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# What are Inferential Statistics?

Surveyor asking questions of a participant.
Article Details
• Originally Written By: Mary McMahon
• Revised By: Phil Riddel
• Edited By: O. Wallace
2003-2015
Conjecture Corporation
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Inferential statistics are data which are used to make generalizations about a population based on a sample. They rely on the use of a random sampling technique designed to ensure 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. It would be impractical to question every single 24-30 year old about his dessert preferences, so instead, a representative sample of the population has been surveyed with the goal of making an inference about the population as a whole.

#### Inferential and Descriptive Statistics

Another way of using survey data takes the form of descriptive statistics. In this case, statements are made that simply describe the data collected. It is possible for the same set of data to be used in a descriptive or inferential way. For example, in the run-up to a US election 1,000 people in a town might be questioned about their voting intentions, with the result that 430 said they would vote Democrat, 410 said they would vote Republican, with 160 undecided or unwilling to say. An example of using this data in a descriptive way would be to state simply that 43% of 1,000 people interviewed in this town intend to vote democrat. An inferential statement would be “Democrats hold 2% lead” — an inference about voting intentions in general has been drawn from a sample.

#### Methods

Before drawing any general conclusions from a sample it is important to employ the correct methods, otherwise these conclusions may not be valid. Common sources of error are in the way the sample is put together, and a number of factors can influence the validity of the sample population. Size is critical, because the smaller the size, the greater the risk that the sample will not be representative of the population as a whole. Care must also be taken to eliminate sources of bias. In the above example, factors such as age, gender, and income may have considerable influence over voting intentions, so if the sample was not composed in such a way as to reflect the general population, the conclusion may not be valid.

Sampling methods must be chosen carefully; for example, if someone took a convenience sample which included every 10th name in the phone book or every 10th passer-by at a mall, this sample might not be valid. Sample bias is also a consideration. For example, it is 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.

#### Uses

The use of inferential statistics is a cornerstone of research on populations and events, because it is usually difficult, and often 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 more general conclusions. For example, it would not have been possible to check the medical records of every single smoker in order to establish a link between smoking and lung cancer, but numerous random samples comparing smokers with non-smokers, and eliminating other risk factors, have firmly established this link.

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. Statements based on informal polls and quick surveys may not be very useful, but in areas such as medical research and clinical trials standards are much tighter, and inferential statistics have provided vast amounts of valuable information. In other areas, they are used every day to make sweeping generalizations about populations that may shape public policy, product design, marketing, and political campaigns.

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 oasis11 Post 3 @Subway11 -While I agree with most of these studies that offer statistical inference I don’t know how accurate some of them are. I hear that coffee is bad for your heart on one study and then in another study I hear that the caffeine reduces the chances of developing dementia and Alzheimer because it improves your memory over time. I think that you can get overwhelmed with the amount of studies out there and some of them have conflicting information. I also wonder if some of the studies have a form of bias that lead the researcher to a specific conclusion. For example, if the researcher is a staunch vegetarian and conducts studies on the consumption of beef as causing diseases like cancer without accounting for the fact that beef contains iron and a good amount of protein that is necessary in all diets it makes me doubt the findings. I think that if you consume foods in moderation there should not be a problem. I take these studies with a grain of salt. subway11 Post 2 @SurfNTurf - That makes sense. I also think that inferential statistics are also used in the health care field. For instance when they survey people that ingest a lot of sugary soft drinks many studies have shown that these people have a higher likelihood of developing pancreatic cancer. This information is valuable because it can help people change their eating habits in order to prevent obtaining this disease. The same can be said of studies of people that eat a Mediterranean diet rich in Omega three fatty acids and antioxidants. It is a well know fact that these people tend to have higher life spans which lead researchers to conclude that adopting this type of diet will lead to a longer and healthier life. This form of statistical inference might improve the lives of millions of people around the world. surfNturf Post 1 I think that the field of statistics is so interesting.I just get confused between descriptive vs. inferential statistics though. I friend of mine explained it this way: she said that taking data like actual test scores in a class or the memory capacity from ten subjects fall into the realm of descriptive statistics. When there are studies that suggest that the United States ranks 31st in math in the world this is also a form of descriptive statistics. Inferential statistics makes an inference on what the scores will look like in the future. For example, if the United States educational system continues its deficient path then the math standings might fall further to say 40th in the world within the next ten years. This is the best inferential statistics example that was presented to me that helped me understand the concept.