Question

A study was conducted to compare the effectiveness of three teaching techniques in teaching English to Year 6 students. The three teaching techniques are – Using video clips, Using worksheets and Using flash cards. Equal number of students were randomly assigned to the three different treatments. The results are shown in the tables below:

		Scores in Statistics
Treatment	N	Mean	Std. Deviation	Std. Error
Using Video Clips	20	27.20	3.05	.96
Using Worksheets	20	23.60	3.31	1.04
Using Flash Cards	20	23.40	3.24	1.02

1. Describe the data shown in the table above.                                                 
2. What does standard error in the table above indicate?                      

Test of Homogeneity of Variances          Statistics Score
Levene Statistic	df1	df2	Sig.
.115	2	57	.802

3. Interpret the Levene Statistic in the table above.                                                                            

ANOVA

Statistics Score

	Sum of Squares	Df	Mean Square	F	Sig.
Between Groups	91.467	2	45.733	4.467	.031
Within Groups	276.400	57	10.237
Total	367.867	59

4. What can you conclude from the ANOVA table above                                  

Dependent Variable: Statistics Score

Tukey HSD
(I) Treatment	(J) Treatment	Mean Difference (I-J)	Std. Error	Sig.
Lecture with video clips	Lecture only	3.600	1.431	.046
	Small group	3.800	1.431	.034
Lecture only	Lecture with video clips	-3.600	1.431	.046
	Small Group	.2000	1.431	.989
Small group	Lecture with video clips	-3.800	1.431	.034
	Lecture only	-.2000	1.431s	.989

           

Explain the Tukey HSD results in the table above.               

Answer 1

a) The above table gives the total score , mean of scores , standard deviation and standard error of three different treatments video clips, worksheets and Flash cards.

From the table of descriptive statistic, the highest mean score treatment is Using video clips which is equal to 27.20 and lowest mean score treatment is Using flash cards which is equal to 23.40 and highest standard deviation is Using worksheets which is equal to 3.31 and lowest standard deviation is Using video clips which is equal to 3.05.

b) The standard error measures the deviation of sample mean from the population mean.

From the above table, the standard error of Using video clips is 0.96, This means that the sample mean of Using video clips is deviated from the population mean by 0.96 units.

From the above table the standard error of Using worksheets is 0.1.04, This means that the sample mean of Using worksheets is deviated from the population mean by 1.04 units.

From the above table, the standard error of Using flash cards is 1.02, This means that the sample mean of Using flashcards is deviated from the population mean by 1.02 units.

c) Levenr's test statistic is used to assess the homogeneity of variances for a variable calculated for two or more groups.

From the above table, the Levene's test statistic value is 0.115 and p - value is 0.802, since the p - value is greater than 0.05, so assumptions of homogeneity of variances is met.

d) From the ANOVA table, the value of test statistic is 4.467 and the p-value is 0.31, which is less than 0.05, so there is sufficient evidence against the null hypothesis, Hence, we conclude that at lest one of the treatment means is significantly different from the otheres.

(e) Tukey HSD is used to test whether the pair of treatment means is significantly different from each other or not.

From the tukey HSD table, we see that the significant value of each pair of treatments is less than 0.05 , so we conclude that each pair of treatments differ significantly from each other.