## Explain what is meant by the term "inferential statistics."

Descriptive statistics describe data (for example, a chart or graph) and inferential statistics allows you to make predictions (“inferences”) from that data. With inferential statistics, you take data from samples and make generalizations about a population.

Inferential statistics use a random sample of data taken from a population to describe and make inferences about the population. Inferential statistics are valuable when examination of each member of an entire population is not convenient or possible. For example, to measure the diameter of each nail that is manufactured in a mill is impractical. You can measure the diameters of a representative random sample of nails. You can use the information from the sample to make generalizations about the diameters of all of the nails.

**There are two main areas of inferential statistics:**

- Estimating parameters. This means taking a statistic from your sample data (for example the sample mean) and using it to say something about a population parameter (i.e. the population mean).
- Hypothesis tests. This is where you can use sample data to answer research questions. For example, you might be interested in knowing if a new cancer drug is effective. Or if breakfast helps children perform better in schools.

With inferential statistics, you take that sample data from a small number of people and try to determine if the data can predict whether the drug will work for everyone (i.e. the population). There are various ways you can do this, from calculating a

**z-score**(z-scores are a way to show where your data would lie in a normal distribution to post-hoc (advanced) testing.
Inferential statistics use statistical models to help you compare your sample data to other samples or to previous research. Most research uses statistical models called the Generalized Linear model and includes Student’s t-tests, ANOVA (Analysis of Variance), regression analysis and various other models that result in straight-line (“linear”) probabilities and results.

Any group of data like this, which includes all the data you are interested in, is called a

**population**. A population can be small or large, as long as it includes all the data you are interested in.
There are two main limitations to the use of inferential statistics. The first, and most important limitation, which is present in all inferential statistics, is that you are providing data about a population that you have not fully measured, and therefore, cannot ever be completely sure that the values/statistics you calculate are correct. Remember, inferential statistics are based on the concept of using the values measured in a sample to estimate/infer the values that would be measured in a population; there will always be a degree of uncertainty in doing this. The second limitation is connected to the first limitation. Some, but not all, inferential tests require the user (i.e., you) to make educated guesses (based on theory) to run the inferential tests. Again, there will be some uncertainty in this process, which will have repercussions on the certainty of the results of some inferential statistics.