Module 2

Question 1

What is a case-control study?

Answer 1

A study comparing cases and controls

Question 2

What is a retrospective case control study?

Answer 2

Researchers looking back on how subjects behaved over time, looking at case group and control gorup

Question 3

Draw the casual model(i.e. the “directed acyclic graph). Include the mediator, and have arrows which show “what we already know”, “what we can prove”, and “what we want to know”

Answer 3

Refer to PCV 2.1

Question 4

What is sampling variability/error?

Answer 4

When you draw a random and representative sample from a population, it is not always going to be the exact same sample every time you draw it.

Question 5

3 students draw a sample of 5 observations from the population. How many samples did each student draw from the population? What is the sample size used in the experiment?

Answer 5

1 sample with a sample size of 5

Question 6

What is a sampling distribution?

Answer 6

First you take several samples and take the mean of each sample. Then, you treat the sample means as the new data set and plot a histogram.

Question 7

What is a sample distribution?

Answer 7

A sample distribution would be a histogram of the values within one sample

Question 8

As you increase the sample size, what happens to the standard deviation, graph shape, and mean of the sampling distribution graph for a NORMAL distribution?

Answer 8

The graph tightens, variability decreases, standard deviation also decreases. The shape of the graph does not change.

The mean of the means does not change with an increased sample size.

Question 9

What is n?

Answer 9

The sample size

Question 10

As you increase the sample size, what happens to the standard deviation, graph shape, and mean of the sampling distribution graph for a UNIFORM distribution?

Answer 10

Mean of the means is unchanged

The standard deviation gets smaller

The shape of the sampling distribution becomes more and more normal

Question 11

What are some synonyms for a normal graph

Answer 11

symmetric
gaussian
bell shaped

Question 12

What is the central limit theorem?

Answer 12

When n is “sufficiently” large, the sampling distribution for a particular statistic(e.g. sample mean) will tend towards a normal distribution even if the underlying population distribution is not Gaussian.

Question 13

What is the normal distribution? What are the two parameters for a normal distribution? If a random variable X is distributed normally, then we denote it as ….

Answer 13

The normal distribution is a continuous probability distribution for real-valued random variable. The two parameters for a normal distribution are the mean (mu) and variance(sigma squared).
(Notation in notes)

Question 14

How does the normal distribution differ from the binomial distribution?

Answer 14

The binomial distribution is a discrete probability distribution. This means that the values that our random variable X could take on were clearly delineated integers, like the number of heads in five coin flips. X could not be a fraction like three and a half heads.

In comparison, the values that the random variable X could take on in a normal distribution could include fractions of a whole unit

Question 15

In a normal distribution, what do the mean and variance tell us about the graph?

Answer 15

1. The mean tells you about the location of the distribution. The shape would remain the same if only the mean of a normal distribution is changed
2. The variance tells us about how widely distributed the values are. The centre of the distributions would be the same but the peak of the graph and the width of the graph would change.

Question 16

The probability of observing random, normally-distributed values within a given range is equal to

Answer 16

the associated area under the curve (AUC)

this works by considering intervals of potential values for X as defined on the x-axis of the p-lot, then calculating the proportion of th total area under the curve that falls within that interval. This would give us the probability of observing a random normal variable from this population with a value in that range.

Question 17

Can you calculate the probability for a single value of X in a normal distribution?

Answer 17

No, when working with continuous distributions like the normal distribution, our probability will always be anchored to an interval.

Question 18

If a random variable X is distributed normally, why do we know about the standard deviations?

Answer 18

1. There is an approximately 68% chance X falls within one standard deviation of the mean
2. there is an approximately 95% chance falls within two standard deviations of the mean
3. There is an approximately a 99.7% chance X falls within three standard deviations of the mean

Question 19

The value you get for the probability density function is not a probability in and of itself. What do you have to do to calculate the actual probability?

Answer 19

Use calculus to integrate the PDF across the desired rand and calculate the AUC which tells you the probability X falls in the range.

Question 20

What is a transformation?

Answer 20

transformations are just functions that map a value in one space to a value in a second space. Usually we can identify functions to “back-transform” the new data to the original space(useful transformations will allow us to do this).

Question 21

What is the log transformation look like(i.e. the calculations)? What are log transformations useful for?

Answer 21

To go from original data to log transformed data: take the log of the x value you are trying to transform, keep the y value the same. TO back transform take the (new) x value to the power of 10.

Log transformation are useful fro mapping right-skewed distributions into more normal distributions in the transformed space.

Question 22

What is the formula for calculating the 95% confidence interval for a population mean? Define each variable.

Answer 22

Refer to notes page

Question 23

Is the confidence interval random?

Answer 23

Yes. Our X bar could be different depending on the specific random sample we take. Moreover, the confidence interval will either cover or not cover the true mean

Question 24

What is the coverage probability?

Answer 24

The fraction of samples that are taken from the dataset that cover the true population mean

Question 25

What is the difference between mu and X bar?

Answer 25

mu is the population mean X bar is the sample mean

Question 26

What is one reason why a CI might have a coverage possible lower than 95%? What are two ways this can be fixed?

Answer 26

If the population data is non gaussian(i.e. very skewed), the our confidence interval is not going to have 95% coverage probability. We can fix this by increasing the sample size. You can also use a log transformation to create a Gaussian distribution, even with a small sample size

Question 27

How well the data conforms to the stated coverage probability depends on the ________(1)

Answer 27

(1) shape of the population distribution and the sample size

Question 28

The standard deviation of the sampling distribution of X bar is known as ______(1). What is the formula for this?

