Question

Compare and contrast the differences between a single sample t test and an independent samples t test. Next describe a hypothetical study using the design of an independent samples t test. List the two groups that you would test.

Answer 1

Diffrences

Sr.no	Single Sample t test	Independent sample test
1	Consists of only one sample	Consists of two samples that are independent and unrelated to each other
2	In hypothesis testing the mean is compared to a predefined value.	In hypothesis testing the mean of first sample is compared to the mean of second sample to determine whether there is significant diffrence between the two samples.
3	assumption of variance does not hold in single sample t test as we have only one sample.	Before performing the t-test the assumption of homoegeneity of variances should be satistified (variances of the two groups should be equal)

Similiarities

1) Both tests are used to compare means

2) The dependent variable (that is the observations in the sample or samples) should be measured on a continuous scale.(Ratio or interval scale)

3) Observations should be independent of each other.

4) the dependent variable should be approximately normally distributed.

Example of independent sample t test

Independent sample t test can be used to test whether final year students marks differed based on their gender.

so here we will have two samples

sample 1 : Marks of final year Male students

sample 2 : Marks of final year Female students

Marks: dependent Variable

Gender : Independent variable

we will test the hypothesis that

H0 : $\mu$ 1=$\mu$2 (Average marks obtained by male students is same as average marks obtained by female students)

against any one of the alternative hypothesis

H1 : $\mu$ 1$\neq$$\mu$2 (Average marks obtained by male students differs significantly from average marks obtained by female students)

H1 : $\mu$ 1>$\mu$2 (Average marks obtained by male students is greater than average marks obtained by female students)

H1 : $\mu$ 1< $\mu$ 2 (Average marks obtained by male students is less than average marks obtained by female students)