The document discusses significance tests and their role in hypothesis testing. It defines key terms like p-value, significance level, confidence level, rejection region, and classification of significance tests. The p-value represents the probability of observing the results by chance if the null hypothesis is true. The significance level is set before data collection and represents the probability of incorrectly rejecting the null hypothesis. A p-value less than the significance level leads to rejecting the null hypothesis.

1. SIGNIFICANCE TEST

2.  Significance tests play a key role in experiments: they allow researchers to determine whether their data
supports or rejects the null hypothesis, and consequently whether they can accept their alternative
hypothesis.
 Statistical significance is the likelihood that a relationship between two or more variables is caused by
something other than chance.
 Statistical significance is used to accept or reject the null hypothesis, which hypothesizes that there is no
relationship between measured variables.
 Statistical hypothesis testing is used to determine whether the result of a data set is statistically significant.
 This test provides a p-value, representing the probability that random chance could explain the result. In
general, a p-value of 5% or lower is considered to be statistically significant.

4. The P-Value and the Significance Level
 Significance comes down to the relationship between two crucial quantities, the p-value and the
significance level (alpha). We can call a result statistically significant when P < alpha. Let’s
consider what each of these quantities represents.
 p-value: This is calculated after you obtain your results. It is the probability of observing an
extreme effect even with the null hypothesis still being true. Importantly, it does not measure
the size of an effect.
 alpha: This is decided on before gathering data. It is the probability of the study rejecting the null
hypothesis despite it being true (i.e. the chance of committing a Type 1 error). It is essential an error
rate and usually set at or below 5%.

5. Level Of Significance
 The level of significance is defined as the probability of rejecting a null
hypothesis by the test when it is really true, which is denoted as α.
 That is, P (Type I error) = α.
 The criterion is based on the probability of obtaining a statistic measured in a
sample if the value stated in the null hypothesis were true.
 In behavioural science, the criterion or level of significance is typically set at 5%.
 When the probability of obtaining a sample mean is less than 5% if the null
hypothesis were true, then we reject the value stated in the null hypothesis.

6. Confidence level
Confidence level refers to the possibility of a parameter that lies within a specified range of
values, which is denoted as c. Moreover, the confidence level is connected with the level of
significance. The relationship between level of significance and the confidence level is c=1−α.
The common level of significance and the corresponding confidence level are given below:
• The level of significance 0.10 is related to the 90% confidence level.
• The level of significance 0.05 is related to the 95% confidence level.
• The level of significance 0.01 is related to the 99% confidence level.

7. Rejection rule

8.  Rejection region:
The rejection region is the values of test statistic for which the null hypothesis is
rejected
 Non rejection region:
The set of all possible values for which the null hypothesis is not rejected is
called the rejection region.
• In the left-tailed test, the rejection region is shaded in left side.
• In the right-tailed test, the rejection region is shaded in right side.
.

9. Classification of tests of significance
For Qualitative data:-
 Standard error of difference between 2 proportions (SEp1-p2)
 Chi-square test or X2
For Quantitative data:-
 Unpaired (student) ‘t’ test
 Paired ‘t’ test
 ANOVA