Welcome to STAT 200

STAT 200 - Lecture 1

Randomness and Uncertainty

Is smoking bad for your health?

• How did the medical community conclude that smoking is harmful?

• Why is this not a trivial conclusion?

• In fact, this conclusion was disputed for years before it was widely accepted.

Is smoking bad for your health?

• In 1950, Richard Doll and Richard Peto launched a large-scale prospective observational study with over 40,000 doctors in England.

• This study provided the first widely accepted evidence that smoking is associated with many diseases.

• You can learn more about this study here and here.

New drugs

• There were over 100 different types of vaccines being tested for COVID-19.

• But how do we determine that a vaccine actually works?

  • Some vaccinated people get sick; others don’t.

• Is the vaccine safe?

  • Some vaccinated people develop serious side effects; others don’t.

How do we deal with uncertainties?

• We need data!

• From the data, we can study the variability and identify patterns or trends in the data.

• But we need to be careful!

• How we collect the data affects how we analyze the data and the type of conclusions we can make.

This is where statistics comes in

• Statistics is the science that studies variability.

• It provides us with techniques to:

  1. design studies;
  2. collect, summarize, and analyze data;
  3. create and interpret models to draw conclusions;

Confirmation bias

• Data are interpreted by people.

• The strong convictions some people have may affect how they collect and interpret the data.

• For example, people tend to focus on evidence that supports their beliefs and disregard other pieces of evidence.

• This phenomenon is called confirmation bias.

• It is not uncommon to see two experts, say a CNN expert and a Fox News expert, talking about the same topic, using the same data, and reaching opposite conclusions.

Data subtleties

• Frequently, people miss some subtleties in the data and make conclusions that are not supported by the data.

• For example, what is your interpretation of the following article: “Soaring markets helped the richest 1% gain $6.5 trillion in wealth last year, according to the Fed”

• The category richest 1% is not static. People move between the categories.

Statistics for all!

• Understanding statistical concepts will enable you to assess and question people’s analyses and conclusions critically.

• Do not just accept someone’s findings. Think!

  • What evidence did they present?
  • Is there any evidence they had missed (or buried 😈);
  • Do the data and their analysis actually allow them to reach such conclusions?

You are awesome!

• You are very capable. THINK! Make your own conclusions!

• Don’t feel intimidated by titles. Skepticism and detailed questioning are part of science!

Datasets and variables

Datasets

• Statistics is all about using data to analyze the variability and uncertainties involved in a study.

• Typically, you can think of a dataset as a table where:

  • every row corresponds to an individual/object.

  • every column corresponds to a variable.

Example: Palmer Penguins Dataset

Artwork by @allison_horst

Dr. Kristen Gorman has collected data on 344 penguins from three islands in the Palmer Archipelago, Antarctica.

Artwork by @allison_horst

Multiple variables were recorded for each penguin, such as: island, species, bill depth, bill length, body mass, sex, among others.

Example: Palmer Penguins Dataset

species	island	bill_length_mm	bill_depth_mm	flipper_length_mm	body_mass_g	sex	year
Adelie	Biscoe	42.0	19.5	200	4050	male	2008
Adelie	Torgersen	38.5	17.9	190	3325	female	2009
Adelie	Torgersen	38.8	17.6	191	3275	female	2009
Adelie	Biscoe	40.5	17.9	187	3200	female	2007
Chinstrap	Dream	51.5	18.7	187	3250	male	2009
Adelie	Dream	40.8	18.9	208	4300	male	2008
Adelie	Biscoe	41.4	18.6	191	3700	male	2008
Chinstrap	Dream	46.5	17.9	192	3500	female	2007
Gentoo	Biscoe	46.1	13.2	211	4500	female	2007
Chinstrap	Dream	50.1	17.9	190	3400	female	2009
Gentoo	Biscoe	47.6	14.5	215	5400	male	2007
Chinstrap	Dream	51.7	20.3	194	3775	male	2007
Gentoo	Biscoe	48.7	14.1	210	4450	female	2007
Adelie	Biscoe	39.7	18.9	184	3550	male	2009
Gentoo	Biscoe	51.3	14.2	218	5300	male	2009
Adelie	Biscoe	35.9	19.2	189	3800	female	2007
Gentoo	Biscoe	44.0	13.6	208	4350	female	2008
Adelie	Dream	39.8	19.1	184	4650	male	2007
Gentoo	Biscoe	46.4	15.0	216	4700	female	2008
Adelie	Biscoe	35.5	16.2	195	3350	female	2008
Gentoo	Biscoe	45.5	13.9	210	4200	female	2008
Adelie	Dream	37.3	17.8	191	3350	female	2008
Gentoo	Biscoe	51.5	16.3	230	5500	male	2009
Gentoo	Biscoe	50.5	15.2	216	5000	female	2009
Gentoo	Biscoe	49.8	16.8	230	5700	male	2008
Gentoo	Biscoe	44.5	14.7	214	4850	female	2009
Adelie	Biscoe	36.4	17.1	184	2850	female	2008
Chinstrap	Dream	48.5	17.5	191	3400	male	2007
Gentoo	Biscoe	47.3	13.8	216	4725	NA	2009
Gentoo	Biscoe	48.4	14.6	213	5850	male	2007

