Tests of Significance: Overview, Questions, Preparation

Statistics 2021 ( Statistics )

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Rachit Kumar Saxena

Rachit Kumar SaxenaManager-Editorial

Updated on Aug 5, 2021 10:56 IST

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. 

Test of Significance

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). 

Test of Significance_2

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?

A: It is a procedure of estimating the truth of data given with a claim to understand its accuracy. 

Q: What are the different types of tests of significance?

A: There are mainly two aspects of the hypothesis one is the null hypothesis, and another is the alternative hypothesis. 

Q: Can you prove the hypothesis?

A: With the analysis of results, the alternative hypothesis can be possibly rejected or supported; however, it is not possible to prove its accuracy. 

Q: Is the null hypothesis or alternative hypothesis good enough?

A: The null hypothesis is a commonly accepted fact; however, that is the opposite of the alternative hypothesis. 

Q: What’s the importance of the null hypothesis?

A: Null hypothesis H0 is the prevalent fact that is accepted. It also appropriately navigates research so; the null hypothesis is commonly the opposite of the investigator or experimenter’s verdict. 

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