1. R. E. Wyllys Copyright 2003 by R. E. Wyllys Last revised 2003 Jan 15
LIS Introduction to Research in Library and Information Science Statistical Hypotheses
R. E. Wyllys
Copyright 2003 by R. E. Wyllys
Last revised 2003 Jan 15
School of Information - The University of Texas at Austin
LIS 397.1, Introduction to Research in Library and Information Science

2. Hypotheses Hypotheses state a relationship among two or more variables
Hypotheses may be stated in positive or negative terms
Hypotheses must be capable of being tested as to whether they are “true” or “false”
School of Information - The University of Texas at Austin
LIS 397.1, Introduction to Research in Library and Information Science

3. Two Types of Hypotheses
General Hypotheses
Concern variables directly related to the problem being studied
Statistical Hypotheses
Are a subclass of general hypotheses
Are tools
Are used in efforts to determine whether general hypotheses are true or false
School of Information - The University of Texas at Austin
LIS 397.1, Introduction to Research in Library and Information Science

4. Statistical Hypothesis
Makes a to-be-tested statement about either
The kind of probability distribution that a certain variable obeys; or
The value of a population parameter (average, total, proportion, etc.)
Must be one of a relatively small number of standard types of statistical hypothesis
School of Information - The University of Texas at Austin
LIS 397.1, Introduction to Research in Library and Information Science

5. Statistical Hypothesis vs. State of Nature
DECISION H is true H is false
Accept H OK error
Reject H error OK
School of Information - The University of Texas at Austin
LIS 397.1, Introduction to Research in Library and Information Science

6. Null Hypothesis vs. State of Nature
Are the erroneous decisions of equal importance?
If not (the usual case), then arrange the wording of the hypothesis so that the more serious error occurs when the hypothesis is true but you decide that it is false. I.e., arrange things so that the more serious error occurs when you reject a true hypothesis. This arrangement yields the Null Hypothesis, H0.
STATE OF NATURE
DECISION H0 is true H0 is false
Accept H OK Type II error
Reject H Type I error OK
School of Information - The University of Texas at Austin
LIS 397.1, Introduction to Research in Library and Information Science

7. Null Hypothesis & Probabilities
P(Type I error) =  = “level of significance of the test” = “risk of the test” = “alpha of the test”
P(Type II error) = 
P(not making Type II error) = 1 -  = “power of the test” = P(correctly recognizing hypothesis as false when it is false)
School of Information - The University of Texas at Austin
LIS 397.1, Introduction to Research in Library and Information Science

8. Null Hypothesis & Probabilities
Primary objective: Avoid more serious error; i.e., ensure that  is small
Secondary objective: Increase chance of recognizing hypothesis as false if it is false; i.e., increase power of test, 1-
For a given , the only way to increase power is to increase size of sample
Power is very hard to determine; in practice,  gets almost all the attention
School of Information - The University of Texas at Austin
LIS 397.1, Introduction to Research in Library and Information Science

9. Test of a Statistical Hypothesis
Statements of
Null hypothesis, H0
Alternative hypothesis (often simply negation of H0)
Level of significance, 
“Critical region”, i.e., what outcomes will lead to rejection of H0 (in practice, this usually means stating threshold value from appropriate statistical table)
School of Information - The University of Texas at Austin
LIS 397.1, Introduction to Research in Library and Information Science

10. Common Types of Single-Variable Statistical Hypotheses
Population mean is some number: “Average daily circulation total is 123”
H0: 1 = 2
Means of two populations are equal: “Average cost per online search using Service A = average cost using Service B”
School of Information - The University of Texas at Austin
LIS 397.1, Introduction to Research in Library and Information Science

11. Common Types of Single-Variable Statistical Hypotheses
H0: 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.”
School of Information - The University of Texas at Austin
LIS 397.1, Introduction to Research in Library and Information Science

12. Common Types of Two-Variable Statistical Hypotheses
H0: XY = 0
Variables X and Y are not correlated in the population: “There is no correlation between the age and the salary of a typical librarian”
H0: Categorical variables X and Y are not associated:
“There is no association between the sex of a library patron and the type of book the patron prefers”
School of Information - The University of Texas at Austin
LIS 397.1, Introduction to Research in Library and Information Science

13. 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
School of Information - The University of Texas at Austin
LIS 397.1, Introduction to Research in Library and Information Science

14. Standardized Tests of Statistical Hypotheses (cont'd)
Traditional Method: Compare absolute value of observed value of test statistic against threshold value from pertinent table
If |test statistic|  tabled threshold Accept H0
If |test statistic| > tabled threshold Reject H0
Computer-Era Method: Use probability of getting observed value of test statistic when the null hypothesis H0 is true (OVTSWNHT)
If P(OVTSWNHT)   Accept H0
If P(OVTSWNHT) <  Reject H0
School of Information - The University of Texas at Austin
LIS 397.1, Introduction to Research in Library and Information Science

15. Comparing the Traditional and Computer-Era Methods
Part of Excel’’s output for “A Worked Example” from pp of Hinton
School of Information - The University of Texas at Austin
LIS 397.1, Introduction to Research in Library and Information Science

16. Evidence in the Sample is Weighed against Risk in order to Tip the Balance toward Acceptance or Rejection
School of Information - The University of Texas at Austin
LIS 397.1, Introduction to Research in Library and Information Science