Variables

• A variable is a characteristic of each individual (or object) of interest.

• Variables can be classified as Categorical or Quantitative.

Categorical Variables

• Categorical variables are variables whose values are categories (e.g., hair color, marital status);

• If there is an intrinsic order for the categories, we say the variable is Ordinal.

  • Pain level: mild, moderate, severe;

  • Your rank in League of Legends: Iron, Silver, Gold, Diamond;

Quantitative Variables

• A variable is quantitative if it is measured on a numerical scale (e.g., income, age, height).

• Note that the units of measurement must be provided.

Caution

A variable is not necessarily quantitative just because its values are numbers. Sometimes numbers are used to represent categories.

Activity

species	island	bill_length_mm	bill_depth_mm	flipper_length_mm	body_mass_g	sex	year
Adelie	Biscoe	36.4	17.1	184	2850	female	2008
Chinstrap	Dream	50.0	19.5	196	3900	male	2007
Gentoo	Biscoe	45.4	14.6	211	4800	female	2007
Adelie	Dream	37.0	16.5	185	3400	female	2009
Chinstrap	Dream	52.8	20.0	205	4550	male	2008
Gentoo	Biscoe	46.1	13.2	211	4500	female	2007
Gentoo	Biscoe	53.4	15.8	219	5500	male	2009
Adelie	Torgersen	36.6	17.8	185	3700	female	2007
Chinstrap	Dream	45.5	17.0	196	3500	female	2008
Adelie	Torgersen	39.6	17.2	196	3550	female	2008
Gentoo	Biscoe	45.1	14.4	210	4400	female	2008
Adelie	Biscoe	40.6	18.8	193	3800	male	2008
Adelie	Dream	39.8	19.1	184	4650	male	2007
Adelie	Dream	37.3	16.8	192	3000	female	2009
Chinstrap	Dream	47.0	17.3	185	3700	female	2007
Gentoo	Biscoe	49.5	16.2	229	5800	male	2008
Adelie	Dream	38.9	18.8	190	3600	female	2008
Adelie	Torgersen	34.4	18.4	184	3325	female	2007
Chinstrap	Dream	51.5	18.7	187	3250	male	2009
Chinstrap	Dream	46.9	16.6	192	2700	female	2008
Gentoo	Biscoe	46.2	14.4	214	4650	NA	2008
Gentoo	Biscoe	48.7	15.1	222	5350	male	2007
Gentoo	Biscoe	51.1	16.3	220	6000	male	2008
Gentoo	Biscoe	50.5	15.9	222	5550	male	2008
Gentoo	Biscoe	48.1	15.1	209	5500	male	2009
Gentoo	Biscoe	49.2	15.2	221	6300	male	2007
Gentoo	Biscoe	50.8	17.3	228	5600	male	2009
Adelie	Torgersen	34.1	18.1	193	3475	NA	2007
Adelie	Dream	39.5	16.7	178	3250	female	2007
Chinstrap	Dream	50.8	19.0	210	4100	male	2009

• Categorize each variable in the penguins data frame as categorical or quantitative.

References & Attributions

Image Attributions

• Cigarettes: Marcus Quigmire from Florida, USA, CC BY-SA 2.0, via Wikimedia Commons.

• Drug vials: Image Attribution: Neilsmith38, CC BY-SA 4.0, via Wikimedia Commons

• Artwork by @allison_horst.

References

Horst, Allison Marie, Alison Presmanes Hill, and Kristen B Gorman. 2020. Palmerpenguins: Palmer Archipelago (Antarctica) Penguin Data. https://doi.org/10.5281/zenodo.3960218.