T-TEST

DR. SAKTHI

Ist YEAR POST GRADUATE STUDENT

DEPT. OF PUBLIC HEALTH DENTISTRY

RAGAS DENTAL COLLEGE & HOSPITAL

CONTENTS

⮚ INTRODUCTION

⮚ T-TEST

⮚ T-DISTRIBUTION

⮚ GENERAL CHARACTERISTICS OF T-DISTRIBUTION

⮚ WHEN TO USE T-TEST

⮚ T-TEST CRITERIA AND APPLICATION

⮚ TYPES

⮚ ALTERNATIVES

⮚ CONCLUSION
INTRODUCTION

● When we are going to conduct a study, we frame a research question, for that we generate

HYPOTHESIS.

● HYPOTHESIS is defined as a tentative prediction or explanation of the relationship

between two or more variables.

Types of hypothesis

⮚ NULL HYPOTHESIS

o That no statistically significant difference exists between the groups

o No statistically significant relationship exists between variables

⮚ ALTERNATIVE HYPOTHESIS

o Logical opposite of the null hypothesis

o that a statistically significant difference does exist between groups
o That statistically significant relationship exists
Test of statistical significance

● A test of significance is a formal procedure for comparing observed data with a claim

(also called a hypothesis), the truth of which is being assessed.

Decision Rule

● All possible values that the test statistics can assume are points on the horizontal axis of

the graph of the distribution of the test statistics

● Critical value divides the area under probability curve into 2 regions.

1.Zone of Rejection (Critical)

2.Zone of Acceptance
Zone of Acceptance

● Size of critical region is given by level of significance α.

● Values lie in the rejection region and non rejection region.

● When the value of test statistic falls into the critical region, H0 is rejected.

● When it falls into acceptance region, H0 is accepted.

TO FIND CRITICAL VALUE?

For example , If the degree of freedom is 29 with p value 0.05 then we have look at the t-
table, to find the critical value.
T-test

● The t-statistic was introduced in 1908 by William Sealy Gosset, a chemist working for

the Guinness brewery in Dublin, Ireland ("Student" was his pen name)

● It is applied to find the significant difference between two means

T Distribution

● Also called as Student’s T distribution

● Compared to the normal distribution, the t distribution is less peaked in the center and

has thicker tails.

Formula

General characteristics of t-distribution

1. The t random variable is continuous.

2. The graph of the density of the t random variable is symmetric and bell-shaped.

3. The mean, median, and mode are equal to 0 and located at the center of distribution.

4. Each t distribution is identified by a parameter δ (a Greek letter delta), called degrees of

freedom.

5. The degree of freedom is always a positive integer.

6. The parameter is a shape parameter in the sense that as δ increases, the variance of the t
distribution decreases. The variance σ2 of the t distribution is larger than 1.0. Hence, the t
distribution is more dispersed than the standard normal distribution.

7. As degrees of freedom increase, the t distribution approaches the standard normal

distribution.

Difference between t distribution and normal distribution

When Compared to the normal distribution, the t distribution is less peaked in the center and
has thicker tails.
 T-distribution with the special feature called degree of freedom
df= (n-1)

When to use T-test

Criteria of t-test

● Randomly selected homogeneous sample

● Quantitative data

● Variability normally distributed

 ● Sample size less than 30

Application of t-test

● To compare the mean of a sample with population mean.

● To compare the mean of one sample with the mean of another independent sample.

● To compare between the values (readings) of one sample but in 2 occasions.

Types

Types of T-test

Paired ‘t’ test Sample drawn from same population before

Unpaired ‘t’ test Sample drawn from two different

population

One sample ‘t’ test compares the mean of the sample data to a

Unpaired t test

A comparative study of oral hygiene status of smokers and non smokers

 Non smokers Smokers
Unpaired t test
Procedure to conduct Unpaired t Test
Mean - 1 Mean - 2
1. As per null hypothesis assume that there is no real difference between the means of two
samples

2. Find the observed difference between means of two samples (X1-X2)

3. Calculate the standard error of difference between the two means

4. Calculate the t value t= X1 –X2/SE

5. Determine the degrees of freedom from the formula

d.f=(n1-1)+(n2-1)=n1+n2 - 2

6. Compare the calculated value with the table value at particular degree of freedom to find
the level of significance (p Value)

EXAMPLE

Groups Sample size Sample mean Sample S.D

Male 15 70.3kg 4.2kg

Female 17 57.4kg 3.1kg

Paired t test

Knowledge of nursing students towards traumatic dental injuries before and after health
education

Before After
Paired t test
 Mean 1 Mean 2

Paired T test

● Applied to paired data of independent observations from one sample only when each

individual gives a pair of observations (before & after)

● Procedure to conduct Paired t Test

1. As per null hypothesis, assume that there is no real difference between the means
of two samples
2. Find the difference in each set of paired observations, before and after (X1-X2=X)
3. Calculate the mean of difference (X)
4. Work out the standard error of mean
5. Determine the t value =X/SE of difference
6. Find the degree of freedom (n-1)
7. Refer to the table and find out the probability of t corresponding to n-1 degree of
freedom

Example

Students Test 1 Test 2 Difference

1 97 90 -7

2 91 96 5

3 65 77 12
 4 76 84 8

5 69 79 10

6 75 69 -6

7 90 79 -11

One Sample t Test

● One Sample t Test examines whether the mean of a population is statistically different

from a known or hypothesized value.

● In One Sample t Test, the test variable's mean is compared against a "test value",

which is a known or hypothesized value of the mean in the population. Test values
may come from a literature review, a trusted research organization, legal
requirements, or standards

Example
The following data represents sample of newborn birth weights in kgs for 10 patients:

2.6,2.7,3.2,2.9,3.0,3.3,5.2,2.3,4.1,3.7
REFERENCE

Jay S .Kim and Ronald J.Daily. Biostatistics for oral health care.1st edition. Blackwell
Munksgard publisheres.2008

Wayne W. Daniel ,Biostatistics A Foundation for Analysis in the Health Sciences, Seventh
edition 2005.Wiley publications.

Peter S, Essentials of Preventive and Community Dentistry; Fifth edition 2013. Arya
publication.

B.K.Mahajan. Methods in biostatistics.7theditis on. Jaypee brothers medical

publishers.2010