Math 140: Chapter 1, Introduction to

Data

Everyone gets a card; each group gets a corner (hearts, diamonds, spades, clubs)

Discuss in your group what we can say about this data (any characteristics)? What could it represent? What couldn’t it represent?

97, 98, 94, 92, 31, 98, 93, 95, 97, 98, 98

Each group share out

Here’s some data…

Everyone gets a card; each group gets a corner (hearts, diamonds, spades, clubs)

Discuss in your group what we can say about this data (any characteristics)? What could it represent? What couldn’t it represent?

4.0, 6.8, 7.1, 7.1, 7.2, 7.4, 7.7, 7.8, 12.1

Each group share out

Here’s some data…

Observations that you or someone else records

Data is more than numbers; it is numbers in context ... the story behind the numbers...

Data is/are…

Talk for two minutes then be ready to share out

Who collects data?

News media; surveys galore!

Any recent news report (based on survey or poll) that you can recall? Radio? TV? Internet?

Who collects data?

Then comes parenthood — and with it, an average weight gain of roughly 3-5 pounds for a man who lives in the same home as his child. Over the roughly 6 years following the birth of their first child, live-in dads picked up an average of about .6 BMI units. For a 5’10” man weighing 175 pounds, that is a weight gain of about 4 pounds.

The results of the study indicated that this was a near-universal phenomenon.

During the same period, the average BMI of men who had not fathered a child tended to decline slightly. The average BMI for men not living with their babies went up as well but not as much as those dads who lived in the same home as their child.

The study used data collected on 10,623 young men over a 20-year period as part of the National Longitudinal Study of Adolescent Health. Many of those tracked were enrolled when they were 12, and some were followed to the age of 34.

Recent LA Times Article...Weighing Fatherhood? Gaining a few pounds comes with the territory.

Using the fatherhood weight-gain setting, let’s discuss:

sample, statistic, variation data set population, parameter experiment, observational study causality, association, confounding variables random selection, random assignment numeric variable, categorical variable

Vocabulary...

Variables record characteristics of people or things

Weight in pounds of women who had babies at Henry Mayo on a particular day

Test scores in my Honors Algebra class

Proportion of people who reported that they wear glasses when they drive

Characteristics, variables …

Sample Statistic(changes from

sample to sample; can vary)

Examples include

Population Parameter(is fixed; does not

change)

Examples include µ, p,

σ

Sample vs. Population …

Always, always comment, answer, compare, contrast… whatever the case.. in context

What are the objects? What was measured? What are the units of measure?

Example… Researchers studied the amount of tofu, in pounds, that a typical American consumes per year.

Context is key!

Consumer beware…

Questions to ask yourself before you believe a poll/survey... Who carried out the survey?

How was the sample selected?

How large was the sample?

What was the response rate?

How were the subjects contacted?

When was the survey conducted?

What was the exact question asked?

Number students off; randomly choose seven students

Come up to board and write where you last went out to eat and how much you spent there (approximately).

What are our variables?

Two types of variables:

What else can we observe about our data? Trends? General statements?

Two types of variables…

Can you think of a categorical data that looks like numerical data… but it isn’t. It’s really categorical. Discuss for a minute…

Sometimes it’s in camo…

Can you think of a categorical data that looks like numerical data… but it isn’t. It’s really categorical. Discuss for a minute…

Always ask yourself, does finding the mean (average) of this data make sense?

Sometimes it’s in camo…

With a partner, one of you come up to the board and write your gender and yes or no to indicate pierced ears or not.

What trends do you see?

Categorical data…

Let’s do this again...Ears Pierced Ears NOT

Pierced

Male

Female

Suppose on a given day we randomly ask 200 Disneyland visitors if they have been on Space Mountain yet that day.

23% said they had been on Space Mountain already. How many of these visitors had been on Space Mountain already?

Finding ‘how many’ from percents…

Suppose we randomly ask another group of Disneyland visitors if they have been on Thunder Mountain yet that day. 14% tell us yes, and this is equal to 42 visitors.

How many total visitors were in our survey?

Finding ‘how many’ from percents…

Sport Injuries ParticipantsBaseball 178,668 15,600,000

Basketball 615,546 28,900,000Bowling 21,133 43,900,000Football 387,948 17,700,000

Ice Hockey 16,435 2,100,000Soccer 178,519 14,500,000Softball 125,875 13,600,000Tennis 19,633 11,000,000

Volleyball 59,225 11,500,000

Rates vs. Raw Numbers…

There are always firefighters at fires. Therefore, firefighters cause fires

x: Person regularly attends religious services y: How long a person lives

x: Number of ministers y: Rum imports

x: HS seniors’ SAT scores y: Students’ first year GPA

Causality vs. Association

x causes y, there must be a controlled, randomized, well-designed experiment

Treatment (explanatory, factor) variable; Response (outcome) variable

Sample size ‘large’

Treatment group (receiving treatment(s); control group (receiving placebo)

Random assignment of subjects (or experimental units)… using an acceptable randomization process

Double-blinding is best

To even consider using the phrase…

Reduce bias

Bias: Systemically ‘off’

Examples: scale, clock

Goal:

Gastric freezing is a proposed treatment for ulcer pain in the upper intestine. In this treatment the patient swallows a deflated balloon with tubes attached. Then a cold liquid is pumped through the balloon for an hour.

The rationale is that the cooling will reduce production of acid and relieve ulcer pain. A study reported in the Journal of the American Medical Association provided gastric freezing to a large number of patients and reported that gastric freezing reduced acid production and relieved stomach pain.

Based on this the (safe and easy) treatment was used for several years.

A later study divided ulcer patients randomly into two groups. The first group was treated by gastric freezing. The second group received a placebo treatment in which the liquid was at body temperature rather than cooled

In the first group 34% of 82 patients improved. In the second group 38% of 78 patients improved. Based on this second study gastric freezing was discontinued as a therapy for ulcers.

Gastro follow-up…

Is it well designed? Why or why not?

Marshmallow videohttps://www.google.com/?gws_rd=ssl#q=jimmy+kimmel+marshmallow+test

Random selection/assignment? Replication? Confounding variables? Control/Comparison group? Double blinded? Placebo?

Why is this an experiment?

https://www.youtube.com/watch?v=RK-oQfFToVg

Random selection/assignment? Replication? Confounding variables? Control/Comparison group? Double blinded? Placebo?

Jimmy Kimmel… “experiment”

Is this an observational study or a controlled experiment?

Experiment? Was there a large sample size? Was randomization used to assign participants to treatment groups? Was the study double-blinded? Was there a placebo?

Was the paper published in a peer-reviewed journal or just posted on internet?

Did the study follow the subjects for a long period of time?

Again, consumer beware…

You and your partner create a list of a total of 3 questions we may use for a survey (data we may collect) this semester; be specific; be “G” rated

Next to each question, write the type of data your question is asking for (categorical or numerical) and justify why it is that type of data

Example: What do you weigh in pounds? This is quantitative data.

But both your names on the paper; write neatly

Exit Ticket…