Statistics Learning

Lately, I’ve been studying statistics to prepare for a potential PhD position. This is quite a new field for me; my background in Software Engineering and Business Administration didn’t provide sufficient training in statistical fundamentals.

Here is a summary of what I’ve learned so far:

Naturally, with a large dataset, data tend to follow a normal distribution. However, when working with a small sample size, the data are considered more volatile and are better modeled by the t-distribution (often referred to in the context of Student’s t-test), rather than the z-distribution.

Once we model the distribution of our data, we can calculate the confidence interval. This represents the range in which we expect the true population parameter (such as the mean) to lie; for instance, with a 95% confidence interval, we can say that if we repeated an experiment 100 times, the true mean would fall within that interval 95 times.

Furthermore, we use the p-value to evaluate the robustness of our conclusions. We generally use a t-test to determine if there is a significant difference between group means. An F-test is used to assess whether variances are significantly different—this is crucial in ANOVA to determine if the explained variance by a model is substantial enough to reject the null hypothesis. Finally, the Chi-square test is employed for categorical data across multiple groups to determine if observed frequencies differ significantly from expected frequencies.

The general logic behind most statistical tests can be summarized by this formula: