Rachit Kumar SaxenaManager-Editorial
What is Test of Significance?
Tests of significance can be defined as the process of comparing data along with the claim for estimating its truth. It is also named as a hypothesis. The claim is proposed regarding a parameter, for instance, population proportion p or mean of the population.
The final verdict is expressed in probability ratio and proves how accurate was the statement of the parameter. The probability ratio explains well how well enough data and claims are, and whether they are agreeable or not.
The statistical interface has two aspects one is the estimation of population value and testing of hypothesis. A null hypothesis shows no relationship between different variables that are being tested. An alternative hypothesis shows a relationship between different variables being studied ( where one variable has to affect others).
Weightage of Test of Significance
The topic is from the Statistics and Probability unit, with a weightage of 10 marks. Other topics covered in the chapter are -
- Measures of Dispersion
- Mean Deviation
- Range
- Standard and variance deviation of grouped and ungrouped data.
Illustrative Examples on Test of Significance
1. Considering the pain reduction after using neosporin on 10 patients of arthritis, the visual analog scale of 10 point is :
0 |
3 |
6 |
1 |
1 |
4 |
0 |
2 |
1 |
5 |
Solution.
X (Mean reduction) = 2.3 points
SD =2.11.
With the use of formula:
t= 2.3-3.0/ (2.11/10^ ½)
= -1.049
n= 10
df = 10-1
= 9
For one-tailed
a = 0.05,
df = 9, the complex value of t is 1.833.
The calculated value 1.049 of t is lesser than the critical value of 1.833.
Therefore, the Null Hypothesis that is the mean reduction in pain, is 3 points that cannot be rejected.
2.A study on 24-hour creatinine excretion in male and female healthy adults for examining if any difference exists. There are 15 subjects in the group in a table:
Men |
16.6 |
19.8 |
17.1 |
15.6 |
20.3 |
24.7 |
18.5 |
17.6 |
22.0 |
24.9 |
18.4 |
16.9 |
21.1 |
17.0 |
23.3 |
women |
23.2 |
22.0 |
21.9 |
14.2 |
23.2 |
24.8 |
25.5 |
28.1 |
21.8 |
20.9 |
18.0 |
19.5 |
20.6 |
16.7 |
17.3 |
Solution.
df= n1+n2-2
= 15+15-2
=28
in men,
y1 = 19.59
s1 = 3.03
in women,
y2 = 21.18
s2 = 3.65
Sp = [(15-1) * (3.03) ^2/ 15+15-2] ^ ½
=3.35
Thus,
t= 19.59-21.18 /3.35 (1/15+1/15) ^ ½
= -1.59/11.2232
= -1.30
The complex value of t is 2.048; whose calculated value is lesser than the critical value.
Hence, the Null hypothesis of equality cannot be rejected.
3.The table below shows the before and after level of serum albumin of randomly picked 8 patients. They are dengue haemorrhagic patients.
Before treatment |
5.1 |
3.8 |
4.0 |
4.7 |
4.5 |
4.8 |
4.1 |
3.6 |
After treatment |
4.8 |
3.7 |
3.8 |
4.7 |
4.6 |
5.0 |
4.0 |
3.4 |
difference |
0.3 |
0.1 |
0.2 |
0 |
-0.1 |
0.2 |
0.1 |
0.2 |
Solution.
Mean difference, d = 0.6/8 = 0.075g/dl
Sd= 0.17.
t = 0.075/0.17/ (8) ^ ½
= 1.25
df = 8-1
=7
Critical value of t is 2.365, as calculated value is less; null hypothesis of difference isn’t possible to be rejected.
FAQs on Test of Significance
Q: What is the test of significance?
Q: What are the different types of tests of significance?
Q: Can you prove the hypothesis?
Q: Is the null hypothesis or alternative hypothesis good enough?
Q: What’s the importance of the null hypothesis?
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