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Statistical Significance

- R.Raveendran

Why should we test significance?

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.

- 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 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
- whether your design is right or wrong
- 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 plt0.05, it

shows that the chances of obtaining a false

difference is less than 5 (1 in 20) plt0.01

1 in 100 plt0.001 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 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

Students t test paired t unpaired t Pearsons correlation ANOVA One way two - way Wilcoxon signed rank test rank sum test Spearmans rank correlation Kruskal-Wallis Friedman Chi square test Kolomogorov-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
- 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

e.g. t test t

SE(XT - XC)

Determining P Find out the degrees of freedom

(df) Use t and df to find out P using a formula

or critical values table

How to interpret P? If P lt alpha (0.05), the

difference is statistically significant If

Pgtalpha, the difference between groups is not

statistically significant / the difference could

not be detected. If Pgt alpha, calculate the

power If power lt 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 1 X YZ 15 df 2 For

paired t test df n-1 For unpaired t test

df N1N2 - 1