basic statistics lecture

Question 1

neurophysiological datasets are usually

Answer 1

multidimensional

Question 2

null-hypothesis (H0)

Answer 2

states no significant differences

Question 3

estimation

Answer 3

process of inferring an unknown quantity of a population using sample data

Question 4

parameter

Answer 4

quantity describing the population

Question 5

three mutually complementary aspects of summary data description

Answer 5

1. frequency distributions (shape)
2. measures of centre (mean, median, mode)
3. measures of dispersion

Question 6

central limit theorem

Answer 6

the sum or mean of a large number of measurements randomly sampled from any population is approximately normal distributed

Question 7

sample variability

Answer 7

the variability among random samples from the same population

Question 8

sampling distribution

Answer 8

probability distribution that characterizes some aspect of sampling variability

Question 9

increments

Answer 9

sample number and the number of repetitions increases the population mean estimation and the normal shape of the sampling distribution

Question 10

type 1 error

Answer 10

false positive
(1-alpha)^N

Question 11

type 2 error

Answer 11

false negative

Question 12

correcting type 1 error

Answer 12

• Bonferroni correction (very conservative)
  alpha*= alpha/number of tests
• False discovery rate (FDR)
  FDR= number of false positives/number of significant features

Question 13

permutation based methods (getting rid of type 1 errors)

Answer 13

• neyman-pearson approach
  Z, t, F and chi-square are derived from this
  base for permutation approach
  crucial difference with other methods -> it evaluates test statistics under their sampling distribution
  does not easily deal with the multivariate nature of electrophysiological data

Question 14

randomization

Answer 14

• hypothesis testing on measures association
• mixes the real data randomly
  variable 1 from an individual is paired with variable 2 data from a randomly chosen individual –> is repeated
• estimate based on randomized data
• whole process repeated numerous times

Question 15

analysis of variance (ANOVA)

Answer 15

• method to compare group means (>2 groups)
• a generalisation of two sample t-test
• variability between groups => variability within groups

Question 16

steps to perform non-parimentrical tests

Answer 16

1. collect trials of two experimental conditions in a single set
2. randomly draw as many trials from this combines set as there were trials in condition 1 and place these in subset 1. place the remaining trials in subset 2. = random partition
3. calculate test statistic
4. repeat steps 2 and 3 many times and construct a histogram of the test statistics
5. use the histogram and calculate the proportion of random partitions that resulted in a larger test statistic than the observed one = p-value
6. if p-value < alpha –> the two conditions are statistically significant

Question 17

non-parametric statistical testing of EEG and MEG data

Answer 17

• EEG and MEG data have spatiotemporal structure
• data are collected in different conditions
• MEG-EEG- data have to deal with the multi comparison problem
• there are a large number of statistical comparisons