Statistical SignificanceStatistical Significance

R.RaveendranR.Raveendran

Heart rate (bpm) Mean ± SEM n

In men - 73.34 ± 5.82 10

In women - 80.45 ± 6.13 10

The difference between means (80.45-73.34) = 7.11

We do not need a stat test of significance, if only :

a. the data from all subjects in a group are IDENTICAL

b. we can collect data from all subjects in a population

Why should we test significance?

We test SAMPLE to draw conclusions about POPULATION

If two SAMPLES (group means) are different, can we be certain that POPULATIONS (from which the samples were drawn) are also different?

Is the difference obtained TRUE or SPURIOUS?

Will another set of samples be also different?

What are the chances that the difference obtained is spurious?

The above questions can be answered by STAT TEST.

Why should we test significance?

Stat test Tests whether two groups are statistically

different from each other

Statistically different? = Truly different?Not just apparently different

You do not need statistics to say these two are truly different. Do you?

But statistics does help us determine

which group of trees is taller

You do not need statistics to say these two are truly different. Do you?

How to find statistical difference?How to find statistical difference?

How does a Stat test work?

Stat test analyses the data (numbers) submitted (by the researcher) to calculate the chances of obtaining a difference when there is none i.e. probability of obtaining a spurious difference.

It does not indicate

(a) whether your design is right or wrong(b) whether the type of data is correct or wrong(c) the magnitude of the difference(d) whether the difference will be practically useful

All it can point out is whether the obtained difference between two groups is REAL or FALSE

What does a Stat test infer?

Stat test Data P value

When p<0.05, it shows that the chances of obtaining a false difference is less than 5% (1 in 20) [p<0.01 – 1 in 100; p<0.001 – 1 in 1000]

Since we consider 5% P is small, we conclude that the difference between groups is TRUE

Truth is something which is most likely to be true and 100% certainty is impossible.

How to test statistical significance?

State Null hypothesis Set alpha (level of significance) Identify the variables to be analysed Identify the groups to be compared Choose a test

Calculate the test statistic Find out the P value Interpret the P value Calculate the CI of the difference Calculate Power if required

Thank youThank you

Null hypothesis

Null hypothesis (statistical hypothesis) states that there is no difference between groups compared.

Alternative hypothesis or research hypothesis states that there is a difference between groups.

e.g.

New drug ‘X’ is an analgesic - (Research hypothesis) New drug ‘X’ is not an analgesic – (Null hypothesis)

Alpha / type 1 error / level of significance

The level of significance is to be set

It is generally set at 0.05 (5%) and not above.

If the P value is less than this limit then null hypothesis is rejected i.e. the difference between groups is not due to chance.

Choosing a stat test

Why should we choose a test?

Choosing a stat test……….

Why should we choose a test?

There are many tests

The selection of test varies with the type of

data, analysis, study design, distribution & no. of groups

Choosing a stat test………

Parametric Non-parametric

Student’s t test paired t unpaired t

Pearson’s correlation

ANOVA One – way two - way

Wilcoxon signed rank test rank sum test

Spearman’s rank correlation

Kruskal-WallisFriedman

Chi square testKolomogorov-Smirnov test

Choosing a stat test……

Determine : Aim of the study – Parameter to be analysed - Data type- [Continuous, Discrete, Rank, Score, Binomial] Analysis type- [Comparison of means, Quantify association, Regression analysis]

No. of groups to be analysed - No. of data sets to be analysed - Distribution of data - [normal or non-normal] Design - [paired or unpaired]

With the above information, one can decide the suitable test using the table given.

Choosing a stat test……1. Data type 2. Distribution of data 3. Analysis type (goal) 4. No. of groups 5. Design

Table downloaded from www.graphpad.com

Table downloaded from www.graphpad.com

Calculating test statistic

difference between group means

variability of groups

XT - XC

SE(XT - XC)e.g. t test t e.g. t test t ==

Determining PDetermining P

Find out the degrees of freedom (Find out the degrees of freedom (dfdf))

Use Use tt and and dfdf to find out to find out PP using a using a formula or ‘critical values table’formula or ‘critical values table’

How to interpret P?

If P < alpha (0.05), the difference is statistically significant

If P>alpha, the difference between groups is not statistically significant / the difference could not be detected.

If P> alpha, calculate the power

If power < 80% - The difference could not be detected; repeat the study with more ‘n’If power ≥ 80 % - The difference between groups is not statistically significant.

Degrees of Freedom

It denotes the number of samples that a researcher has freedom to choose.

The concept can be explained by an analogy :

X + Y = 10 df = 1X+ Y+Z = 15 df = 2

For paired t test df = n-1

For unpaired t test df= N1+N2 - 1