Independent Samples T-Test and ANOVA

Question 1: Independent Samples T-Test

The independent sample T-test is a statistics of choice when making simple straight forward comparisons that involves two independent samples. An example is a situation when we are studying the effects of standardized algebra test on senior school students. Here we are aiming to find out if there is any significant ‘Gender’ difference in performance of the students in the test. Our independent variable is ‘Gender’ measured by both “Male” and “Female” which form our samples. Therefore the group membership doesn’t overlap and makes the comparison of the dependent variable to be made between the two groups. The independent variable is the one that is being manipulated while the dependent variable is the factor being measured where in our case is the ‘standardized algebra test scores’ (Howell, 2010).

To begin the t-test, we first have to clearly label the ‘factors’ in the study that is our independent and dependent variables. Then we make a table to record the results of each student and their respective scores. Our aim is to find out if the mean tests of our samples scores are significantly different from one another (Keselman, Othman, Wilcox, & Fradette, 2004). We then calculate the mean of each sample, then the variance of the groups. The T-test value is gotten by dividing the difference between group means or averages with the variability of the groups. Note that you have set a value called alpha level or the confidence level which takes care of the risk level whereby in social research it is recommended to use an alpha value of 0.5. Then you can check the calculated value in the t-tables taking care of the alpha value. Then you may plot the values gotten as this gives a good visual presentation and easy interpretation of the results (Lowry, n.d.).

 

Question 2: Analysis of Variance (ANOVA)

Analysis of variance popularly known as ANOVA is a statistical procedure used to compare two sample means and the results can be used to infer that the means of the corresponding population distribution do differ. While in t-test only two samples distribution are compared, ANOVA can be used to compare more than two variables that require complex statistical measures to be used. This is used when one independent variable has over two levels or means. One way ANOVA is usually more appropriate to use in this case rather than multiple t-tests because ANOVA is a more robust measure that allows the user to avoid inflated alpha that may lead to “Type 1 error” (Hutchinson, n.d.).

If we were to conduct a study on high school students’ opinions of the quality of cafeteria food and a scale of 1 to 10 is used (where 1 = ‘worse than dog food”, 10 = ‘pretty perfect’) ANOVA is a more appropriate tool for the analysis. So in this study our main aim is to measure the difference in grading of cafeteria food in the different students grade levels. Our independent variable is therefore “grade level” and the dependent variable being “rating cafeteria food”. Therefore we can calculate a one way ANOVA test for this data. The F-score and the P-value calculated will indicate whether the effect of the independent variable is significant (Hutchinson, n.d.).

The limitation of ANOVA is that it computes all the values simultaneously and therefore cannot tell us where individual differences that affect rating of “cafeteria food” in terms of which grade had the most difference. This necessitates for additional tests to be latter carried out to find out the individual differences in the contribution of each grade in rating cafeteria food and these tests will include independent t-tests (Howell, 2010).

REFERENCES

Howell, D. C. (2010) Fundamental statistics for the behavioral sciences, 7th edition, Belmont, CA: Thomson/Wadsworth

Hutchinson, T (n.d.) ‘ANOVA applied to examination scores’, vol. 49, no. 3 (2000), p. 104, EBSCOhost, viewed 15 September 2012.

Lowry, R. (n.d.) T-test for the significance of the difference between the means of two independent samples, [online], retrieved 15 September 2012 from http://vassarstats.net/textbook/ch11pt1.html

Keselman, H, Othman, A, Wilcox, R, & Fradette, K (2004) ‘Research Article The New and Improved Two-Sample t Test’, Psychological Science (Wiley-Blackwell), 15, 12, pp. 47-51, Academic Search Premier, EBSCOhost, viewed 15 September 2012.

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