), Mann (1992) and Elmore et al. (1997)], in order of performance that can be used to determine the disposition of a null hypothesis: (1) state the null hypothesis (Ho), (2) choose a statistical test for testing Ho [See the Decision Model], (3) specify a significance level () and a sample size (n), (4) find / assume the sampling distribution of the statistical test under Ho, (5) define the region of rejection, and(6) compute the value of the statistical test, using the data obtained from the sample(s). If the computed value is in the region of rejection, reject Ho. If the computed value is outside the region of rejection, Ho cannot be rejected at the chosen level of significance.
Definition: Significance level of a test is the probability of rejecting Ho when in fact it is true. The size of the rejection region depends on the value assigned to . The commonly used values of are 0.01, 0.05, and 0.10. In social science research, the most common value of is 0.05.
Definition: The critical value or critical point is the place on a curve at which the rejection and nonrejection regions are divided.
Decision Model
The Decision Model is a chart designed to facilitate a decision about which statistical procedure is most appropriate in the analysis of a set of data. (See Figure 1) A few questions about a set of data can lead quickly to a decision about which statistical procedure is most appropriate. The questions are: (1)
What type of measurement scale produced the data -- nominal, ordinal, or interval/ratio scale? (2) Were the data related or independent? Was there an absence of association between observations or were the observations related as in a pretest/posttest of the same group? (3) How many groups were measured? (4) How many measurements were involved? By answering these questions and following the Decision Model downward, the appropriate statistical procedure can be identified.
The Matrix view of the Decision Model provides another quick reference in determining the appropriate procedure. (See Table 2) The variables are in the left column; the procedures of choice according to the measurement scale are in the other three columns.
Table 2: Matrix View of the Decision Model
| Groups/Measures | Nominal | Ordinal | Interval/Ratio |
| 1 Group/ 1 Measure | Descriptive / Detailed One Variable | Descriptive / Detailed One Variable | |
| Independent Data 2 Groups/ 1 Measure >2 Groups/1 Measure | Mann-Whitney U Kruskal-Wallis | Independent Group t-Test One Way ANOVA | |
| Related Data 1 Group/2 Measures (Relation) 1 Group/2 Measures (Gain/Loss) 1 Group/>2 Measures | Spearman Rank Wilcoxon Signed Rank Friedman | Pearson Product Moment (Fisher t-Test) Paired t-Test | |
| 1 Group(% Data)/ 1 Group (Raw Data) 2 or >2 Groups Test of Independence | X2 Goodness of Fit X2 Test of Independence | ||
| Conditions: 1. Data is in categories and category frequencies are analyzed. | Conditions: 1. Data is ranked and ranks are analyzed. | Conditions: 1. Assume random sample 2. Assume normal curve |
Exercise
1)Classify each of the following as nominal, ordinal, interval, or ratio level data.
1)Horsepower of motorcycle engine
2)Rating of newscasts in Houston as poor, fair, good, excellent
3)Temperature of outdoors in degrees of Celsius
4)Time required by drivers to complete a course
5)Salaries of cashiers of Day-Night convenience store
6)Political party preference of faculty members
7)Age of students enrolled in a martial arts course
8)Weight of beef cattle fed a special diet
9)Ranking of contestant in a beauty contest
10)Number of pages in the telephone book for Nashville
2)In the statements that follow, which are inferential statistics and which are descriptive.
1)The average price of homes sold in Rhea County during the week of June 6-13 was $83,564.
2)According to the Census Bureau, 20% of all Americans workers carpool to work.
3)The National Eye Institute halted a clinical trial on eye surgery, calling it ineffective and possibly harmful to vision.
4)The Gallup Poll says 1 of every 20 Americans is a member of a Country Club.
5)Drinking decaffeinated coffee can raise cholesterol levels by 7%.
6)According to the Court Administrator in Nashville, 10% of the civil actions in 1998 were decided in less than 6 months.
7)Cigarettes were associated with 29% of the 4,470 civilian fire deaths in 1989.
3)Critique the statement, “statistics is a language.”
4)Compare, contrast and illustrate the four functions of statistics – summarizing, describing, generalizing, and experimenting.
Using This Book
If the following information is committed to memory at the mastery-level of learning (instant, total recall), a student using this book will be able to conduct statistical research using the Decision Model to determine which statistic to use. Each chapter then can be used to produce a p-value for any hypothesis.
The Four Questions
1. Type of data?
2. Related or Independent data?
3. How many measures?
