Assignment 2: Analysis ProblemAnalyzing with ANOVA By Wednesday, Decem

QUESTION

Assignment 2: Analysis ProblemAnalyzing with ANOVA
By Wednesday, December 8, 2010, post your results to the M6: Assignment 2 Dropbox.
Calculate a two-way ANOVA for the following situation. Suppose you are a school psychologist in a classroom setting and you want to find the effect that five teaching styles have on three types of learning activities with respect to knowledge gained. Answer the following questions:
What are the independent variables, and what are the dependent variables?
What would be an appropriate null hypothesis?
What is the research design?
What is the measurement instrument?
What is the confidence level?
What are the f values using the following data?
The data that actually appears in the table are samples; two samples from each treatment group were taken. (Do not be concerned with the specific meaning of the data, as this is used as an example so that you concentrate on the process of using this version of ANOVA.)
Teaching Style 1 Teaching Style 2 Teaching Style 3 Teaching Style 4 Teaching Style 5
Learning Activity
A 106, 110 95, 100 94, 107 103, 104 100, 102
Learning Activity
B 110, 112 98, 99 100, 101 108, 112 105, 107
Learning Activity
C 94, 97 86, 87 98, 99 99, 101 94, 98
There is an f test for each of the hypotheses, and the f test is the mean square for each main effect and the interaction effect divided by the within variance. The numerator degrees of freedom come from each effect, and the denominator degrees of freedom is the degrees of freedom for the within variance in each case.
It is assumed that main effect A has a levels (and A = a 1 df), main effect B has b levels (and B = b 1 df), n is the sample size of each treatment, and N = abn is the total sample size. Notice the overall degrees of freedom are once again one less than the total sample size.
Data from the question Teaching Style 1 Teaching Style 2 Teaching Style 3 Teaching Style 4 Teaching Style 5 Learning Activity 106, 110 95, 100 94, 107 103, 104 100, 102 A Learning Activity 110, 112 98, 99 100, 101 108, 112 105, 107 B Learning Activity 94, 97 86, 87 98, 99 99, 101 94, 98 C (a) The independent variables are the type of learning activity and the teaching style. The dependent variable is the knowledge gained. There are 3 levels for the factor œLearning activity and 5 levels for the factor œTeaching style (b) Null Hypothesis (H0): There is no significant difference between the three types of learning activities, no significant difference between the five teaching styles and there is no interaction between learning activities and teaching styles (c) The research design is measuring the knowledge level and conducting a 2-factor ANOVA to check if there is a significant difference between the main levels and if there is an interaction. (d) The measurement instrument could be a test or a quiz given to the subjects in this experiment (e) We can use a 95% confidence level, so that = 0.05 (f) Factor 2 Teaching Style 1 Teaching Style 2 Teaching Style 3 Teaching Style 4 Teaching Style 5 Factor 1 Learning Activity 1 106 95 94 103 100 110 100 107 104 102 Learning Activity 2 110 98 100 108 105 112 99 101 112 107 Learning Activity 3 94 86 98 99 94 97 87 99 101 98 From the¦

NOVA table, we note that the p-value for Factor 1 is 0, and that p-value for factor 2 is 0.0001. Since these are < 0.05, both the factors are significant. There is significant difference between learning activities and significant difference between teaching styles. Since the p-value for interaction is 0.1221 (>0.05), there is no significant interaction between learning activities and teaching styles. ANOVA OUTPUT FROM EXCEL Two factor ANOVA Factor 2 Means: Teaching Style 1 Teaching Style 2 Teaching Style 3 Teaching Style 4 Teaching Style 5 Learning Activity 1 108.0 97.5 100.5 103.5 101.0 102.1 Factor 1 Learning Activity 2 111.0 98.5 100.5 110.0 106.0 105.2 Learning Activity 3 95.5 86.5 98.5 100.0 96.0 95.3 104.8 94.2 99.8 104.5 101.0 100.9 ANOVA table Source SS df MS F p-value Factor 1 512.87 2 256.433 28.28 .0000 Factor 2 449.47 4 112.367 12.39 .0001 Interaction 143.13 8 17.892 1.97 .1221 Error 136.00 15 9.067 Total 1,241.47 29

ANSWER:

CLICK REQUEST FOR  AN EXPERT SOLUTION