standard deviation and t-test

Question 1

what is standard deviation used to measure?

what does a smaller and larger value mean

Answer 1

-measure of variation, spread from the mean of the results

-smaller SD = less variation, data in a narrow range, points close to the mean= could be more reliable

-larger SD= more variation, greater range could be less reliable

Question 2

explain the standard deviation equation

Answer 2

√(∑(x−¯x)^2 divided by n-1)

x−¯x = subtract mean from each sample

n= number of samples

Question 3

what is a t-test used to measure?

paired vs unpaired?

Answer 3

-if there is statistically significant difference between two means when sample size is less than 25 and data is nromally distributed

unpaired- two unrelated sets of data e.g 2 different sample sites

paired- measuring effect of treatment before and after e.g heart rate before and after exercise for same individual

Question 4

explain the unpaired t-test equation

Answer 4

t= (¯x1−¯x2) / √(s1^2/n1) + (s2^2/n2)

¯x 1 = mean of first sample
¯x 2 = mean of second sample
s1 = standard deviation of 1st sample
s2 = standard deviation of 2nd sample
n1= number of measurements in first sample
n2= number of measurements in second sample

Question 5

explain the paired standard deviation equation

Answer 5

t= ¯d√n / Sd

¯d = mean of difference between the first and second result
n= number of samples
Sd= standard deviation of the differences

Question 6

what does it mean when the t value is much greater than the critical value at p=5%

Answer 6

there is a significant difference before and after treatment and as such we can reject the null hypothesis