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Question 1

What is a “two way” table?

What’s another name for two way table?

Answer 1

When we want to examine the relationship between two categorical variables we tabulate one against the other.

Another name– cross tabulation.

Question 2

How do you know if an association exists between 2 categorical variables?

Answer 2

if the distribution of one variable varies according to the value of the other.

Question 3

What’s the formula for calculating the expected frequency in each cell?

Answer 3

(row total x column total)/ overall total

Question 4

What does a large and small X2 say about the null hypothesis?

Answer 4

Large X2 suggests the data DON’T support the null hypothesis since the observed data are not what we would expect under the null hypothesis.

Small X2 suggests the data do support the null hypothesis since the observed data are close to what we would expect under the null hypothesis.

Question 5

What’s the formula for degrees of freedom for a chi squared test?

Answer 5

v = (r- 1) x (c-1)
r = number of rows in the table
c = number of columns in the table

Question 6

Knowing the test statistic, X2, and degrees of freedom allows us to know what information?

Answer 6

we can obtain the probability of obtaining the observed, or more extreme, data if the Null Hypothesis were true (a P-value).

Question 7

What is the degrees of freedom for:

• chi squared test for independence
• chi squared test for trend

Answer 7

The chi-squared test of independence is designed to provide evidence against the null hypothesis of independence. That means that if there is a sufficiently large dependence of any kind between the two variables, the test will provide evidence against the null.

The chi-squared test for trend is designed to provide evidence against the null hypothesis of no linear trend. So the dependence between the variables needs to be in the form of a linear trend for the test to detect evidence against the null.

While the chi-squared test of independence can be used for a table with any number of rows (r) and columns (c), and has a (r-1)*(c-1) degrees of freedom, the chi-squared test for trend requires that one of the variables has 2 categories and one of the variables can be ordered. The chi-squared test for trend always has 1 degree of freedom because it is focused on one kind of dependence, a linear trend across ordered categories.

Question 8

With what sample sizes can you use X2 (chi squared)?

Answer 8

For 2 x 2 Tables

If the total sample size N >40, then X2 can be used.

If N is between 20 and 40, and the smallest expected value is at least 5, X2 can be used.

r X c (r rows and c columns with r > 2 and c >2)

The X2 test is valid if no more than 20% of the expected values are less than 5 and none are less than 1.

Question 9

What are the six steps necessary to determine whether there is an association between two categorical variables?

Answer 9

1. display data as a 2 way table
2. calculate row or column percentages as appropriate
3. declare null hypothesis and calculate chi squared value
4. calculate degrees of freedom
5. refer to chi squared distribution to get p-value
6. interpret p- value

Question 10

What is correlation?

Answer 10

The method used to assess the degree to which two quantitative variables are associated with each other.

quantifies the strength of the association between two quantitative variables

Question 11

What is linear regression?

Answer 11

describe the relationship between two variables and predict the value of one variable given the value of another variable.

When one of the variables is thought to depend on the other, it is more appropriate to quantify the relationship between them. (quantify = regression)

Question 12

what is an effective and simple way of looking at two quantitative variables?

Answer 12

scatterplot

Question 13

In a scatterplot, what’s usually plotted on x and y axis?

Answer 13

It is standard to plot:

The explanatory variable on the x-axis (horizontal axis)
The response variable on the y-axis (vertical axis)

Example:
to examine whether haemoglobin changes with age:

age = the explanatory variable
haemoglobin = the response variable

Question 14

what is a correlation coefficient?

Whats the standard way of calculating this?

Answer 14

measures the degree of linear association

The standard method is to calculate the Pearson’s correlation coefficient, denoted r.

Question 15

Name 2 features of the correlation coefficient.

Answer 15

• • measures the scatter of the points around an underlying linear (straight line trend)
• • can take any value from -1 to +1

Question 16

what does the line for a positive and negative correlation coefficient look like

Answer 16

r +. line increasing, as one variable increases, the other variable increases.

r - . line decreasing, as one variable increases, the other variable decreases.

Question 17

what is r = 0

Answer 17

no correlation, but sometimes this could be due to a strong non-linear correlation like a U shape

Question 18

Definition of Pearson’s correlation coefficient.

Answer 18

Measures the scatter of points around an underlying linear trend.

Question 19

All variables must be independent for use in a correlation. true or false.

Answer 19

true. all observations should be independent, this means that only one observation for each variable should come from each individual in the study.

Can’t– In a study of pregnant women, blood pressure and estrogen levels were observed at different gestational ages.

Question 20

what are 3 points to remember in the presentation of correlation?

Answer 20

The data should be shown in a scatterplot.
The correlation coefficient, r should be given to two decimal places.
The number of observations should be stated.

Question 21

correlation is most useful for generating hypothesis or causation?

Answer 21

generation hypothesis. can’t show causation.

Question 22

does it matter what’s plotted on the x and y axis for correlation and regression studies?

Answer 22

It matters in regression, not in correlation. Though usually for correlation, it’ll be plotted with the same consistency as regression.

x- axis– explanatory/ independent variable
y- axis– response/ dependent variable.

Ex–BP is explained by age. So BP on y axis, age on x axis.

Question 23

For regression, what goes on the different axii?

Answer 23

x- axis– explanatory/ independent variable
y- axis– response/ dependent variable.

Ex–BP is explained by age. So BP on y axis, age on x axis.

Question 24

How to define the line of best fit for a regression line?

What does the regression line tell us?

Answer 24

The one that minimizes the sum of the square of the residuals.

The regression line gives an estimate of the average value of y for any value of x.

Question 25

What are 3 assumptions that underlie linear regression?

Answer 25

The response variable y has a Normal distribution for each x
The variability of y must be the same across x
The relationship between x and y should be linear

Question 26

when is it valid to use a regression?

What assumptions need to be made?

Answer 26

For a regression analysis to estimate a broadly sensible line:
– The relationship should be at least approximately linear.

For p-values and confidence intervals to be correct there are more assumptions:

• • Residuals should be spread out about the regression line about as much at the left hand end and at the right hand end.
• -Residuals should be approximately normally distributed.

Question 27

what is multi-variable analysis?

Answer 27

we look at one response variable and multiple explanatory variables

Question 28

what are two ways of analysis to control/ address issue of confounding?

Answer 28

1. stratification

separating study subjects into groups according to their exposure to the confounder

2. regression models

analysis of the association of a quantitative response variable with several explanatory variables (quantitative or categorical) simultaneously

Question 29

why do we need multiple variable analysis methods?

Answer 29

When considering the effects of explanatory variables one-by-one, results can be confounded.

Question 30

what are 2 techniques for describing sampling uncertainty in estimates?

Answer 30

• confidence intervals

- hypothesis tests, p- value

Question 31

what is a confidence interval?

Answer 31

A confidence interval for an estimate describes the range of uncertainty in what the true population value might be

Question 32

what is a hypothesis/ significance test

Answer 32

A significance test quantifies the evidence in data against a null hypothesis, using a p-value

Question 33

what is the general formula for calculating the confidence interval?

Answer 33

CI: estimate ± multiplier x SE(estimate)

Question 34

what are the general steps for calculating significance test?

Answer 34

1. state null hypothesis
2. calculate test statistic (z or t)
3. look up calculated statistic to find p value
4. interpret p value