Chapter 6 - Statistical Data

Question 1

We collect data from ___________ and use them to ____________.

Answer 1

real world experiences, draw conclusions

Question 2

We choose a ___________ to study, collect measurements from a small representative subset or ________ of that population, then apply our findings back to the larger population to assess if they ____.

Answer 2

population, sample, and fit.

Question 3

What is a simple model?

Answer 3

An average or a mean

Question 4

What is one way to calculate a simple model?

Answer 4

Calculate an average, then look at the difference between each data point and the average value.

Question 5

How can we observe how well our data fits the model?

Answer 5

Take the sum of the squared differences (Standard Deviation)

Question 6

How do you quantify model accuracy?

Answer 6

Model + Error

Question 7

What does the frequency distribution indicate in the deviation around the average? There are two main take-aways

Answer 7

• Flat Distribution = More deviation
• Skewed Distribution = a few outliers pulling the average up or down

Question 8

What does the Standard Deviation measure?

Answer 8

The amount of variation among the individuals you sampled.

Question 9

How does the Standard Deviation measure variation among variables?

Answer 9

By comparing the values / measurements of each value to the mean of all values.

Question 10

How do you retrieve the Standard Error?

Answer 10

1. Take a bunch of subsamples
2. Calculate the mean of each subsamples
3. Calculate the standard deviation of the subsample means

Question 11

What is a Confidence Interval?

Answer 11

Calculating the top and bottom levels within which a measurement will fall 95% of the time.

Question 12

What do we use to find the Confidence Intervals?

Answer 12

A formula to calculate the range of values in which 95% of the actual measurements occur.

Question 13

What do Confidence Intervals indicate?

Answer 13

Being 95% sure that the true population means that 95% of your population will fall within that range.

Question 14

What is the equation of the simplest model?

Answer 14

Linear Model: y = mx + b

Question 15

True or False: Not all relationships can be modelled well using a straight line.

Answer 15

True

Question 16

What are the stages of constructing a Model?

Answer 16

1. Stating a Problem
2. Developing a Hypothesis about a population
3. Make a prediction
4. Collect data from sample
5. Fit a model to the data points
6. Test how well model represents

Question 17

What does it mean if a model does not explain variation (relationships) between data points very well?

Answer 17

We have less confidence bin that model to predict what’s going on in the broader population.

Question 18

What are two ways to compare means?

Answer 18

1. Independent Sample T-Tests
2. Analysis of Variance (ANOVA)

Question 19

What does ANOVA stand for?

Answer 19

Analysis of Variance

Question 20

Which method of comparing means takes “two groups that are independent of each other”?

Answer 20

Independent Sample T-Test

Question 21

Which method of comparing means takes “more than two groups”?

Answer 21

Analysis of Variance

Question 22

When comparing means, how can you determine whether the difference between the means is “real”?

Answer 22

By analyzing the p-value.

Question 23

What does the p-value indicate in comparing differences in means?

Answer 23

It incorporates
- the magnitude of difference in means
- the sample size within each group, and
- the variation of values in each group to make its judgement

Question 24

The __________ tells you whether the difference between groups is probably just a function of random chance or whether it’s something that likely holds true throughout the population.

Answer 24

p-value

Question 25

How can you test whether two numeric variables are significantly related to one another?

Answer 25

By using a correlation coefficient or linear regression analysis.