Exam 3 Lecture 3

Question 1

If your data follow a __________, then your data have a ‘normal distribution’.

Answer 1

Bell curve. If your data have a normal distribution, then you can use common statistical analysis tools.

Question 2

Extreme values are ___________. Central values are _____________.

Answer 2

Extreme values are rare. Central values are common.

Question 3

Explain what happens when you get further from the central tendency.

Answer 3

The further you get from the central tendency, the fewer the data points. Most values in the data set are close to the middle/central tendency.

Question 4

Normal Distributions

Answer 4

The data values in a dataset follow a patten
The distribution of data values is as expected (no weird numbers, no clusters of numbers that are not near the central tendency)
This is a naturally occurring distribution in many situations
- IQ, SAT, GPA, BP, height
But some data are NOT NORMAL

Question 5

When the distribution is normal, the following are true:

Answer 5

Mean = median = mode
It is symmetrical. Half of data are on the left, half the data are on the right.

Question 6

Normal Distributions

Answer 6

The shape of the curve allows us to predict how people will score.
The distribution is proportional
- 68% will score within 1 standard deviation from the mean
- 34% will be a little better than average
- 34% will be a little worse than average
The slope isn’t that steep

• 95% will score within 2 standard deviations from the mean (27% more)
• Slope is really steep!
• 99.7% will score within 3 standard deviations from the mean (4.7% more)
• Slope starts to flatten out
• These #s are rare.

Question 7

What is a histogram?

Answer 7

A bar graph that is specifically designed to tell you how frequent a data value is in a dataset.

Question 8

Normal Distributions
LOTS of statistical tests- which is how we compare or associate variables- ASSUME a normal distribution.
If the data aren’t normal, then ?

Answer 8

You fail to meet assumptions of the statistical test and the results are not reliable.

Question 9

Typical statistical tests are comparing MEANS. What is the caveat to this?

Answer 9

That comparison might not be fair if the data aren’t normal.

Question 10

Normal distributions mean the data are ____________.
You can predict more because there is a __________ to responses.

Answer 10

Normal distributions mean the data are predictable. You can predict more because there is a pattern to responses. Helps compare means & variance.

Question 11

To know if the DISTRIBUTION is NORMAL, you need to find the _______________

Answer 11

Mean, mode, and median

Question 12

Once you know the distribution is normal, to understand the DISTRIBUTION, you need to know _________________

Answer 12

The mean and the standard deviation.

Question 13

3.5 4.0 4.5 5 5.5 6.0 6.5
What is the mean and the SD?

Answer 13

The mean is 5 and the SD is .5

Question 14

If the mean is 311 and the SD is 5, how should the values be arranged on a bell curve?

Answer 14

296 301 306 311 316 321 326

Question 15

Data that fits a bell curve is predictable. When we know what the data ‘look like’ it is easier to analyze. Data that fit a bell curve all increase __________… that rare values are rare!

Answer 15

Increase reliability that rare values are rare. (And common/average values are common).

Question 16

What is it called if the distribution is too tall or too flat? What are some examples of this?

Answer 16

If the distribution is too tall or too flat, this is KURTOSIS. It is KURTOTIC.
- Too many people clumped near average (this makes the distribution tall)
- Too many people far from average in tails (this makes the distribution flat)
Tall= leptokurtic
Flat= platykurtic

Question 17

What is it called when the distribution is tipped to the left or right?

Answer 17

SKEW (aka, off-center)
- Too many people above average (positively skewed)
- Too many people below average (negatively skewed)
It’s a measure of asymmetry

Question 18

What happens to the mean, median, and mode when the graph is skewed?

Answer 18

Mean is not equal to median is not equal to mode.
- Mean is in the center, but the peak (mode) is not.
- Mean is less meaningful. It doesn’t tell you what is most likely in a sample. It overvalues the tail (those far away from typical).

Question 19

How can one tail be too long?

Answer 19

One boundary, one open end (wait time, weight, income)
Zero-inflation (alcohol -> lots of non-drinkers)

Question 20

What is zero-inflation in a skewed distribution?

Answer 20

Lots of zeros!
Alcohol -> lots of non-drinkers.
This skew tells us that it is more common to be a non-drinker or a light drinker than a heavy drinker.

Question 21

What is only 1 boundary in a skewed distribution?

Answer 21

There is only one boundary.
For example, flights. There is only one boundary (on time to forever). This skew tells us that the flight most often takes off on time or close, but sometimes it can be HOURS.

Question 22

Only 1 boundary in a skewed distribution example with doctors

Answer 22

This skew tells us that it is uncommon for doctors to run on time; most of them make us wait a long time!

Question 23

Not everyone conforms…
Overall, your dataset can look ‘normal’ but there can still be a few data points that don’t fit expectations. What do you do with unexpected values?
What are unexpected values?

Answer 23

(If it is too many unexpected values, you have a problem with your data/study)
- An extremely low value
- An extremely high value
- A value that is very far from the mean

Question 24

Outliers versus errors

Answer 24

Is the outlier an ERROR?
- Errors add BIAS to your results.
- Errors can alter the MEAN and the VARIANCE

Is the outlier REAL?
- Sometimes a number is unlikely but not impossible
- These data can alter the MEAN and the VARIANCE, but is it BIAS?
- There is no single rule about what an outlier is. All data ‘behave’ differently (HR has a known range, brain activity does not)

Keep or chuck?
HR= 1000 (Error! This is impossible).
Drinks per day= 60 (Unlikely but not impossible!)

Question 25

Data literacy= asking: Did they have a plan?
When to keep vs. discard data
Errors vs. outliers

Answer 25

With all data, the goal is always to use as much as possible! Some people think- if a data point looks weird, chuck it! But it’s not that simple!
- Yes, errors add BIAS
- But chucking data can also introduce BIAS
- To avoid BIAS, you need a REALLY CLEAR plan about what you are chucking, and why.

Errors= not real data -> always discard
Outlier= real data -> test/ discard or transform
- When a data point is so extreme that it throws off the central tendency, the variance, or the distribution, it is called an influential outlier
- Statisticians have rules about discarding a data point. They also have multiple ways to transform a data point to make it more ‘manageable’ but still ‘different’/
A good statistician tries to use all available data whenever possible.

Question 26

When a data point is so extreme that it throws off the central tendency, the variance or the distribution, it is called an

Answer 26

Influential outlier