Stats test

Question 1

Why would you want to use statistical tests

Answer 1

• The reason is that we don’t know whether the difference is actually real! • The group is not the full population of people (e.g. all the people in the world imagining throwing balls), and we only have a small sample that we can test • There is always some measurement error (and other random factors), which can influence the results - maybe one of the four people was having an excellent day? • In other words, what if in reality, there is no difference, but the enhanced MEPs were just luck, i.e. were due to chance? • If the difference is just due to chance, then it should –on average –go away if we run this experiment many times (because random factors will average out)

Question 2

The t-distribution

Answer 2

• What can we use to represent the chance distribution? Is it the z-distribution?
• We can’t use a z-distribution because we would need to know the population
standard deviation –but that is exactly the problem, we don’t know anything about
the population… That’s what we’re trying to find out!
• Instead we use a t-distribution!
• The t-statistic takes into account both the expected mean and a measure of the
standard error of the mean based on the sample

Question 3

Formula for t distribution

Answer 3

t =M -m
sM

M= mean of the pop
m of the sample
sM The standard error of the mean

Question 4

Experimental design

Answer 4

1. We want to know if our group mean differs from some other specific value
   (e.g. the known population mean, the mean value we would expect if the result
   was due to chance etc.)
2. We want to know if two groups (often a “treatment” or “experimental”
   group and a “control” group) differ
3. We want to know whether measurements from the same group under
   different conditions (usually “treatment” and “control”) differ.

Question 5

One-sample design:

Answer 5

We have one group with values coming from different people. This is compared
to a single value.
Advantages:
- Can be used to compare group data to known values
Disadvantages:
- We may not always know population values
- We may want to compare two groups, or to investigate the change of
behaviour over time

Question 6

Between-groups/ independent-measures design:

Answer 6

• The measurements are independent
• We don’t have to worry about learning effects due to repeated exposure
  Disadvantages:
• People in the different groups might be quite different in various ways:
  Personality, motivation, level of schooling etc. We need large sample sizes to
  average out these effects, or we need to counterbalance all factors that we
  know might influence the results
• We cannot study behaviour over time

Question 7

Within-group design/ repeated-measures design

Answer 7

There is a single group which provides data for both conditions, i.e. the values
from each condition come from the same people
Advantages:
- We don’t have to think about differences in baseline factors such as
personality, motivation, schooling etc. because this will always affect both
conditions equally.
- We can study changes in behaviour over time
- We can usually test less people
Disadvantages:
- Measurements are not independent ➔we need to calculate the variance
differently
- People know the treatment after the first condition and can’t be naïve in the
second round. This might not work for every experiment
- We need to carefully counterbalance the conditions to avoid unwanted
order effects

Question 8

H0

Answer 8

H0 = Sample is drawn from a population μ = 10 (due to chance)
H1 = Sample is drawn from a population μ > 10 (not due to cvhance)
Remember: We will assume that H0 is true until we are sufficiently convinced that our
result is “very unlikely” under this hypothesis

Question 9

sM formual

Answer 9

sM =s
/n
s = standard deviation
sample
n = sample size

Question 10

standard deviation calculation

Answer 10

To get the standard deviation, we can calculate the variance and take the msquare root of the variance
You can simply calculate the variance “by hand” if you know all the single raw values from each participant X1 to X4 by calculating the sum of squared differences (SS)
s2=SS/d,f
d.f=n-1

Question 11

Non –directional hypotheses

Answer 11

• Much of the time in psychology you will be interested in whether there isany difference between the two things you are measuring
• For this we would use a non-directional hypothesis
• In our one-tailed t test example this would be something like:
H1 = Our sample is drawn from a population μ > 10 OR μ < 10
• In words that might sound like:
It was hypothesised that there would be a significant difference in MEPs
between performing a mental imagery task and at baseline.
• Of course, this does not really make sense for this experiment, but there are other experimental questions where you would use a non-directional hypothesis

Question 12

Directional hypotheses

Answer 12

• For a directional hypothesis, we would use a one-tailed test (this is what we
had in our original example):
H1 = Our sample is drawn from a population μ > 10
• In words this would look like:
It was hypothesised that MEPs would be significantly higher when
performing a mental imagery task, compared to baseline.
• Of course, it does not make sense to hypothesise the reverse in our example
experiment, but there are other experiments where you may also be
interested in a lower difference

Question 13

The independent-measures t test

Answer 13

Often we do not want to compare our measure to a fixed value. Instead, we want to know whether two groups, which are exposed to different experimental conditions, differ in a particular measure.

Question 14

Comparing Means

Question 15

effect of size measure

Answer 15

Question 16

conventional cut-off values suggested
by Cohen

Answer 16

d = 0.2 small effect (mean difference around 0.2 standard deviations)
d = 0.5 medium effect (mean difference around 0.5 standard deviations)
d = 0.8 large effect (mean difference around 0.8 standard deviations)

Question 17

Change in variation due to treatment

Answer 17

Question 18

important assumptions to consider before deciding whether
to run t tests on your data:

Answer 18

-ThrB) The populations from which the samples are drawn must be normal (however, this assumption can
be violated for larger sample sizes as t tests are quite robust)
A) If comparing two populations (independent-measures t test), the samples must have equal
variances (if the variances are not homogenous, calculating the pooled variance becomes a
problem; see Gravetter & Wallnau, Chapter 10, pages 314-315, for a solution)