June 22, 2024

Thesopranosblog

It's Your Education

Hypothesis Testing

As the name implies Hypothesis Testing is testing a hypothesis. Suppose that we have long believed that the mean age of the inhabitants of a small town was 35. Our hypothesis would be that the mean age of this town is still 35 years of age. To make sure that this is still true we decide to take a sample of 10 people and find the mean of these 10 is 42 years of age. Does this mean that the average of the population of this town has increase? Or is finding the average age of 10 people selected at random a realistic outcome of sampling 10 people? This is the question that Hypothesis Testing resolves.

Statistics is steeped in probabilities, and Hypothesis Testing is no different. If we decide that the Mean age of this town is now greater than 35, we must be open to the possibility that we could be wrong. That is, the population of the town may still be 35, when our Sample Data says that the Mean of the population is greater. This is an error and we want the probability of this outcome to be low, so we set the probability of this happening to a low number, usually something like 5%. This means if we can show that the probability of making this error is less than or equal to 5%, we are willing to conclude that the population of the town is now greater than 35, based on the Sample Mean of 42.

There are two characteristics of the Sample that are important to its Significance. The first is the Mean of the Sample. If the Mean of the Sample of 10 were 48 instead of the original 42, we can see intuitively that is would be easier to believe that the Mean of the population has increased. If on the other hand the Mean of the Sample were 36, it would be more difficult to believe the Mean age of the Population has changed. A Sample Mean of 36 from a population which has a Mean of 35 is much more likely that getting a Mean of 42 from the same Population.

The second characteristic of the Sample that affects its Significance is its Size. Instead of a Sample Size of 10, suppose we were to take a Sample of 20 people and found this Mean to be 42. Would not this Sample be more Significant than that of the Sample of Size 10? Yes, it means that if the Population has a Mean of 35, it is more likely to get a Sample Mean of 42 from a Sample Size of 10 that it would be from a Sample Size of 20, and is therefore more significant.

Like I said at the start, Hypothesis Testing is counter intuitive at first. Check my website and get a clear and visual explanation.