# Inferential Statistics

Making descriptions of data and drawing inferences and conclusions from the respective data

## What is Inferential Statistics?

Inferential statistics enables one to make descriptions of data and draw inferences and conclusions from the respective data. Through inferential statistics, an individual can conclude what a population may think or how it’s been affected by taking sample data. Inferential statistics is mainly used to derive estimates about a large group (or population) and draw conclusions on the data based on hypotheses testing methods.

Inferential statistics uses sample data because it is more cost-effective and less tedious than collecting data from an entire population. It allows one to come to reasonable assumptions about the larger population based on a sample’s characteristics. Sampling methods need to be unbiased and random for statistical conclusions and inferences to be validated.

### Summary

• Inferential statistics enables one to make descriptions of data and draw inferences and conclusions from the respective data.
• Inferential statistics uses sample data because it is more cost-effective and less tedious than collecting data from an entire population.
• It allows one to come to reasonable assumptions about the larger population based on a sample’s characteristics.

### Population Parameters, Sample Statistics, Sampling Errors, and Confidence Intervals

A statistic is a metric used to provide an overview of a sample, and a parameter is a metric used to provide an overview of a population. The two primary estimation types are the interval estimate and the point estimate. The interval estimate (e.g., confidence interval) provides one with a range of values in which a parameter is likely to be found. A point estimate is one estimate of a parameter (e.g., sample mean).

Seeing as a sample is merely a portion of a larger population, sample data does not capture information on the whole population, resulting in a sampling error. Sampling error can be defined as the difference between respective statistics (sample values) and parameters (population values). The sampling error is inevitable when sample data is being used; therefore, inferential statistics can be ambiguous. To minimize the uncertainty created by sampling errors, probability sampling methods can be applied in data analysis.

Confidence intervals allow for interval estimations for population values (or parameters) by utilizing statistical variabilities. Confidence intervals account for sampling errors. As with interval estimates, confidence intervals provide a range of values in which a parameter is likely to be found, and therefore, show the likelihood of point estimate uncertainty. Point estimates and confidence intervals can be used in combination to produce better results.

Every confidence interval is accompanied by a confidence level, which indicates the probability of the interval. A 95% (percent) confidence interval shows that if the same study is conducted numerous times with a completely new sample each time, it is likely that 95% of the studies will have an estimate that lies within the same range of values. It applies to estimates and not necessarily to parameters.

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### Hypothesis Testing

Hypothesis testing makes use of inferential statistics and is used to analyze relationships between variables and make population comparisons through the use of sample data. The steps for hypothesis testing include having a stated research hypothesis (null and alternate), data collection per the hypothesis test requirements, data analysis through the appropriate test, a decision to reject or accept the null hypothesis, and finally, a presentation and discussion of findings made.

Hypothesis testing falls under the “statistical tests” category. Statistical tests account for sampling errors and can either be parametric (includes assumptions made regarding population distribution parameters) or non-parametric (does not include assumptions made regarding population distribution parameters).

Parametric tests tend to be more trusted and reliable because they enable the detection of potential effects. Parametric tests assume that the population from which sample data is derived is normally distributed. The sample size provides an adequate representation of the population from which it was derived. The groups, variances, and measures of spread are comparable.

### Other Testing Methods

There are other testing methods, including correlation tests and comparison tests. Correlation tests examine the association between two variables and estimate the extent of the relationship. Examples of correlation tests are the Pearson’s r test, Spearman’s r test, and the Chi-square test of independence.

Comparison tests are used to determine differences in the decretive statistics measures observed (mean, median, etc.). Examples of comparison tests are the t-test, ANOVA, Mood’s median, Kruskal-Wallis H test, etc.