biostats

steps to conducting a statistical analysis

1. establish the research question

2. formulate a hypothesis

3. select an appropriate statistical test

4. sample correctly

5. collect data

6. perform statistical test(s)

7. make decisions

strong research is done

intentionally

what is a priori?

concept that means your research question was pre-determined

what is a fishing expedition?

skipping steps 1-4 of conducting a statistical analysis, essentially playing around with data to see what you get

secondary data analysis

steps 4 and 5 of the statistical analysis are conducted first and the data is collected for a non-research purpose (steps 1-3 must be specified before 6)

discrete data

set values in a particular range (whole number, category that a measurement fully belongs into)

nominal data

type of discrete data that has no meaningful order (differences in categories are not incremental)

ordinal data

type of discrete data that has a natural order, but the difference between categories is not necessarily incremental or equal

continuous data

can be any value in a particular range (including decimals)

interval data

type of continuous data that has a natural order and the difference between each unit is the same, has a zero value, but it does not mean the absence of that factor

ratio data

type of continuous data that has a natural order and the difference between each unit is the same, but a zero means the absence of that value

eye colour is an example of ____ data

nominal

comparing BSc vs MSc is a type of ____ data

ordinal

a measurement in degrees Celsius is a type of ____ data

interval

a measurement of a patient’s weight is a type of ____ data

ratio

hierarchy of data

continuous>ordinal>nominal

can you convert continuous data to categorical? vice-versa?

yes, no

measure of ‘spread’ for mean

standard deviation

measure of ‘spread’ for median

interquartile range (difference between 75th and 25th percentile values)

measure of ‘spread’ for mode

range

what is most commonly used: mean, median, or mode?

mean

what is preferred if measurements are skewed?

median

point estimate

result calculated from dataset

confidence interval

describes uncertainty around the point estimate

is a narrower or wider CI range more certain?

narrower

what factors influence the width of a CI?

1. size of CI calculated. larger % = wider range of values that fall within

2. variability around point estimate observed. CI based on point estimate and SD so a greater variability = higher SD = wider range

3. sample size. larger = more certainty

null hypothesis

independent variable has no effect on the dependent variable (or if you are trying to see if two options are equivalent, it is that there is a different between two options)

alternative hypothesis

independent variable has a significant effect on the dependent variable

p value

probability that the null hypothesis is correct (observed effect is due to chance alone)

factors that influence the p-value

1. effect size: larger difference = less likely it is due to chance

2. variability around point estimate observed in sample: more variability = less certainty = higher p-value

3. sample size: more subjects = more certainty = lower p-value

how do you determine p-value if you are given a point estimate with a CI?

• determine null value

  • measuring a difference between groups = 0 (number subtracted from itself)

  • ratio or proportion = 1 (number divided by itself is 1)

• if 95% CI crosses null value = p-value is greater than 0.5 (not significant)

• if 95% CI does not cross null value = p-value is less than 0.5 (significant)

type I statistical error

occurs when you reject H0 and it is true (false positive)

type II statistical error

occurs when you accept H0 and it is false (false-negative)

probability of a type I error

denoted by alpha and set to 5% or 0.05 (p-value that is set)

probability of a type II error

denoted by beta and typically set to 20%

statistical power

likelihood that a study will detect an effect if there is one (also the probability of rejecting H0 when it is false, ie probability of being right?)

how do you calculate statistical power?

1-beta (beta is usually 20%, therefore power is 80%)

factors that influence statistical power

1. sample size: larger = higher power

2. standard deviation: smaller = higher power

3. effect size: greater effect size (difference between groups) = higher power

4. significance level (alpha): lower alpha = lower power (more evidence needed to reject null hypothesis

5. one or two-tailed test: one-tailed = higher power, two-tailed = lower power (need a more extreme p-value to fall into shaded area)

two-tailed test

unsure of which side HA falls on so you use 2.5% on each side of the distribution

one-tailed test

you know HA falls on one side so you use 5% on each side of the distribution (be cautious of tests that use this)

how is sample size of subjects calculated?

based on change expected to see in primary outcome

primary outcome

answers the primary/most important question

secondary outcome

other relevant outcomes from a study, but less important, usually hypothesis-generating only

composite outcome

pooling outcomes together

what type of test would you use if you had a categorical independent variable and a categorial dependent variable?

Chi-square (x²)

what type of test would you use if you had a categorical independent variable and a continuous dependent variable?

t-test, ANOVA

what type of test would you use if you had a continuous independent variable and a continuous dependent variable?

regression

paired t-test

both sets of measurements come from the same subject

unpaired t-test

outcome measures across groups come from different subjects

when to use ANOVA over t-test?

if you have more than 2 independent variables

why is doing multiple t-tests problematic?

increases chance of type I error

efficacy

capacity of a treatment to produce the desired effect in a controlled environment

effectiveness

actual effect of treatment in real life

accuracy

how close the measured value is to the true value

precision/reliability

variability across measurements

validity

how well the variable assesses outcome of interest

sensitivity

can a test correctly identify those with a disease (sensitive = low rate of false negative - type II error)

specificity

can a test identify those without a disease (specific = low rate false positive - type I error)

statistical significance

difference between 2 interventions resulting in p<0.05

clinical significance

difference between two interventions that is meaningful to a patient and their health outcomes