Significance level, Type I and Type II Error, Confidence interval

In inferential Statistics, we take a value from the sample (a statistic), and infer things about the unknown population parameter. When we use inferential statistics, we can assume that, for instance, the scatterplot we created from a sample represents the overall population. Inferential Statistics can either be point estimations, or interval estimations. In other words, point estimation analyzes a specific value, while interval estimation analyzes a range of values.

 

1. Hypothesis testing (included in point estimation)

Hypothesis Testing is a form of point estimation. In hypothesis testing, we develop two hypotheses; one we’re trying to prove to be true, or we’re trying to show, and one we assume to be true to begin with. Things like a t-test (for means), or a z-test (for proportions) are types of basic hypothesis tests. Other hypothesis tests will be the two sample options of those listed before, as well as, ANOVA, Chi-Squared tests, and correlation tests.

1) Five steps of hypothesis testing

A. Assess assumptions

B. Determine hypotheses and set the significance level

C. Calculate the test statistic

D. Calculate the p-value

E. Conclude and interpret

 

2) Sets of hypotheses

* there will never be equality in the alternative hypothesis.

A. Ho: θ ≤ θo, Ha: θ > θo

B. Ho: θ ≥ θo, Ha: θ < θo

C. Ho: θ = θo, Ha: θ ≠ θo

 

3) Significance level

A. α-level: represents the probability of a type I error.

* α = 0.05 → We have a 5% chance of making a type I error.

B. β-level: represents the probability of a type II error.