Inferential statistics are statistics which are used to make inferential statements about a population. These statistics rely on the use of a random sampling technique which ensures that a sample is representative. A simple example of inferential statistics can probably be found on the front page of almost any newspaper, with any article claiming that “X% of Y population thinks/does/feels/believes Z.” A statement such as “33% of 24-30 year olds prefer cake to pie” relies on inferential statistics. In this case, every single 24-30 year old has not been surveyed about their dessert preferences. Instead, a representative sample of the population has been surveyed with the goal of making an inference about the population as a whole.

The use of inferential statistics is a cornerstone of research on populations and events, because it is difficult and sometimes impossible to survey every member of a population or to observe every event. Instead, researchers attempt to get a representative sample and use that as a basis for their claims. This differs from descriptive statistics, which describe only the data itself in statistical terms.

A number of things can go wrong with inferential statistics. For this reason, researchers try to be very careful about how they are used, and they take care to test their data and survey sample to confirm that the information is accurate. The goal is to demonstrate that an observed difference or trend is real, and is not a simple fluke of the data or the sample population. This may be done by creating a conflicting hypothesis and seeing if it can be proved. In the cake versus pie example, for example, a researcher might ask if the data supports a claim that more 24-30 year olds like cake than pie.

A number of things can influence the validity of the sample population used in inferential statistics. Size is critical, because the smaller the size, the greater the risk that the sample will not be representative of the population being studied. Sampling method is also important; for example, if someone took a convenience sample which included every 10th name in the phone book or passers-by at a mall, this sample might not be valid. Sample bias is also a consideration. For example, it's possible that 24 to 30 year olds attending a pie lover's convention are more likely to enjoy pie than cake, which would mean that a survey on dessert preferences which used conference attendees as a sample would not be very representative.

Analyzing statistics can be challenging, yet inferential statistics are used every day to make sweeping generalizations about populations which may shape public policy and other issues. Researchers who work with inferential statistics try to keep their methods and practices transparent and as rigorous as possible to ensure the integrity of their results.