Summary
Highlights
To overcome the issue of the unknown population mean in frequentist statistics, we assume an exact value for the population parameter. If there is no effect of the diet, the difference in the population will be exactly zero. This assumption is called the null hypothesis. It provides an unambiguous, exact value to fix the distribution, making it a test statistic distribution. If the null hypothesis is true, the mean of this distribution is zero.
Inferential statistics uses limited samples to make inferences about entire populations. We use sample statistics to make decisions about population parameters by specifying statistical hypotheses: a null and an alternative hypothesis. This video explains the necessity of the null hypothesis.
The video presents an example of testing whether a raw meat diet is healthier for cats than canned food. Cats are divided into two groups, and their health is rated after two months. A sample difference in health of 1.12 is observed, but this difference could be due to chance.
To account for chance, we need to understand the distribution of our sample statistic if we were to sample indefinitely. Knowing this distribution allows us to determine probabilities and make informed decisions. The shape of the distribution is influenced by the statistic type, sample size, and population variation. Standardizing the sample statistic by dividing it by the standard error transforms it into a standardized probability distribution.
Using frequentist statistics, we cannot directly calculate the probability of a true population difference favoring a raw diet because we don't know the exact location of the probability distribution. We know its shape and scale but not its mean or location, which is determined by the unknown population mean. To pin it down, we would need to make assumptions about its exact location.
Instead of trying to prove a guessed value, we formulate a null hypothesis and aim to show it's unlikely to be true. If our sample difference is large enough to fall far in the tail of the distribution, with a very small probability, we can reject the null hypothesis. The alternative hypothesis, specified beforehand, determines which tail we examine. The next video will cover how to find probabilities and decide on rejecting the null hypothesis.