hypothesis

Researchers ought to conduct a thorough and objective observation. In doing so, we may start from formulating a question and hypothesis prior to making prediction, performing experiments, and analyzing results. Hypotheses are different from theory, where we need evidence to establish the fact revolving around proposed hypotheses. A research or investigation is a mean to substantiate evidence and support the hypothesis. Thus, hypothesis needs to comply with cases and variables introduced in a study.

Proving or disproving a research hypothesis requires representative evidence which may help us substantiate our claims. In general, we need a large amount of data following a rigorous and well-documented procedure. However, inviting all potential subjects is not feasible due to time and resource constraint. Considering the amount of limitation we have, how do we determine the minimum required amount of data to answer our research question?

In statistics, proving or rejecting an assumption requires a rigorous formal approach, which highly depends on the formulated hypothesis. The current post will help us in conducting a statistical test to measure hypothesized proportional difference among categorical variables. Another common name assigned to such a formal step is the test of independence. We shall see various tests we have, how they work and when to use them.

When we have a normally-distributed data, parameters \(\mu\) and \(\sigma\) from our PDF can completely explain the behaviour seen in our sample. With \(\mu\) represents the central tendency and \(\sigma\) the spread, we can directly compare similarly distributed samples. Often, we need to confirm how much our average value differs from other observations. In doing so, we are facing a mean difference problem in our venture of statistics. This lecture will help us proving mean differences in one-sample and two-sample problems.

The limitation when using T-Test is its inability to directly compare multiple group at once. Often times, we are interested to see whether our groups of interest present with at least on differing average value. To alleviate this issue, we can assign a generalized form of a T-Test. We will do so by analyzing between and within group variances. This analysis resulted in the sum of square with two degree of freedoms, one coming from the number of groups and another from the calculation of withing group variability.