |test statistic| > tabled threshold Reject H 0 Computer-Era Method: Use probability of getting observed value of test statistic when the null hypothesis H 0 is true (OVTSWNHT) –If P(OVTSWNHT)   Accept H 0 –If P(OVTSWNHT) <  Reject H 0

4. School of Information - The University of Texas at Austin LIS 397.1, Introduction to Research in Library and Information Science Common Types of Single- Variable Statistical Hypotheses H 0 :  =  0 –Population mean is some number: “Average daily circulation total is 123” –Handled by t-test H 0 :  1 =  2 –Means of two populations are equal: “Average cost per online search using Service A = average cost using Service B” –Handled by t-test and ANOVA –Samples can be independent or dependent (paired, repeated)

5. School of Information - The University of Texas at Austin LIS 397.1, Introduction to Research in Library and Information Science Common Types of Single- Variable Statistical Hypotheses H 0 :  1 =  2 =  3 =..., etc. –Means of Populations 1, 2, 3,..., etc. are all equal: “Average number of books borrowed per student per semester is the same for freshmen, sophomores, juniors, and seniors.” –Handled by ANOVA –Samples can be independent or dependent (repeated, replicated)

6. School of Information - The University of Texas at Austin LIS 397.1, Introduction to Research in Library and Information Science H 0 :  =  0 Test statistic

7. School of Information - The University of Texas at Austin LIS 397.1, Introduction to Research in Library and Information Science H 0 :  = 25 1 Adapted from Hinton, pp. 62-67 Example 1 :

8. School of Information - The University of Texas at Austin LIS 397.1, Introduction to Research in Library and Information Science H 0 :  = 25 Output of Excel’ s Descriptive Statistics procedure Example:

9. School of Information - The University of Texas at Austin LIS 397.1, Introduction to Research in Library and Information Science H 0 :  1 =  2 with Dependent Samples Dependent samples consist of pairs of observations for each sample element The crucial evidence is the set of pairwise differences: D i = d i2 - d i1 Test statistic

10. School of Information - The University of Texas at Austin LIS 397.1, Introduction to Research in Library and Information Science H 0 :  1 =  2 with Dependent Samples 1 Adapted from Hinton, pp. 83-86 Example 1 :

11. School of Information - The University of Texas at Austin LIS 397.1, Introduction to Research in Library and Information Science H 0 :  1 =  2 with Dependent Samples Output of Excel’ s t-Test: Paired Two- Sample for Means procedure Example:

12. School of Information - The University of Texas at Austin LIS 397.1, Introduction to Research in Library and Information Science H 0 :  1 =  2 with Independent Samples where and Test statistic

13. School of Information - The University of Texas at Austin LIS 397.1, Introduction to Research in Library and Information Science H 0 :  1 =  2 with Independent Samples Example 1 : 1 Adapted from Hinton, pp. 88-90

14. School of Information - The University of Texas at Austin LIS 397.1, Introduction to Research in Library and Information Science H 0 :  1 =  2 with Independent Samples Example: Output of Excel’ s t-Test: Two-Sample Assuming Equal Variances procedure

15. School of Information - The University of Texas at Austin LIS 397.1, Introduction to Research in Library and Information Science H 0 :  1 =  2 with Independent Samples Example: Output of Excel’ s ANOVA: Single Factor procedure

16. School of Information - The University of Texas at Austin LIS 397.1, Introduction to Research in Library and Information Science An ANOVA Table

17. School of Information - The University of Texas at Austin LIS 397.1, Introduction to Research in Library and Information Science H 0 :  1 =  2 =  3 with Independent Samples Example from pp. 122-124 of Hinton Output of Excel’ s ANOVA: Single Factor procedure

18. School of Information - The University of Texas at Austin LIS 397.1, Introduction to Research in Library and Information Science ANOVA The ANOVA procedure is capable of dealing, in a single experiment, not only with several levels of one factor but also with several levels of each of several factors. This capability has contributed, in a major way, to research in countless fields of science and technology since R. A. Fisher invented ANOVA in the 1920s, ranging from agriculture (e.g., the Green Revolution) to pharmaceuticals to the manufacturing of integrated circuits. Without ANOVA, we would not eat as well and cheaply as we do, we would not be as healthy, and we would be nowhere near as far along in the computer and communications revolution.

19. School of Information - The University of Texas at Austin LIS 397.1, Introduction to Research in Library and Information Science ANOVA and Sir Ronald Fisher An even more important achievement was Fisher's origination of the concept of the analysis of variance. This is a statistical procedure used to design experiments that answer several questions at once, instead of just one. Fisher's principal idea was to arrange an experiment as a set of partitioned subexperiments that differ from each other in one or several of the factors or treatments applied in them. The subexperiments are designed in such a way as to permit differences in their outcome to be attributed to the different factors or combinations of factors by means of statistical analysis. This was a notable advance over the prevailing scientific method of varying only one factor at a time in an experiment, which was a relatively inefficient procedure. It was later found that the problems of bias and multivariate analysis that Fisher had solved in his plant-breeding research are encountered in a great deal of other experimental work in biology, and indeed in many other scientific fields as well. From: Encyclopedia Britannica Online, 2002

20. School of Information - The University of Texas at Austin LIS 397.1, Introduction to Research in Library and Information Science Sir Ronald Aylmer Fisher 1890-1962