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One Way ANOVA Does coffee help people become sober more quickly after drinking too much? A sample of 40 volunteers were randomly assigned to 1 of 4 groups of 10 subjects each. One of these groups serves as a control and received no alcohol. Subjects in each of the other 3 groups drink a fixed amount in 1 hour period. The next 1/2 the subjects in the second group drink 2 cups of decaffeinated coffee, and subjects in the third group drinks 2 cups of regular coffee,& subjects in the 4th group drink 2 cups of water. Finally, all subjects are given a reaction-time test to determine mental alertness with the lower the score on the test, the quicker the reaction time and thus greater alertness. Use alpha=.05 to determine the statistical significance.

a. What are the independent & dependent variables for this study? Independent: Participants Dependent: Scores

b. Why did the researcher randomly assign the subjects to the four groups? The purpose of random assignment is for internal validity. (Random selection is external validity.)

c. Prior to examining whether the group means differ it is necessary to test the assumption of homogeneity of variance. 1. Do we meet this assumption? The sig level from the test of Homogeneity of Variances is larger than the α level. sig=0.550 > α=0.05 therefore we fail to reject the null hypothesis.

2. What specific information on the printout did you use to come to this conclusion? We used the sig (.550) in the Test of Homogeneity of Variances.

3. What are the other assumptions that underlie the application of analysis of variance procedures? Population normally distributed, 3 or more independent groups, variances are equal

d) 1. Is the average reaction time the same for all four groups?  sig = .014 < α = 0.05 therefore we reject.

2. What specific information on the printout did you use to come to your conclusion? We used the sig in the ANOVA table to find that sig = .014 < α = 0.05. Therefore there is a    difference.

e) The ω2 = .186 for these data. What does this represent?        W2 =  SSB - (K - 1)(MSw) divided by  SST + MSw                   = 2107.500 - (4-1)173.789/8363.9 - 173.789       = 0.19     18.6% of the proportion of variance in dependent variable (reaction time) is associated   with    the methods used.

f) According to the Tukey results on the attached printout, what pairs of groups differ?  Groups 2,3 and 2,4    Groups 3,2 and 3,4       (Look at the Sig. in the Tukey table and compare to alpha (0.05). g) To whom, if anyone, can we generalize our findings?  You cannot generalize to anyone due to the subjects being volunteers.

h) Write a brief results section describing the findings of this experiment based on the analysis you have just completed. You do NOT have to present results in tables.

A One way ANOVA was used to determine the mental alertness of subjects who drank coffee after drinking too much alcohol.The independent variable represented the different types of groups: 1)subjects who reieved no alcohol, 2) subjects who drank 2 cups of decaffinated coffee, 3) subjects who drank 2 cups of regular coffee, and 4) subjects who drank 2 cups of water. The dependent variable was the score measuring the results based on the subjects. See table 1 for the means and standard deviations for each of the four groups. The test for Homogenity of variance was not significant Leveene (3,36) = .715 (F stastic); p (sig level)> alpha 0.05) indicating that this assumption underlying the application is met. The Oneway ANOVA of reaction time revealed a statiscally significant main effect (F(3,36)=4.042; p<0.05) indicating that not all 4 groups have the same reaction time. The W2 = 0.19 indicates that approximatley 19% of the variance in reaction time is attributed to differences between the 4 groups of students. Post hoc comparisons using Tukey procedures were used to determine which pairs of the 4 groups differed. The results indicated that subjects in group 2 (M=212.30) precieved higher gains that did subjects who drank water (group 4) (M=211.50) or subjects who drank regular coffee (group 3). The effect size of these two significant effects were 1.39, 1.25, 1.22.

Assistantships 1. What are the independent and dependent variables for this study? Independent: Assistantship Status    Dependent: Scores (Perceptions of Gains)

a. What is the purpose of random selection of subjects? "The purpose of random selection of the subjects is to give a generalized ability (external    validity)."

b. What was the purpose of random assignment of subjects to groups? "The purpose of random assignment of subjects is for internal validity."

2. Prior to examining whether the group means differ it is necessary to test the assumption of homogeneity of variance. Do we met this assumption? -Look at sig in Test of Homogeneity and compare to alpha. If the sig is larger than the alpha, then yes, we meet the assumption of homogeneity of variance. "Sig = 0.596 > alpha = 0.05 Yes, we meet homogeneity of variance." "Therefore, we fail to reject the null hypothesis.  Ho = M1 = M2     Ho = M1 ≠ M2" What specific information on the printout did you use to come to this conclusion? "The sig in the Test of Homogeneity was used to come to this conclusion."

3. The first question we'd like answered is whether all groups are the same in their perceptions of gains. This is answered by conducting a Oneway Analysis of Variance using assistantship status as the independent variable and perception of gains as the dependent variable. OR Is the average reaction time the same for all four groups? What is your conclusion from this analysis? - Look at the ANOVA table then at Sig. "p=.001 < α = 0.05 therefore we reject." What specific information on the printout did you use to come to your conclusion? "The OneWay ANOVA tells us that the sig (0.01) is less than the alpha = 0.05. Therefore, there is a difference between the groups."

4. What is the proportion of the variance (W2) in perception of gains is function of experience in assitantships? W2 = SSB - (K - 1)(MSw) divided by SST + MSw "36% of the variable in gains can be explained by assistantship status. 36% of the perceptions of gains."

5. Assuming that you concluded that all 4 groups were not the same in their perceptions of gains,which pairs differ? Use the Tukey post hoc to answer this question and calculate effect size for those pairwise differences. - Use the Mean under Descriptives. Put the numbers in order from lowest to highest. - Use Q = (X1 - X2) divided by square root of MSw/n 7.00    9.50     12.25     16.00                  7.00                          9.50        2.5     -                 12.25      5.25     2.75    -                 16.00      9.00     6.50     3.75      -

"If Q > Q(cv) then there is a difference." Q(cv) = alpha, df, df2 = ____ (Use the table to help.)"

