1) Statistical tests of significance involve comparing observed data to a claim or hypothesis to assess if it is true. A test calculates a p-value which indicates the probability the data agrees with the claim by chance. 2) Conducting a significance test involves stating the null and alternative hypotheses, selecting a significance level, finding the p-value, and comparing it to the significance level to determine if the null hypothesis can be rejected. 3) The Student's t-test can be used to assess if a sample mean is significantly different from a population mean or if two sample means from the same population are significantly different from each other. It involves calculating a t-value and comparing it to a table value.

1. By .Dr syed Ziyad furqan
STATISTICAL TESTS OF
SIGNIFICANCE AND STUDENT`s
T- TEST

2. Statistical tests of Significance
A test of significance is a procedure to compare
observed data with a claim also called hypothesis,
the truth of which is being assessed.
The claim is a statement about a parameter, like the
population proportion (p) or the population mean (µ).
The results of a significance test are expressed in
terms of a probability that measures how well the
data and the claim agree.
Statistical tests are performed to determine
statistical significance of results.

3. Steps in Testing of Statistical
Significance
1)State the Null Hypothesis and Alternative
hypothesis
2) Select a alpha level of significance
3)Find the P-value (using a table or any statistical
software)
4)Compare P-value with α- value and decide whether
the null hypothesis should be rejected or accepted
5)Interpret the result by stating if the results are
statistically significant or not.

4. Null and Alternative Hypothesis
The null hypothesis (denoted by H0 ) states the value
of a population parameter (such as proportion, or
mean) is equal to some claimed value.
The term null is used because this hypothesis
assumes that there is no difference between the two
means or the recorded difference is not significant.
The alternative hypothesis (denoted by Ha) states
the value of population parameter is not equal to
some claimed value.
The alternative hypothesis is the claim that
researchers are actually trying to prove is true.

5. Null and Alternative Hypothesis
Example- Null hypotheses states: Hypothesized
Population mean (µ0) for weight of tablets is100 mg
which is equal to population mean (µ).
So, H0 : µ=100
Alternative hypothesis states: Population mean (µ)
is significantly different from µ0 (100mg).
So, Ha : µ > 100 or µ < 100 or µ ≠ 100
If , Ha : µ > 100 then Right- T
ailed test is
performed.
If , Ha : µ < 100 then Left- T
ailed test is
performed.
If, Ha : µ ≠ 100 then Two- T
ailed test is
performed.

7. ALPHA LEVEL OF SGNIFICANCE
The significance level (α) the probability of making
type 1 error (rejecting the null hypothesis when it
was in fact true).
is referred to as pre-
The term significance level
chosen probability.
As this quantity represents an
error rate, lower values are
generally preferred.
Its values generally ranges
from 0.05 to 0.10.

8. P-VALUE
P- value is the calculated chance that type 1 error
has occurred.
The smaller the p-value, the stronger the evidence
that you should reject the null hypothesis.
When the p- value is less than 0.01, the result is
called highly significant.
If we choose significance level of 0.05, p-value less
than 0.05 (typically ≤ 0.05) will be statistically
significant.
A p-value higher than 0.05 (> 0.05) is not
considered statistically significant.

9. TYPES OF SIGNIFICANCE
TEST
NON-PARAMETRIC
PARAMETRIC TESTS
Student`s t- test
Analysis of variance
(ANOVA)
Regression
Correlation Z - test
TESTS
Chi- squared test
Wilcoxan Signed-
Rank test
Kruskal-Wallis test

10. Used for drawing conclusions or interpretations for
small samples.
(I) Application of t-test to assess the significance
difference between the sample mean and
population mean:
The calculation of t-value involves the following steps:
(i) Null Hypothesis: Null hypothesis (Ho): sample
mean (X
̅ ) = population mean (µ) or Ho = X
̅ = µ
(ii) Test statistics: T-value is calculated by the
following formula:
STUDENT`s T- TEST

11. X
̅ = Sample mean
S = standard deviation of sample
n = number of unit in sample
(iii)Degree of freedom: It is one less than the
number of units in the sample. Degree of freedom
(d.f. or v) = No. of units in the sample – 1( n – 1)
(iv)Level of significance: Any level of significance
can be considered to test the hypothesis but
generally 1 % (0.01) or 5% ( 0.05) levels of
probability is considered for testing the hypothesis.
(v)Table value of t: After calculating the t- value with
the above formula, the tabulated value of t is noted
from Fishers and Yates table at given degree of
freedom and 5% level of significance. Then
calculated value of t is compared with the tabulated
value of t.

13. (vi) Test criterion. If the calculated value of t
irrespective of (+) or (-) sign is less than the
tabulated value, then the Null hypothesis is
accepted.
But, if the calculated value of t is greater than the
tabulated value of t the null hypothesis is rejected.
(II) T-test to assess the significance difference
between the means of two samples drawn from
the same population:
The procedure of this test is as follows:
(i) Null hypothesis: H0 = µ1 = µ2
where µ1 and µ2are the standard deviations of the
sample I and sample II respectively.

14. (ii) Test statistics: Next, the value of t is calculated
by the following formula:
(iii) Degree of freedom: (d.f.) = n1+ n2 – 2
(iv)Level of significance: The level of significance is
generally considered at 5% (0.05) level of
probability.
(v)Tabulated value of t: Value of t is recorded from
the Fisher and Yates table at the given degree of
freedom and at 5% level of significance.
(vi)Test criterion: At last, the calculated value of t is
compared with the table value of t. If the calculated
value of t exceeds the table value, the observed
difference is considered statistically significant and
hence null hypothesis is rejected.

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