inferential statistics Flashcards
using something that can be observed (from a sample) to make an inference about something that cannot be observed (an entire population)
when we analyse our data we assume there is/is no difference between our experimental groups.
is no difference
how do we calulate the probability
calculate probability of observing differences in sample if there is no difference between populations
As the t-value gets bigger, the probability gets..
smaller
If it’s less likely that the null hypothesis is correct, is it more or less likely that the results are due to actual differences between our two experimental groups?
more
is the t value is the largest what does that mean about the null hypothesis
the null hypothesis is least likely to be correct
As the t-value gets bigger, the probability of observing our results if the null hypothesis is correct gets…
smaller
the t value helps us find the probability of….. our results, if the null hypothesis is ……..
the t value helps us find the probability of OBSERVING our results, if the null hypothesis is CORRECT
The smaller the t-value, the bigger the probability of the null hypothesis being…
incorrect
the t value gets ….. as the probability of observing our results gets …..
the t value gets BIGGER as the probability of observing our results gets SMALLER
steps for sign test
work out type of hypothesis
work out the signs for each number
add up all the pluses and the minuses, discards =
the lowest of the + and - is the S value
N is total minus the equals
find critical value for 0.05
significiance statement
how to word a significance statement for the sign test
the s value is…… and which higher/lower/equal to the critical value of ….. wmt the difference is not/is significant
lower/equal is significant
higher is not significant
what could be a reason that data is ordinal and not interval
you cannot assume the data is ordinal because eg verbal errors cannot be assumed of equal size
what does p<0.05 mean
probability is less than 95% suggesting the results are not due to chance
what are the 3 factors that affect the t value
difference between means
dispersion of the data
size of samples
how can the difference between means affect the t value
The bigger the difference between the means of two samples, the bigger the t-value
As the difference between the means get bigger, the probability of observing our results if the null hypothesis is correct gets…
smaller
the bigger the difference between the means, the …. the probability of observing our results if the null hypothesis is correct.
smaller
As the dispersion of the samples’ distributions gets bigger, the t-value gets…
smaller
The bigger the dispersion, the … the probability of observing our results if the null hypothesis is correct, and so the …. likely it is that the null hypothesis is correct.
bigger, more likely
The bigger the dispersion, the …… the t-value.
smller
The bigger the dispersion, the …. likely it is that our null hypothesis is correct.
more
The smaller the t-value, the …. likely it is that our null hypothesis is correct.
more
The smaller the dispersion, the bigger the probability of observing our results if the null hypothesis is incorrect. true or false
true
The smaller the t-value, the more likely it is that our null hypothesis is correct. true or false
true
The bigger the dispersion, the less likely it is that our null hypothesis is correct. true or false
false
As the sample size increases, the t-value gets..
biggger
As the sample size gets bigger, the probability of observing our results if the null hypothesis is correct gets…
smaller
so the less likely null is correct
As the sample size decreases, it becomes ….. likely our null hypothesis is correct.
more
probabilities are always expressed as either…
fractions
percentages
a number between 0 and 1
If a t-value gives a probability of 0.03 this means there is a …. probability of obersving our results if the null H is ….
3%
correct
If a t-value gives a probability of 12% this means that there is a …. probability of observing our results if the null H is ….
12%
correct
what is p value
probability of observing our results if the null hypothesis correct
what does a p=56% mean
if the null hypothesis is correct, there is a 56% probability of observing our results
a bigger t value gives a …. p value
smaller
As the p-value gets smaller, is the null hypothesis more or less likely to be correct?
less
Grace and Ruby carry out separate experiments. Grace gets a p-value of 17% and Ruby gets a p-value of 13%. Who is more likely to reject the null hypothesis?
ruby
As the p-value gets bigger, there is a bigger probability of observing our results if the null hypothesis is correct. True or False?
true
James and Sophie carry out separate experiments. James gets a p-value of $0.04$ and Sophie gets a probability of $4\%$. Who is more likely to reject their null hypothesis?
equally likely
what do we use a t test for
to decide whether to accept or reject our null hypothesis
how do we know what size of p value will mean accept or reject thenull H
the experimenter decides at the begining of the study, they create a significance level
If a researcher decides on a significance level of 5% for their experiment, then they will decide that their null hypothesis is incorrect if they obtain a p value of
5% or less
What is the name of the value at which a researcher switches from accepting the null hypothesis, to rejecting it?
significance level
If the p-value a researcher obtains is smaller than or equal to the significance level that they selected, then they…
reject the null H
If Jack sets his significance level at 20 %
and then obtains a p-value of 19.9% in his study, can he reject the null hypothesis?
Yes, because his p-value is below the significance level.
A type 1 error is when researchers…
incorrectly reject the null hypothesis, and say there is a real difference between two experimental groups when there isn’t one.
if a researcher chooses a significance level of 15% what is the proability of making a type 1 error
15%
what does the significance level tell us
how likely we are to make a type 1 error
as the significance level gets smaller is it more or less likely that type 1 errors will occur
less likely
if researchers dont want to cause any type 1 errors what might they do
set the significance level really low
if a the significance level is low what is less likely to happen in regards to the null H and type 2 error
it is less likely itll be rejected
and increases possibility of a type 2 error
what is a type 2 error
failure to reject the null hypothesis when there actually was a difference between experimental groups
fail to reject the null hypothesis, and say there isn’t a difference between the two experimental groups and conclude their results happened by chance when there actually is a difference
To balance the risk of a Type 1 and Type 2 error, what value do we usually set the significance level at?
5%
setting SL at 5% means what in terms of nullH
we reject the null hypothesis is theres less than 5% probability of it being correct
Petra is investigating the effectiveness of reading on patients with anxiety. She selects a significance level of 5% and obtains a p-value of 0.05. She rejects the null hypothesis
typ1, 2 or no error
none
. Osman is investigating the effectiveness of consistent sleeping patterns on patients with depression. He selects a significance level of 0.06% and obtains a p-value of 0.06. He fails to reject the null hypothesis, even though consistent sleep patterns were actually effective for many patients.
1,2 or no error
2
Kate is investigating the effectiveness of exercise on memory recall. She selects a significance level of 10% and obtains a p-value of 8%. She rejects the null hypothesis, even though exercise didn’t actually improve memory recall.
1, 2, no error
1
Hanna is investigating the effect of pets on happiness levels for people with depression. She sets the significance level at $0.11\%$, but accepts her null hypothesis. Which error is most likely to have occurred?
2
If a researcher sets their significance level at 5% and gets a p-value of 14% should they reject the null hypothesis?
no
What is the name of the probability of observing our results if the null hypothesis is correct?
p value
Jack sets his significance level at 5% and obtains a t-value (t=2.178). The critical t-value for his significance level is t=2.086. Can Jack reject the null hypothesis?
Yes, because his obtained t-value is bigger than the critical t-value.
We reject the null hypothesis if the obtained t-value is…
bigger than, or equal to, the critical t-value for our significance level.
as the sample size increases what happens to the t value
it increases
For the unrelated t-test, what is the degrees of freedom?
The total sample size across the two groups subtract 2
For the related t-test, what is the degrees of freedom?
For a related t-test, the degrees of freedom is the sample size subtract 1
when is an alternative hypothesis needed
when we reject the null hypothesis
if the null hypothesis was: no different between heights of first borns and second borns.
and it was rejected, what would the alternative hypothesis be
first borns are taller than second borns
the alternative hypothesis is the hypothesis that is our results are …..
unlikely to have happened by chance and there is a real difference between the experimental groups
is the opposite of the null hypothesis.
which is one tailed, which is two tailed
directional is one tailed
non directional is two tailed