Post hoc comparison using Tukey procedures were used to determine which pairs of the four groups differed. The results indicate that that students who had received both research and teaching assistantships (M = 16.00) perceived higher gains that did students who had received only a teaching assistantship (M = 9.500) or students who had no assistantship experience (M = 7.00). The effect sides for these two significant effects were 1.587 and 2.198, respectively, indicating the groups differed by more than 1.5 and 2 standard deviations. 6. Do students who work as grad assistants, perceive greater gains than those who do not? Use the Scheffe test to compare first three groups combined (students with assistantship experience) with last group(those with no experience). (1+2)-3=0 (1-3)+2=0 (2-3)+1=0 (1-2)+3=0 (3-1)-2=0 (3-2)-1=0

7. Do students who have served as a research assistant differ in perception of gains from those who have not been a research assistant? Use Scheffe to compare the first two groups combined with the last two groups combined.

8. Can we assume that the type of assistantship experience caused the group differences we observed? "No, because there was no random assignment of the groups."

9. To whom, if anyone, can we generalize our findings? - Always deals with external vadility. "We could generalize back to the students in the groups."

10. What are your substantive conclusion based on these anyalyses? "RARA & TA (GR 1 & 2) received greater gains, than those who were only TA's.     Students who were RATA had greater gains than those who did neither experience."

11. Write a brief results section describing the findings: A Oneway Analysis f Variance (ANOVA) was used to examine the question of whether students' experiencing different types of assistantships durin their graduate program perceived different levels of growth and development. The independent variable represented the different types of assistantship experience with four groups represented: (1)students having had both research and teaching assistantships, (2) students having had only research assistantships; (3) students having had only teaching assistantships; and (4) students having no assistantship experience. The dependent variable was a scale measuring perceptions of gains as a result of graduate school. See Table 1 for the means and standard deviations for each of the four groups. The test for homogeneity of variance was not significent (Levene ((df1)=3,(df2)=28) = .639 (Look under Levene)(F stastic); p (sig level)>0.05) indicating that this assumption underlying the application of ANOVA was mt. The oneway ANOVA of students' perceptions of gains revealed a statistically significant main effect (F(3,28) = 7.104 (look at F in ANOVA table); p< 0.05) indicating that not all four groups of graduate students perceived the same levels of gains. The ŵ2 = .364 indicated that approximately 36.4% of the variation in perception of gains is attributable to differences between the four groups of students. Post hoc comparison using Tukey procedures were used to determine which pairs of the four groups differed. The results indicate that that students who had received both research and teaching assistantships (M = 16.00) perceived higher gains that did students who had received only a teaching assistantship (M = 9.500) or students who had no assistantship experience (M = 7.00). The effect sides for these two significant effects were 1.587 and 2.198, respectively, indicating the groups differened by more than 1.5 and 2 standard deviations.

Multiple Regression 1. Does multicollinearity appear to be a problem? Why or why not? - Goto the VIF in the Collinearity Stats. If the VIFs are less than 10, you do not have a   problem. "No, because all VIFs are less than 10."

2. Does the set of independent variable explain a significant proportion of the variance in student achievement? What info did you use? - Goto the ANOVA chart. - Look at sig. If P < sig (0.05) then its significant. "Yes, the sig value on the ANOVA table (p = ___) < sig (0.05) is less than alpha."

3. What proportion of the variance in student achievement is explained by the set of independent variables? What did you use to determine your answer? - Look at the Correlations table and look at R square. "45.4% of the vairance in student achievement is explained by the set of independent   varables. R2 = 0.453 (model summary)"

4. Which of the independent variables have a significant influence on student achievement? What particular information on the printout did you use? - Look at the sig values on the coeffecients chart. Must be < sig (0.05). " All independent variables except values (0.963) have a significant effect on student  achievement."

5. What is the relative importance of the independent variable in their influence on student achievement? What particular information on the printout did you use? - Look at the coefficients chart and at the t column. Rank by highest to lowest. "Self concept (5.976), Independent (4.407), emphasis (3.508), ses (2.583), ethnic (2.446)      The t column in the coefficient chart was used."

6. Are family socialization practices (EMPHASIS and INDEPEND) more important than family background (SES) in influencing student achievement? Why or why not? - Look at B in unstandardized coefficients. Only look at the 3 mentioned and write the gain. "Yes, they have a larger Beta. For every change in independent there is a gain of 1.228.       For every change in ethnic there is a gain of 4.643. for every change in SES, there is a gain     of 0.940."

7. How do you substantively interpret the coefficient for ETHNIC? Explain. - Look at the B in unstandardized coefficients. "Hispanic students usually score 4.643 points higher than white students."

SAMPLE RESEARCH SCENARIOS An experimental psychologist wants to test the hypothesis that memory for pictures is better than memory for words. The psychologist performs an experiment in which one group of students views 30 slides with words and another group views 30 slides with pictures. Students are then given a recall test. T-TEST

An educational researcher is interested in determining the relative influences of socioeconomic background, educational aspriations, ability, and gender on academic achievement. MULTIPLE REGRESSION

The federal government is interested in testing whether an advertising campagin for gasoline conservation is effective. For a sample of subjects, they record the amount of gasoline used in a one month period prior to the advertising campaign and then for one month following the campaign. T-TEST

A nutritionist wants to determine whether there are differences in the sugar conten of three different breakfast cereals. ONE WAY ANOVA A sales manager is interested in whether there is a relationship between the amount of money he spends on advertising each month and his net profit each month. He gathers data each month for two years. MULTIPLE REGRESSION