p value
TRANSCRIPT
P value and its significance
DR.RENJU.S.RAVI
1
INTRODUCTION
Statistics involves collecting, organizing and interpreting the data
Descriptive statistics :
Describe what is there in our data.
Inferential statistics :
Make inferences from our data to more general conditions.
Inferential statistics
Data taken from a sample is used to estimate a population parameter.
Explain the relationship between the observed state of affairs to a hypothetical true state of affairs.
Hypothesis testing (P-values) Point estimation (Confidence intervals)
Definition
p-value is defined as the probability of obtaining a result equal to or more extreme than what was actually observed.
The p-value was first introduced by Karl Pearson in his Pearson's chi-squared test .
The smaller the p-value, the larger the significance because it tells the investigator that the hypothesis under consideration may not adequately explain the observation.
The vertical coordinate is the probability density of each outcome, computed under the null hypothesis. The p-value is the area under the curve past the observed data point.
steps in significance testing
Stating the research question
Determine probability of erroneous conclusions
Choice of statistical test / to calculate test statistic
Getting the ‘p’ value
Inference
Forming conclusions
Stating Research Question
Research question.
Idea is to assume the state of affairs in
the two treatment populations. Eg: Is
mean Hb in urban and rural children
the same?
Null and Alternate Hypothesis Ho(Null Hypothesis): Assumes that the two population being
compared are not different.
HA/H1 (Alternative Hypothesis): Assumes that the two groups are different.
Two competing Hypothesis are not treated on an equal basis
Special consideration is given to the null hypothesis.
We test the null hypothesis and if there is enough evidence to say that the null hypothesis is wrong ,we reject the null hypothesis in favour of the alternative hypothesis.
Rejecting null hypothesis suggests that the alternative hypothesis may be true.
Determine probability of erroneous conclusions
Truth
H0(no difference) H1(difference exists)
Decision AcceptH0
Right Decision
Type II Error
RejectH0
Type I Error Right Decision
Type I error/ False positive conclusion stating difference when there is no difference
Probability (Type I Error) =
Usually set at 1/20 or 0.05. never 0 and it
should be below the value of ‘α’ for concluding
statistical significance.
The probability of a type I error is distributed at
the tails of the normal curve i.e. 0.025 on either
tail.
Type II Error/ false negative conclusion
Stating no difference when actually there is i.e. missing a true difference
Occurs when sample size is too small. Probability (Type II Error) = Conventionally accepted to be 0.1 – 0.2
Power of a study =(1- ) Researchers consider a power 0.8 – 0.9
(80-90%) as satisfactory.
Cut off for p value
Arbitrary cut-off 0.05 (5% chance of a false +ve conclusion.
If p<0.05 statistically significant- Reject H0, Accept H1
If p>0.05 statistically not-significant- Accept H0, Reject H1
Testing potential harmful interventions ‘α’ value is set below 0.05
Low p value
• If p is very small (<0.001), then the null
hypothesis appears not realistic because
the difference could hardly ever arise due
to chance, when the null hypothesis is
true.
• In order to arrive at the p value we
need to compute the test statistic
which is
)(ObservedSE
edHypothesizObserved
Test Statistic
Step 4. Getting the ‘p’ value
Each test statistic has a sampling distribution from which ‘p’ values for the corresponding value of the ‘statistic’ can be noted from available tables.
Step 5. Inference
If the obtained ‘p’ value is smaller than the level of ‘α’ - statistically significant , null hypothesis is rejected
‘p’ value more than the level of ‘α’ – not significant, null hypothesis cannot be rejected
Step 6. Conclusion
If the results are statistically significant, decide whether the observed differences are clinically important.
If not significant, see if the sample size was adequate enough not to have missed a clinically important difference
‘The power of the study ‘ tells us the strength which we can conclude that there is no difference between the two groups.
Statistical significance does not necessarily mean real significance• If sample size is large, even very small
differences can have a low p-value.
• Lack of significance does not necessarily mean that the null hypothesis is true.• If sample size is small, there could be a
real difference, but we are not able to detect it
One/Two sided p values
If we are interested only to find out whether the test drug is better than the control drug, we put the α of 0.05 under only one tail of hypothesis - called one tailed test.
To know whether one drug performs better or worse than the other, we would distribute the of 0.05 to both tails under the hypothesis i.e. 0.025 to each tail – two tailed test.
P-Value
0
0
0
Upper/Right-Tailed
Lower/Left-Tailed
Two-Tailed
‘p’ value-Points to remember…
The P-value is the smallest level of significance at which H0 would be rejected when a specified test procedure is used on a given data set.
0.05 is arbitrary cut off value
Type 1 error (α)- false positive conclusion
Type 2 error (β)- false negative conclusion
THANK YOU