This document discusses p-values and their significance in statistical hypothesis testing. It defines a p-value as the probability of obtaining a result equal to or more extreme than what was observed assuming the null hypothesis is true. Lower p-values indicate stronger evidence against the null hypothesis. The document outlines the steps in hypothesis testing which include stating hypotheses, determining acceptable type I and type II error rates, selecting a statistical test to calculate a test statistic, determining the p-value, making inferences, and forming conclusions. It emphasizes that statistical significance does not necessarily imply real-world significance.

1. P value and its
significance
DR.RENJU.S.RAVI
1

2. 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.

3. 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)

4. 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.

5. 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.

6. 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

7. 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?

8. 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.

9. Determine probability of erroneous
conclusions
Truth
H0(no
difference)
H1(difference
exists)
Decision Accept
H0
Right
Decision
Type II
Error
Reject
H0
Type I
Error
Right
Decision

10. 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.

11. 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.

12. 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

13. 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.

14. Test Statistic
• In order to arrive at the p value we need to
compute the test statistic which is
Observed  Hypothesized
SE(Observed)

15. 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.

16. 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

17. 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.

18.  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

19. 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.

20. P-Value
0
0
0
Upper/Right-
Tailed
Lower/Left-
Tailed
Two-
Tailed

21. ‘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

22. THANK YOU