week 3- Data analysis comparing means Flashcards
distribution of the mean of the sample
less variance than population mean
what standard deviation is used to measure the sample mean
the standard error
hypothesis testing
- H0 is the null hypothesis and H1 is the alternative hypothesis.
- Initially, you assume the null hypothesis is true and, on this basis, calculate the probability of measuring a sample mean (M) greater or equal to what you actually did measure.
- If this probability is very small, you conclude that H0 cannot be true, and reject it in favour of H1.
calculating the probality
Initially, you assume that H0 is true (i.e. you assume that μ = 170 cm) and calculate the t statistic based on this assumption
t= m-u/sm
sm= s/ squrt-n
The t statistic represents how much greater (or less) the sample mean (M) is than the hypothetical mean (μ = 170 cm), relative to the standard error.
If the value t statistic is large that implies, relative to the standard error, the difference between M and μ is large.
Crtical Values of the t statistic
How large must the t statistic be for you to need to reject H0 in favour of H1?
You determine this critical value by looking it up in a t table
What is a Significance Level?
-This significance level indicates the probability that, if you reject the null hypothesis, you do so incorrectly.
-In other words, it is probability that you have made a type 1 error (i.e. saying that the null hypothesis H0 is false when it is in fact true).
-Obviously, the greater the critical value for the t statistic, the less likely you are to make a type 1 error.
If the mean of your sample (M) is 10 standard errors of the mean (sM) greater than the hypothetical population mean (μ) you can be much more confident in rejecting -H0 than if it is only one standard error of the mean (sM) greater than the hypothetical population mean (μ) .
One-tailed or two-tailed test?
-If the H1 states that the mean will be greater than the hypothetical population average, then you need to perform a one-tailed t test.
-Similarly, if the H1 states that the mean will be less than the hypothetical population average, then you need to perform a one-tailed t test.
However, if H1 states that the mean is simply different (i.e. might be greater or might be less than average) then you need to perform a two-tailed t test.
Degrees of Freedom
-To calculate the t statistic you need to estimate you variance of the sample.
-When your sample has only a few degrees of freedom (i.e. you have not sampled many individuals), your estimate of the variance is not likely to be accurate.
-Thus, to keep the probability of making a type 1 error constant, you need to have a more conservative test – -one with a larger critical value for the t statistic.
This is why the critical values of the t statistic increases as df decreases.
Effect size
Do this always (regardless of whether your result is significant or not).
While the t statistic varies depending on how many people you sample, ideally you want the effect size measurement to be independent of the number of people you sampled.
There are number of different effect size measures (e.g. Cohen’s d).
one of them is the- the percentage of variance accounted for by the treatment and is denoted by r2
effect size
r2=t2/t2+df
You can (roughly) interpret r2 as follows
r2=0.01- small effect
r2=0.09- medium effect
r2= 0.25 large effect
this is only a rough guide
repeated measures test
- You can only do this t test when:
- There are two conditions
- Each sample in one condition can be paired with another sample in the other condition
- Most commonly occurs when you have the same subjects in both conditions
- For each subject, you subtract condition 2 from condition 1 to obtain a single difference score for each subject.
- You then perform a one-sample t test on this difference score to test whether this difference is equal to a certain amount (usually zero).
Independent Measures t test
As always, you start by making two hypotheses
H0: The means will be the same in the two conditions
H1: The mean of condition 1 will be greater than the mean of condition 2.
single sample t test
Tests to determine if the mean of a sample (M) is equal to a constant (μ
repeated measures t test
Tests to determine if the mean difference between two repeated measures (MD) is equal to a constant (μ), which is almost always assumed to be zero. If μ = 0, the test is for whether the mean is the same in both conditions
