Univariate data analysis

Learning outcomes

The study of variability important to help answer: "what happened?"
Univariate tools such as the histogram, median, MAD, standard deviation, quartiles will be reviewed from prior courses (as a refresher)
The normal and t-distribution will be important in our work: what are they, how to interpret them, and use tables of these distributions
The central limit theorem will be explained conceptually: you cannot finish a course on stats without knowing the key result from this theorem.
Using and interpreting confidence intervals will be crucial in all the modules that follow.

New Boeing planes will generate 0.5 TB of data per flight. Read about this, and other sources of data: "every piece of that plane has an internet connection, from the engines to the flaps to the landing gear".
All students, but especially the 600-level students should read the article by Peter J. Rousseeuw, Tutorial to Robust Statistics it is easy to read, and contains so much useful content.

Introduction [05:59]
Histograms [04:50]
Basic terminology [06:41]
Outliers, medians and MAD [04:42]
The central limit theorem [06:56]
The normal distribution, and standardizing variables [05:54]
Normal distribution notation and using tables and R [05:48]
Checking if data are normally distributed [05:57]
Introducing the idea of a confidence interval [covered in class]
Confidence intervals when we don't know the variance [07:59]
Interpreting the confidence interval [07:52]
A worked example: calculating and interpreting the CI [03:37]
A motivating example to see why tests for differences are important [08:29]
The mathematical derivation for a confidence interval for differences [covered in class]
Using the confidence interval to test for differences to solve the motivating example [covered in class]
Confidence intervals for paired tests: theory and an example [11:59]