STAT 1: Basic Statistical Definitions

Question 1

Define significance level

Answer 1

• the threshold at which we are prepared to accept a Type I error (false positive)
• when you reject a null hypothesis that is actually true
• the probability you will make the mistake of rejecting the null hypothesis when it is true
• commonly 0.05

Question 2

What is a type I error?

Answer 2

• a false positive
• rejecting a null hypothesis that is actually true
• usually what we are looking to reduce

Question 3

Define type II error

Answer 3

• a false negative
• accepting a false null hypothesis

Question 4

What are p-values?

Answer 4

• it measures the probability of getting a more extreme result, if the null hypothesis were true
• a value between 0-1
• it tells us the odds of getting our experimental data if the null hypothesis is correct
• if p-value is lower than significance level, reject H0

Question 5

Why do you reject null hypothesis is p-value is lower than significance level?

Answer 5

• let’s say p-value is 0.02 and the significance level is 0.05
• it is saying that the probability of getting the experimental result if H0 is true, is 2%
• this is a more extreme value (less likely to happen) than our significance level

Question 6

What is pseudoreplication?

Answer 6

• the process of artificially inflating the number of samples or replicates
• the degrees of freedom are over-inflated

Question 7

What are degrees of freedom?

Answer 7

• the number of independent pieces that went into calculating an estimate
• ( n - 1 )

Question 8

Name the different type of variables?

Answer 8

Continuous variables:

• can take any value
• numerical

Categorical (nominal) / Discrete (numerical) Variables:

• fit into categories
• no intrinsic ordering

Ordinal variable:

• similar to categorical but with a clear ordering of categories
• e.g. strongly agree to don’t know to disagree
• distance between options are hard to measure

Question 9

Describe the shape of this distribution

Answer 9

• positive skew
• discrete data

Question 10

What is central tendency?

Answer 10

• the tendency of the observations to centre around a particular value
• there are three measures of tendency:
• mean
• median
• mode

Question 11

What is dispersion?

Answer 11

• the size of the distribution of values
• e.g. standard deviation, IQR, variance

Question 12

What is standard deviation?

Answer 12

• the average amount all values deviate from the mean

Question 13

What is the population?

Answer 13

• it refers to all the cases that we want our inferences to apply to

Question 14

What is our sample?

Answer 14

• since it is unlikely to sample the whole population, you take a sample from the population

Question 15

What is a technical replicate?

Answer 15

• every single experiment is taken from the same sample
• e.g. taking a blood sample from one person and measuring gene expression multiple times
• gives an accurate measurement of one sample
• also tells us how accurately we are measuring the results
• if numbers are very different each time, we know not to trust any single measurement

Question 16

What is a biological replicate?

Answer 16

• each measurement comes from a different sample that comes from a different individual
• e.g. tells us about the gene expression in a group

Question 17

What is the difference between biological and technical replicate?

Answer 17

• technical replicates test the variability of the testing protocol
• biological replicates test the variability between samples

Question 18

What is standard error?

Answer 18

• the standard deviation of the sample means
• sample means = means from different samples

Question 19

What is the difference between standard error and standard deviation?

Answer 19

• standard error quantifies the variations in the means from multiple set of measurements
• whereas standard deviation quantifies the variation within a set of measurements
• confusingly, it is possible to estimate standard error from a single set of measurements

Question 20

How does increasing sample size affect standard error?

Answer 20

• as sample size gets larger, dispersion gets smaller
• this means the mean gets closer to the population mean
• they have an inversely proportional relationship
• as sample size increases, standard error decreases

Question 21

Define 95% confidence interval

Answer 21

• if the experiment is repeated many times and 95% confidence intervals are taken for each sample, 95% of the intervals will contain the population mean

Question 22

What type of data is the mode used for?

Answer 22

• used in categorical data

Question 23

What type of data is the mean used for and why?

Answer 23

• used for continuous data
• useful as it is fairly stable from one sample to another

Question 24

What type of data is the median used for and why?

Answer 24

• continuous data
• preferred in distribution where there are a few extreme values