Inferential statistics is one of the two branches of statistics that enable people to make descriptions of specific data and draw conclusions and inferences from that data. It is used to derive estimates from large populations of data and come up with conclusions based on different hypothesis testing methods. Inferential statistics uses sample data since it’s more affordable and less tedious than collecting the entire data from a population. The sampling methods used are supposed to be random and unbiased for the statistical conclusions to be termed as valid.
Sampling error in inferential statistics
With the sample size being smaller than the population size, some of the population is not captured by the sample data. The lack of capturing leads to a sampling error, which is the difference between the parameters and the measures sample values. Sampling errors occur anytime one uses a sample, whether the sample is unbiased and random or not. This leads to uncertainty in inferential statistics.
Estimation of population parameters from the sample statistics
In inferential statistics, the characteristics of populations and samples are explained by numbers called parameters and statistics. A parameter is a measure that is used to describe the entire population while statistics is the measure that describes the sample. The difference between the statistic and the parameter is the sampling error. People use inferential statistics in estimating the parameters in a way that accounts for the sampling error since the entire population is never known. You can use point estimates and interval estimates in estimating the population.
Hypothesis testing is described as the formal process of statistical analysis using inferential statistics. Hypothesis testing is used in the comparing of populations or the relationships between variables in the samples. The hypothesis is tested using statistical tests, which also estimate the sampling errors before the inferences are made. Statistical tests are divided into parametric tests or non-parametric tests. However, parametric tests are considered more powerful statistically. However, parametric tests have three assumptions. It assumes that the population where the sample comes from has a normal distribution of scores. It also assumes that the sample size is large enough to represent the population. Lastly, it assumes that the variances of the groups being compared are similar. If your data violates these assumptions from the parametric tests, then you are supposed to use the non-parametric tests. Not-parametric tests do not assume anything about the distribution of population data.
For statistical significance to be tested, proper tests need to be conducted to produce a test statistic. The test statistic is used to compare the value of the sample statistic with the specified value by the bull hypothesis. The tests are also used to produce a p-value if the null hypothesis is true with the probability of obtaining the test statistic. For one to choose when to reject the null hypothesis, they must choose a level of significance that is denoted by α.