Inferential statistics are a sub-study of statistics that help to generalize the outcomes or results of the sample for the entire population. A sample is a subset of the population.The basic idea of the sample statistics is to compute mean, correlations, proportions and many other statistical values that might differ from the entire populations or might be similar to the populations. A basic idea behind inferential statistics is the use of sample scores for hypothesis testing to infer some of the most interesting questions that researchers encounter. It’s a quantitative technique to check the null hypothesis and alternative hypothesis. To perform inferential statistics of the population random samples are selected. It involves the probability distribution for running inferential statistics.
All the means of the samples become normally distributed as when it reaches around the true mean of the population as and when we increase the size of the sample. This further implies that the variability of the sample decreases by increasing the sample. It involves the estimation i.e judging the characteristics of a population and test the hypothesis i.e calculating the evidence for or against the research problem.
The mean of that distribution µ with standard deviation :
where σX represents the standard deviation of the population. The selection of a statistical test depends on the type of data that is collected.
Variables are divided into three categories: nominal, ordinal and interval
The table shows that the test that can be used to investigate the hypothesis. For instance, we can use chi-squares when data is nominal or Friedman’s two-ways can be used when data is ordinal etc.
Nominal Data: When the sample is placed within two or more categories.
Ordinal Data: When the data is represented in rank.
Interval Data: Uses a continuous scale also distributed normally.
HYPOTHESIS TESTING :
Hypothesis testing is a sort of analytical inference that involves testing the analytical question based on the study.
The hypothesis to be tested is called the null hypothesis: Ho.
We test the null hypothesis against an alternative hypothesis: Ha.
It is important to run hypothesis testing in order to check the reliability of the sample chosen. The hypothesis obtained from the researcher’s hypothesis about any social event is called a hypothesis. It is usually assumed that the hypothesis is true or accurate while investigating.
Testing hypotheses subject to either confirmation or disconfirmation of test hypotheses. To check or test the hypothesis we need to decide how much difference should be there between the means in order to reject H0( null hypothesis). To measure the foremost important step is to choose a level of significance for the hypothesis tests.
Type 1 error : This error occurs when we reject the null hypothesis when it is true. The level of significance decides to accept or reject the null hypothesis. However, the lower the level of significance, the greater the probability that we will make a Type II error.
Type II error: This error occurs when we fail to reject the null hypothesis when it is actually false.Type II error is more common than type 1 error.
For example, in an experiment the level of significance at 0.05 for rejecting the null hypothesis and the coin turns tail 87 times on 150 throws, the statistician might not be able to reject the null hypothesis.r more will the researcher be able to reject the null hypothesis. Then it is clear that Type I and Type II errors cannot be eliminated. Although they can be minimized, minimizing one type of error will increase the probability of committing the other error. The lower we set the level of significance, the lesser is the likelihood of a Type I error and the greater the likelihood of a Type II error. Conversely, the higher we set the level of significance, the greater the likelihood of a Type I error and the lesser the likelihood of a Type II error.
Test the hypothesis, determine the error, find solutions and conduct the test effectively.