Question

1. What is the null and alternative hypotheses for a one tailed “greater than” test?
2. In general, if some data we are working with is not normal, what one-sample test would you use (assume transformations do not work)?
3. What are the assumptions for a one sample t-test?
4. What are the assumptions for a two-sample t-test?
5. In terms of coding, what is different between the two-sample t-test and the Welch approximation?
6. Why would we use a paired t-test? Compare the two-sample t-test to the paired t-test.

Answer 1

1. One tailed is test where we check the sample mean is the correct estimate of population mean, under certain level of significance

Null hypothesis : The mean of the population is mu is equal to any value mu_o ( say ) , mu = mu_o

Alternate hypothesis : The mean of the population is mu is greater than the value mu_o ( say ) , mu > mu_o

in case of data not being normal, for one tailed, we will use t test

where, t = ( x_bar - mu_o ) / ( SE(x_bar)*(n-1)^1/2 ) , where X_bar is sample mean, SE(x_bar) is standard deviation of x_bar and n is sample size

Assumptions for one sample t test:

data should be continuous or ordinal

sample should be random

sample size should be less ( n < 30 )

population should follow normal distribution

Assumptions for two sample t test:

data should be continuous or ordinal

sample should be random

sample size should be less ( n < 30 )

population should follow normal distribution

variance of the two samples should be same ( homogeniety of variance )

In terms of coding one sample t test is performed using command

t.test( x,y ), when it is two sample t test, for x and y

when Welch test is used an additional command, var.equal = FALSE is used

.t.test( x,y ,var.equal = FALSE), when it is two sample t test, for x and y and variance are not equal

paired t test is used when we check the difference of the sample sample before and after any operation, for example, before and after weight of sample on a diet

So, in paired t test we check for the significance difference between the before and after effect of treatment whereas in two sample t test we check for the overall difference in means of to samples.

In paired t test same sample value is tested twice before and after the treatment, whereas in two paired t test two different sample values are taken