Biostats test 3

Question 1

null hypothesis for chi squared test

Answer 1

H0: no association, variables are independent

Question 2

How does H0 translate to cell frequencies?

Answer 2

Cell counts are proportional to the marginal (row and column) totals.

Question 3

Formula for expected frequencies

Answer 3

In formula: E = (row total x column total) / n

Question 4

What does chi quared test measure

Answer 4

If the differences between observed and expected frequencies are large enough to reject H0

Question 5

DF for a 2x2 table

Answer 5

1

Question 6

Formula for DF of a cross-table

Answer 6

df = (rows – 1) x (columns – 1)

Question 7

What do we use to test effect size of chi squared test

Answer 7

Phi for 2x2, Cramer’s V for cross-table. Only do this for if test is significant, then will inform about the strength of the association.

Question 8

Chi squared goodness of fit test

Answer 8

Determines whether the distribution of observed frequency counts differs from some other distribution

Question 9

Odds formula

Answer 9

prob event/prob non-event

Question 10

Risk formula

Answer 10

risk for specific/total

Question 11

Sensitivity

Answer 11

the proportion of positives that are correctly identified as such (so sick people being diagnosed as having the condition)

Question 12

Specificity

Answer 12

the proportion of negatives correctly identified as such (healthy people being diagnosed as not having the condition)

Question 13

Prevalence

Answer 13

The number of cases of a disease, number of infected people, or number of people with some other attribute present during a particular interval of time

Question 14

Sensitivity formula

Answer 14

TP / (TP + FN)

Question 15

Specificity formula

Answer 15

TN / (FP + TN)

Question 16

PPV definition

Answer 16

The likelihood that a person who has a positive test result does have the disease, condition, biomarker, or mutation (change) in the gene being tested

Question 17

PPV formula

Answer 17

PPV = TP / (TP + FP)

Question 18

NPV formula

Answer 18

NPV = TN / (FN + TN)

Question 19

Bayes

Answer 19

demonstrated how prior probabilities may affect estimated probabilities for events.

Question 20

Cohen’s kappa

Answer 20

measures inter/intrarater reliability

Question 21

Cohen’s kappa formula

Answer 21

2(ad – bc) / (r1 x c2 + r2 x c1)

Question 22

What is regression analysis used for

Answer 22

Predict values of an outcome variable on the basis of other variables. Aim is to build a model that describes variability in a dependent variable (Y) as a function of one or more independent (X) variables:
Yi = f(X1i, X2i, …). Causality may very well play a role.

Question 23

What does pearson’s R squared represent in OLS output

Answer 23

the proportion of total variation which is being explained: ssmodel/sstotal

Question 24

What does an outlier in the Y space do to the correlation coefficient

Answer 24

Pulls the correlation towards it, boosting it

Question 25

What does an outlier in the X space do to the correlation coefficient

Answer 25

Pulls the correlation towards it, lowering it

Question 26

Simpson’s paradox

Answer 26

a phenomenon in statistics where a trend that appears in several groups of data reverses when the data is combined. In other words, a relationship between two variables that holds within individual groups can disappear or even reverse when the data from those groups is pooled together.

Question 27

When is Spearman’s rank used

Answer 27

variables are at ordinal data level, the relationship is monotonic, but non-linear or
outliers might affect Pearson’s r too much

Question 28

What are model coefficients in a regression equation

Answer 28

the terms in your function that optimally relate predicted values of the dependent variables to observed values, often denoted as b0, b1, b2

Question 29

What you should look for in your data before you start a regression analysis

Answer 29

Correct mistakes, check for outliers, stratification, non-linearities, … for all possible predictors!

Question 30

What is each factor in this equation: Yi = b0 + b1X1i + ei

Answer 30

b0 is called the intercept (it is a constant). b1 is the regression coefficient for X1
= (estimated) slope for best fitting line in scatter plot of X versus Y. ei is a prediction error, a residual –it is the difference between a predicted and an observed Y value (for a given X value). Yi = predicted value of Y on basis of model + prediction error.

Question 31

What is H0 for OLS regression

Answer 31

H0: no relation between X1 and Y. b1 = 0, no effect of changes of X1 on Y. r2 = 0, no variance explained by the model

Question 32

Aim in OLS for finding values

Answer 32

want to find values for b0 and b1 that optimally relate outcomes of Y to values of X1

Question 33

Predicting Y without any information about X

Answer 33

Mean of Y would be best guess because unbaised. This total prediction error = total sum of squares. Without predictors, SS total = SS error (sum of squares of residuals). All the variability in Y would be unexplained error.

Question 34

Predicting Y when you do have info about predictors

Answer 34

Adding predictors to your model, you hope to make better predictions.
By adding predictors, you hope that the ratio of SS total and SS error (sum of squares of residuals) improves, eg that a larger percentage of the variance in Y can be explained.
Better model, < SS error.

Question 35

‘best fitting’: Least squares criterion (OLS regression)

Answer 35

The ‘best fitting model’ is the one for which SS error reaches a minimum.

