Statistics are often based on samples
Statistics often use samples to draw conclusions about a whole population. Samples are a smaller portion of a whole item and are used because often the population is just too big to record the information needed using every available member of the population. This means that the sample used has to be representative of the population. For example, a sample of a donut would be a piece of that donut. It couldn't be just any piece either. It would have to have a bit of everything found on the whole, real donut. Let's say you want to sample a cream donut. This donut has cream inside, chocolate frosting, and the bread of the donut. A sample piece would have to contain a bit of cream filling, a bit of chocolate frosting, and some of the bread to be a representative sample. The population being sampled is the donut itself.

Scientists use samples because they can't measure everything. For example, no scientist could capture and weigh every squirrel in the United States, or even in the city of Chicago. But scientists still want to know about squirrels. So they take a sample of the squirrels in Chicago. Let's say they catch and weigh 500 squirrels out of all the thousands of squirrels in Chicago. They can then draw conclusion about all the squirrels in Chicago based on what their sample said. The sample is the 500 squirrels the scientist actually weighed, and the population would be all the squirrels in Chicago. If the sample squirrels weighed on average 1 pound each, then a scientist would then conclude that all the squirrels in Chicago weighed on average 1 pound.

Some Very Basic Statistics
Scientists like statistics. They are helpful in testing ideas, but sometimes they are very complex. A simple statistical measurement is an average. What does an average mean? An average was mentioned earlier when we talked about the squirrels. If 500 squirrels weigh on average 1 pound, what does that really mean? Try this experiment to help you. Have a teacher or other adult fill 10 bags with beans or M&M's or anything that's easy to count. Tell this adult not to put more than 20 of these things in any given bag, but that they can put as many as they want up to 20. Take a piece of paper and label lines with spaces 1 through 10. Count the number of beans in each bag, writing down the total number of beans on your paper. Repeat until you have counted the beans in all the bags. Next, add up the total number of beans from all the bags. Write this number down on your paper. Now divide this number by the number of bags you used (in this case 10). The number that results will be the average.

But what does it mean? Take the squirrel example. When they say the average Chicago squirrel weighs 1 pound, it means that if you just chose a Chicago squirrel, picked it up and weighed it (don't try this at home), it would be very close to 1 pound in weight. Chicago squirrels are unlikely to weigh much more than 1 pound or much less than one pound.

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Test Design effects Statistical Results
Statistics are only as good as the data they are based on. This means that scientists need to carefully consider how they will test their theories to get valid results. One key is to be consistant in the collection process. Once the scientist picks a methodology, they should stick with it throughout the study, if they want to use all the data they have collected. When method changes, they have introduced variability in their data, making it harder to determine what is really happening. If too many things are different from collection to collection, the scientists won't know what is causing changes to occur.

If scientists don't use the same methods at each sample, they won't be able to compare or join results. But by being consistent in their study methods, scientists can get a better overall picture of their subjects. When looking at the results of a scientific study, pay attention to if they say their conclusions are statistically significant (which means they meet specific mathematical requirements) and how they conducted their study. Sometimes statistically significant "results" really aren't if the study itself was flawed.

The scientific system of testing and re-testing theories is one way to help insure the accuracy of results. One study is repeated by other scientists to see if the results hold up each time they are tested.