Answer 28

the standard error of X bar formula in notes

Question 29

What are the three differences between a distribution of gaussian observations vs a distribution of sample means?

Answer 29

Distribution of Gaussian observations: - made up of individual observations from the populaiton - Centered at population mean mu - Variability quantified by standard deviation Distribution of sample means - Made up of sample means calculated from infinite samples of size n from the popualtion - Centered at population mean mu - Variability quantified by standard error

Question 30

When calculating confidence intervals, we assume that the true value of mu is equal to

Answer 30

X bar

Question 31

How do you calculate the margin of error? How do you calculate the width of the 95% confidence interval?

Answer 31

Refer to notes

Question 32

As n increases, the width of the 95% confidence interval goes _____(1).

Answer 32

(1) down

Question 33

What effect would lowering the standard deviation have on the standard error, the margin of error, and the width of the confidence interval?

Answer 33

It would lower all of them

Question 34

What is the formula for calculating sample variance?

Answer 34

Refer to notes sheet

Question 35

What are the three rules that are relevant to log transformed data?

Answer 35

1. The mean of the logged data is almost equal to the median of the logged data 2. The log of the median(of the regular data) is equal to the median of the logged data. This is because the median is an observable value in the dataset 3. The log of the mean(of the regular data) is NOT equal to the mean of the logged data.

Question 36

When you do 10 raised to the power of the mean of the log data. what do you get?

Answer 36

the median of the raw data

Question 37

You just calculated the confidence interval for the mean of the data in log dollars. If you exponentiate these values, what would the new interval tell you?

Answer 37

The confidence interval for the median of the raw data

Question 38

What does stratified mean?

Answer 38

Stratification is the process of dividing members of the population into homogeneous subgroups before sampling.

Question 39

What is a histogram?

Answer 39

Graphs with bars that count values in dataset and give us an overview of the data distribution. tell us the skewness of our data

Question 40

What are the drawbacks of a histogram?

Answer 40

1. Hard to see the centre of distribution to compare "typical" values 2. Hard to plot the two distributions together on the same graph

Question 41

What is a density plot? What is the drawback of a density plot?

Answer 41

Similair to a histogram but you have lines instead of bars. The height of the line represents the amount of points at that particular x value in our dataset. Tell us the skewness of our data It is hard to see the centre of distribution to compare typical values

Question 42

The standard deviation of the sampling distribution is called the standard error. How do you calculate the standard error?

Answer 42

sigma/sqrrt(n)

Question 43

Write the formula to calculate variance.

Answer 43

On notes

Question 44

As n increases, the width of the CI goes

Answer 44

down

Question 45

What is a Q-Q plot?

Answer 45

A method for comparing the location(center), spread and shape of one distribution against another. - Sample vs. theoretical distribution: Does the shape of my data look gaussian - Sample vs. Sample: Do these two data sets have the same distribution?

Question 46

What are the benefits of boxplots?

Answer 46

Can be used to compare 2 different sets of data. Can see the center and spread, but somewhat harder to see the complete shape of the distrivtuon.

Question 47

How do you calculate the width of the 95% confidence interval? How do you calculate the margin of error?

Answer 47

Refer to notes

Question 48

What is the general form for calculating the 95% confidence interval for one population mean?

Answer 48

Estimate +/- 2(SE)

Question 49

How do you calculate the 95% confidence interval for a difference in population means? Include the two ways of calculating the standard error of the difference ein means

Answer 49

Refer to notes

Question 50

What do you get if take 10 raised to the power of the difference in means ON THE LOG SCALE?

Answer 50

The ratio of the medians in real dollars! i.e. how many times the median for one is greater than the median for the other

Question 51

What is paired data?

Answer 51

Data where every observation in one group has a corresponding observation in the other. The pairs are based on similar characteristics between individuals in the group, or you can also pari a person with themselves

Question 52

When given paired data, how do you calculate?

Answer 52

You calculate the mean of the paired differences

Question 53

What is independent data(unpaired)?

Answer 53

Different individuals independent of one another. There is a group with and there is a group without

Question 54

When given unpaired data, how do you calculate?

Answer 54

Use the difference in population means(i.e. the longer version of the confidenc interval)

Question 55

what would the null value be for mean paired difference in paired t-test?

Answer 55

0

Question 56

what would the null value be for difference in means for unpaired t-test?

Answer 56

0

Question 57

What are the 6 steps involved in hypothesis testing?

Answer 57

1. Specify a precise null hypothesis about the population 2. Specify the outcome variable 3. Specify the Type I error rate/a/significance level. Is usually 0.05 or 5% 4. Choose an estimator from your data that is relevant to the hypothesis - Ould be the mean for a continuous outcome 5. Calculate the confidence interval (1-a) x 100% 6. Reject(if null is not in interval) or fail to reject the null hypothesis

Question 58

How do you know a fake coin sequence?

Answer 58

It will have long streaks of H's or T's

Question 59

What is the p-value? How do we know when or when not to reject the p-value?

Answer 59

The p-value is the probability, when the null hypothesis is true, of observing test static as or more extreme than what occurred in the sample. If p vale if less than alpha value then reject the null.

Question 60

What is a type I error?

Answer 60

Reject the null hypothesis when its true

Question 61

What is a type II error?

Answer 61

Fail to reject the null hypothesis when its false

Question 62

Are hypothesis tests constructed to control the rate of type I errors or type II errors?

Answer 62

Type I Errors

Question 63

How can you minimize type II error?

Answer 63

Increase the size of the sample