Question 35

Yi

Answer 35

predicted value on basis of model + prediction error

Question 36

SStotal

Answer 36

Sum of squared difference scores between Y values and mean of Y (the total variability in Y around its mean) ; SSmodel + SSerror. But in the case when nothing is known about the predictors (so-called null model), SStotal = SSerror

Question 37

SSerror

Answer 37

sum of the squared differences between the actual observed values of the dependent variable (Y) and the values predicted by the model. (Yi - Yhat)^2

Question 38

SSmodel

Answer 38

Sum of squared differences between the mean of Y and the predicted value of Y. The amount of variability in Y that is explained by the model. (Y hat - Y bar)^2. Variance explained.

Question 39

Model fit is proportion of

Answer 39

total variability in Y (SStotal) accounted for by sum of squares model prediction (SSmodel). so SSmodel/SStotal

Question 40

A Standardized (Beta) regression coefficient

Answer 40

indicates how many standard deviations the dependent variable changes with a standard deviation change of the predictor

Question 41

How can beta values be interpreted

Answer 41

in terms of the importance the predicators have in the predictive power of the model
Larger |value|, more influence
Looking at Beta values is useful with multiple regression models –different coefficients may all reach statistical significance, but their impact may differ

Question 42

indicator coding

Answer 42

creating dummy variables with values 0 or 1

Question 43

dummy variables

Answer 43

Dummy variables have values 0 or 1, where 0 means: ‘does not have the property’ and 1 means ‘has the property’. To code k categories, you need k - 1 dummies.

Question 44

reference category

Answer 44

an original level value that does not have its own dummy variable is the reference category

Question 45

synergy

Answer 45

if an interaction term is significant and its b is positive, the predictors have synergy (they strengthen each other)

Question 46

Multiple predictors

Answer 46

With two predictor X1 and X2, b1 indicates how Y will change with a unit change of X1, while holding X2 at a constant value
b2 indicates have much Y changes with a unit change of X2, holding X1 constant

Question 47

What does multiple regression allow us to estimate

Answer 47

the unique contribution of a predictor Xk to the outcome, given the other X variable(s) in the model. Please note that multiple regression therefore provides a way of adjusting / accounting for potentially confounding variables by including these in the model

Question 48

B value for a dummy

Answer 48

the estimate of the mean difference on the DV between the dummy level and the ‘uncoded’ reference. For example, blow, tells you how much the mean outcome for “low” differs from the mean outcome for “standard.” If the coefficient is significant, id differs significantly.

Question 49

Modelling interaction between x1 and x2

Answer 49

create a new variable X1ByX2 which is simply the product of the two original ones

Question 50

synergy

Answer 50

if an interaction term is significant and its b is positive, the predictors have synergy (they strengthen each other)

Question 51

anti-synerg

Answer 51

If an interaction term is significant and its b is negative, anti-synergy (they weaken each other)

Question 52

Adjusted R2

Answer 52

R2 may become spuriously high if your model is ‘overspecified’ (ie., if it has too many predictors relative to the number of cases). Adjusted R2 attempts to compensate for the spurious increase in predictive power. So more conservative, protects against type I error

Question 53

Standard error of estimate in model summary

Answer 53

can be interpreted as the average magnitude (in original units of measurement) of predication error

Question 54

steps in evaluation of MLR output

Answer 54

1. Check significance of F-test:
if p < α reject H0
2. Check size of R2 : if large enough (whatever that means, context matters) → relevant model
3. Check significance of t-tests for coefficients
(for each, if p < α reject H0 )
4. Check sign and size of unstandardized (b) coefficients for substantive interpretation (‘how much does Y change with unit chance in X’)
5. Check absolute value of standardized (beta) coefficients for relative importance

Question 55

What does the F-value of multiple regression output tell us

Answer 55

If the F-test is significant (if 𝑝 < 0.05), it suggests that the model provides a better fit to the data than a model with no predictors.

Question 56

Sequential analysis

Answer 56

test whether adding predictors leads to a significant improvement of our model.
We want to know whether the R2 change (model 2 versus model 1) is significantly different from zero.
Use the F-change test to answer the question whether the more elaborate model 2 is better than model 1

Question 57

Homoscedastic model

Answer 57

magnitudes of the error terms do not depend on the x-value. the spread of errors remains constant with the values of the predictor

Question 58

Why is homoscedasticity good

Answer 58

If the assumption is not met, the fit of the model (multiple r2) may be overestimated
Actually, you cannot really speak of the fit of the model, because the fit changes with values of the predictor

Question 59

heteroscedasticity

Answer 59

Heteroscedasticity occurs when the residuals have non-constant variance across levels of the independent variable. the spread of errors changes with the values of the predictor.

Question 60

independence of residuals assumption

Answer 60

the error for yi+1 should not depend on the error for yi

Question 61

consequences of multicolinearity

Answer 61

At best: the model contains redundant elements. 
→ The model is more complex than needed
Worse: coefficient values may change erratically in response to small changes in the model or the data, and / or the ordering of your model building process (case 4, previous slide) 
→ The model is unstable
→ Model is hard to interpret / unreliable /invalid

Question 62

multicolinearity indicators

Answer 62

• Significant F-test, but insignificant coefficients for specific IV(‘s)?
Suspect, but it could be that IV truly does not relate to DV
• Large changes in coefficient values when a predictor variable is added or deleted?
’case 4’. Really suspect!!
• IV is significant as single predictor, but insignificant in multiple regression model? Smoking gun!