Sample of 72 Caucasian male dentists aged 35-44 years: xbar=127 and s=7.
Hypotheses: H 0 : =127mm Hg vs. H A : 127mm Hg.
Find that P-value for this one-sample t-test is 0.279.
Since P-value > 0.05, we retain H 0 , i.e. the sample was drawn from a population where =127.
We say that there is not a significant difference between the sample mean and the population mean at the 5% level i.e. the blood pressure of male dentists does not differ significantly from other men.
Independent-samples (or unpaired) t-test: Test if the population means estimated by 2 independent samples differ significantly (e.g. group of male and group of females) example
Is the average height between males and females enrolled in EBD1 significantly different?
Females: xbar=164.7, s=5.92, n=58
Males: xbar=177.6, s=7.27, n=31
Do these data support the contention that male and female EBD1 students differ in average height?. The hypotheses are H 0 : 1 = 2 and H A : 1 2
Results: An independent samples t-test in SPSS produces a P-value<0.0001 indicating that there is evidence that males and females differ significantly in mean height (males being taller). The small P-value indicates that there is a very small probability that this difference occurred by chance.
Suppose I gave you all the EBD1 test before lectures and tutorials commenced. After attending the 6-week EBD1 unit, suppose I gave you the EBD1 test again.
I end up having, for each of the 119 students in the class, 119 pre-test and 119 post-test scores. I subtract the pre-test score from the post-test score to obtain an improvement (hopefully!!) for each student. These 119 differences form a single sample.
To assess whether attending the EBD1 course significantly improved students comprehension of EBD, we test H 0 : =0 vs. H A : >0
H 0 says that no improvement occurs, while H A says that post-test scores are higher on average. We calculate the mean difference in the sample and the standard deviation.
Hopefully, a P-value<0.05 is obtained so we can reject H 0 of no difference and conclude that the improvement in test scores was unlikely to have occurred by chance alone and therefore there is strong evidence that the EBD1 course was effective in raising the scores!
An ANOVA (Analysis of Variance), sometimes called an F test, is a test that measures the difference between the means of two or more groups
It is closely related to the t test - the major difference is that, where the t-test measures the difference between the means of two groups , an ANOVA tests the difference between the means of two or more groups .
For i groups, the null hypothesis is: H 0 : 1 = 2 = 3 …. = i ..(all group means in the population are equal
H A: At Least 1 group mean in the population differs from the others