2. Carrying out statistical tests: Differences

Question 1

statistical test for differences -> T-tests

-> Test for measurements

Answer 1

• > mean different from actual value
• > means of two measurements of sample sample different
• > mean of different sample different
• > mean of experimental group different from control

Question 2

The problem with statistical tests -> weird logic

Answer 2

1. ) Null hypotheses -> there is no real effect
2. ) measure how big the found effect is
3. ) determine how likely the actual effect is to occur in sample if no real effect in population

4.) If probability is more than 5 % -> accept null hypothesis -> effect is significant
If probability less than 5 % -> reject null hypothesis and accept alternative hypothesis -> effect is significant

Question 3

One-sample t-test

Answer 3

This tests whether the mean value of a measurement is different from an expected value E.

It is calculated how many standard errors the actual mean is from the expected mean. The further away it is, the less likely it happened by chance.

t = (Sample mean (x) - E) / Standard error

If p > 0.05 -> greater than 5 % probability of this happening by chance -> no evidence to reject null hypothesis
If p < 0.05 -> less than 5 % probability of chance -> reject null hypothesis and accept alternative hypothesis -> mean is significantly different from expected value E.

t generally has to be greater than around 2 or less than -2 for difference to be significant.

Question 4

Paired t-test

Answer 4

Test whether the mean value of two measurements made on single sample of identifiable individuals are different.

Example:

• > patients before and after treatment
• > plant during the day and night
• > reaction time with left and right hand

This test has two stages:
1.) the difference needs to be calculated between two measurements
2.) a one sample t-test is used to determine the mean difference. D is different from zero.
There is N - 1 degrees of freedom -> number of pairs of measurements

t = mean difference / SE of difference

Question 5

Error bars

Answer 5

overlapping -> not significantly different

no overlapping -> may be significantly different

Question 6

Two sample t-test

Answer 6

test whether the mean values of measurement on two separate samples are different.

1.) Calculate difference of means
2.) compare with measurement of variability of difference between the means.
SE of difference = √(SE1 squared + SE2 squared)

Example:
(Mean of women - mean of men) / √(SE1 squared + SE2 squared)