Hypothesis, p-value and types of error Flashcards
we need to first see how we’re measuring these variables.
how do can quantify oral health condition?
dmft score
In a statistical test, how do we know that the difference between the 2 resulting groups is the real difference or if it is just happening by chance?
how do we know if an association is statistically significant?
we see if the difference in results between 2 groups is bigger or smaller than the expected sampling variability
this comes to the procedure of hypothesis testing
What is step 1 in hypothesis testing
Assume the null hypothesis
what is a null hypothesis?
there is no difference between the two variables
If the null hypothesis is true, where do we expect the majority of the difference to be around?
0
if the experiment is repeated 1000 times and if the null hypothesis is true, what type of distribution are u expecting?
centre of the majority will be 0
what would the expected observed difference measured by
standard error
in this case, how can standard error be calculated? (dont learnt the formula)
using the equation - dont learn it off by heart for the exam
what does the standard error measure?
the sampling variation:
It is the expected difference we would expect between the 2 groups if the null hypothesis is true
After predicting the sample variation assuming the null hypothesis is true, you do the computer simulation
what does the computer simulation entail?
in this scenario, if there is no difference in age group, you would have the majority of the difference of DMFS score between the 2 grous around what number?
(if null hypothesis is true)
0
in this scenario, the standard error is 0.5
what implications does that have on expected differences in DMFS score?
you expect the difference between the 2 scores to be 0.5
step 3: do an experiment
we observed the difference of 4 between 10-year old and 6 year old
step 4: what do we then do in this step?
we compare the observed difference vs expected sampling variability —> p-value
this is a calculation:
what actually is a t-test
the ratio between the observed vs expected difference
what does the value of t reflect?
how likely or unlikely that we observe our current difference is the null hypothesis is true
what does every t value correspond to?
a p value
the bigger the value of the t the …….. the p value will be
smaller
what is the definition of a p value?
what is the chance that we can observe a difference as big as (in this case 4)
If the chance for our observed difference is 4, if the null hypothesis is correct, and the chance is very small, what might be the actual case?
is it just that the null hypothesis is still correct but we happened to be very lucky to observe such a huge difference or logically does that mean null hypothesis is wrong?
what is the only feasable explanation?
null hypothesis is incorrect and we should reject it
what is step 5?
do we reject or not reject the null hypothesis
when do we know if to reject the null hypothesis based on p value?
as long as p value is smaller than 0.05 we can reject the null hypothesis
does statistical significance imply clinical significance?
no
does statistical significance imply cause and effect relationship?
no
increasing the standard deviation increases the standard error
a bigger standard error means we do expect a bigger diff between the 2 age groups.
therefore the chance to observe the difference as big as 4 (according to the example), this will give us a p value of 0.12 (bigger p value), meaning we cannot reject the null hypothesis as it is not smalelr than 0.05, therefore cannot reject the null.
what number represents the null hypothesis?
0
what p value does a 95% confidence interval correspond to?
0.05%
what p-value does a confidence interval of 99% correspond with?
1%
types of error
if the null hypothesis is true and in reality there is no diff between the 2 groups, we perform the statistical test and we accept the null
if we make this decision: accept the null hypothesis when the null hypothesis is true, what is the outcome?
correct acceptance
if we reject the null hypothesis when the null hypothesis is actually true, what is the type of error?
Type 1 error
false positive
(alpha-error)
if we accept the null hypothesis when the null hypothesis is actually false, what is the type of error?
type II error
false negative
(beta-error)
what do we call the correct rejection of the null hypothesis?
