Research Design in Occupational Education
SOLUTIONS TO STATISTICS PROBLEMS
1. Describe information or data through the use of numbers
3. a = .75; b = 1.75
2.5 hours - 5.125; 4.5 hours - 8.625
4. Representative sample (Random); Normal distribution; Interval measures; Linearity; Homoscedasticity
5. Multiple regression predicts the value of one variable from the values of two or more variables.
6. We must be careful about predicting beyond the data and the variables we are predicting must be like those upon which the regression equation was built or the prediction has no basis.
1. See Inferential
2. See Inferential
3. The level of significance is the probability of a Type I error that an investigator is willing to risk in rejecting a null hypothesis.
1. When attempting to determine if the difference between two means is greater than that expected from chance; the data is from a normal population and at least ordinal in nature
3. n1 = n2 = 5
5. df = 5 + 5 - 2 = 8
6. The calculated value of -4 was compared with the table value of ±3.355 (based on .01 level of significance and 8 degrees of freedom). Since |-4| > |3.355|, we reject the null hypothesis.
1. The purpose of ANOVA is to test for significant differences among two or more groups.
2. Single classification ANOVA tests a relationship between a dependent variable and one independent variable, while multiple classification ANOVA tests a relationship between a dependent variable and two or more independent variables.
3. The variance is an average distance of the raw scores in a distribution of numbers from the mean of that distribution.
4. The average variance of subgroups are compared to the variance of the total group.
5. Calculate the sums of squares of deviations of the observations from their mean; calculate the sums of squares for the total group by combining the subgroups; subtract the within group sums of squares from the total group sums of squares to derive the among group sums of squares; divide the among and within sums of squares by their degrees of freedom to obtain their means squares; divide the among mean square by the within mean square to obtain the calculated F value
6. among group mean square and within group mean square
7. Representative sample (Random); Normal populations; Representative samples; At least ordinal measurement; Homogeneous variances
8. There are no significant differences among the means of number of chinups junior high boys can do after varying weeks of practice.
The calculated F value of 8 was compared with the table F value of 6.93 (based on .01 level of significance and 2 and 12 degrees of freedom). Since 8 > 6.93, we reject the null hypothesis.
1. The purpose is test the difference between an actual sample and another hypothetical or previously established distribution such as that which may be expected due to chance or probability. Nonparametric techniques are usually easier to computer and can be used on nominal data.
3. A one way classification is used when the number of responses, objects, or people fall in two or more categories; a two way classification is used when the number of responses, objects, or people fall in two or more categories with two or more groups.
4. one independent variable = (r - 1), where r is number of levels of independent variable
5. Data in frequency form (nominal data); Independent observations; Sample size adequate; Distribution basis must be decided on before data is collected; Sum of observed frequencies must equal sum of expected frequencies.
6. It corrects when there is only one degree of freedom.
7. Parametric statistics test hypotheses based on the assumption that the samples come from normally distributed populations and there is homogeneity of variance. The level of measurement is at least ordinal or interval. Nonparametric statistics test hypotheses that do not require normal distributions or variance assumptions and are designed for ordinal or nominal data.
8. Ordinal or nominal