Statistical Analysis: Independent and Correlated Samples T-Test

This report provides a detailed analysis of the T-test, an inferential statistical test used to determine if there is a significant difference between the means of two groups of data. It distinguishes between directional and non-directional tests, explaining how each is used to predict or simply identify the effect of an independent variable on a dependent variable. The report further differentiates between independent sample T-tests, which compare means from different populations, and correlated sample T-tests, which compare means from the same population under different conditions. Practical examples are provided, including an analysis of the effect of noise levels on intellectual performance and a comparison of weight loss programs. Both examples include the results of one-directional T-tests, demonstrating the significant differences observed and referencing the use of independent measures tested by T-Test with p-values less than 0.05. The document concludes with a list of references.

T-TEST ANALYSIS
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T.TEST ANALYSIS
The t-test is an inferential test used to determine whether there is a significant difference
between the means of two groups of data(Mertler & Reinhart, 2016). Usually, it has one
dependent variable and one Independent variable. The research wants some degree of confidence
that the difference between the two variables is not by chance
There are two types of t-test; directional and non-directional tests. The non-directional
test usually predicts that the variable will have an effect on the dependent variable but the effect
is not specified, It does not show the direction of difference but rather the difference alone(Ary et
al; 2018). An example of this to test the significant difference between males and females in
math performance, only the performance difference will be established.
The directional test also know as one-tailed test predicts the nature of the effect of the
independent variable on the dependent. It shows the direction of the difference variable.
Example: do male students perform better than female students in maths, this will show the
difference in mean and state which group performs better than the other.
Independent sample T.Test compares sample means from different populations regarding
the same sample variable(Bushmitch & Cozby, 2016). Example the test seeks to determine if the
difference in the hours spent by married respondents and those spent by single respondents is
significantly different or occurred by chance.
Correlated sample test compares a certain number of sample means from the same
population measured under two different conditions or a certain number of matched pair
measured under condition A and the other under condition B(Ary et al; 2018). Example, could

T-TEST ANALYSIS
massage therapy affects performance, the sample performance is tested before the massage and
after the message.
LOW NOISE LOUD NOISE
8 5
7 4
7 4
6 4
7 3
The above test is one directional test since we can determine the difference in means of
the loud noise and the low noise.
There is a significant difference in the effect of noise on performance on the intellectual
task. Intellectual performance in low noise (M=7) was significantly lower than intellectual
performance in loud noise (M=4)the difference was found by independent measures T.Test p
value<0.05
Participant calorie reduction fat reduction
1 3 6
2 4 6
3 3 3
4 5 7
5 2 4
6 5 6
7 3 7
8 4 6
This is a correlated sample test the T.Test is one directional

The was a significant difference between the weight loss using the Fat reduction program
(M=3.65) than for the calorie reduction program (M=5.625). The difference was found to be
significant using independent measures tested by T.Test p-value <0.05
REFERENCE.
Ary, D., Jacobs, L. C., Irvine, C. K. S., & Walker, D. (2018). Introduction to research in
education. Cengage Learning.
Bushmitch, D., & Cozby, R. (2016). U.S. Patent Application No. 14/499,297.
Mertler, C. A., & Reinhart, R. V. (2016). Advanced and multivariate statistical methods:
Practical application and interpretation. Routledge.