E-module 2 - Choosing statistics

Question 1

What are the 2 types of analysis of data?

Answer 1

Correlation

Comparison

Question 2

Definitions of correlation and comparison as types of data analysis.

Answer 2

Correlation
- hypothesis tests to evaluate relationship between variables

Comparison
- hypothesis tests to evaluate differences between groups/populations

Question 3

What are the 2 types and 4 subtypes of data?

Answer 3

Types

• Quantitative - numeric information
• Qualitative/Categorical - information that can’t be measured

Subtypes

• Quantitative gives rise to CONTINUOUS and DISCRETE (counted) data
• Qualitative/categorical gives rise to NOMINAL (unordered) and ORDINAL (ordered) data

Question 4

Which subtypes of data are PARAMETRIC and NON-PARAMETRIC?

Answer 4

PARAMETRIC
- continuous quantitative

NON-PARAMETRIC

• discrete quantitative
• nominal categorical
• ordinal categorical

Question 5

What is the principle segregating continuous and discrete data?

Answer 5

Continuous can be subdivided (potentially) infinitely where discrete cannot
- e.g. age is continuous if measured exactly in months, days, hours etc, but discrete if measured in years (overlap here within a category between continuous and discrete data)

Question 6

What is important to remember about continuous vs discrete data?

Answer 6

Means or rates are always continuous data. Likelihood is they were generated using discrete data BUT they themselves are continuous

e. g. heart rate is continuous but number of heartbeats in a minute is discrete
- this is because continuous data can take ANY value (e.g. 2, 2.5, 3) but discrete data cannot take certain values (e.g. 2, 3 but NOT 2.5)

Question 7

When do you check for normality in data?

Answer 7

When you have CONTINUOUS data - discrete and qualitative data is ALWAYS NON-PARAMETRIC

Question 8

What does normality measure?

Answer 8

Measures central tendency and dispersion of data

Question 9

What are the 2 tests used for testing normality and their conditions?

Answer 9

Shapiro-Wilk test - n<50

Kolmogorov-Smirnov test - n>50

Question 10

When can the data be conferred as normal or not normal?

Answer 10

p-value of normality test

if p<0.05 data is NOT normal, otherwise data is normal

Question 11

What are the 3 outcomes and subsequent distributions of data after normality testing?

Answer 11

YES - Gaussian/Normal distribution
NO - Skewed distribution
NO - Kurtosis

Question 12

What are the 2 main features of normal distributions?

Answer 12

• 68-95-99.7 rule - 2/3rds of data lies within 1 SD of the mean, 95% within 2 SDs, 99.7% within 3 SDs
  AND
• Distribution is symmetrical

Question 13

What are the features of skewed distributions?

Answer 13

ASYMMETRICAL

• mean, median and mode all separated (usually found together in normal dist.) (mode at top of curve, median just downslope from top, mean just further downslope from the median)
• skew is named according to which direction has the long tail e.g. right/positive skew = long positive/right tail and vice versa
• uneven tails with many data points at high/low end of range

Question 14

What are the features of Kurtosis?

Answer 14

Kurtosis is where data is heavy or light-tailed with respect to a normal distribution

• heavy-tailed = outliers create a wide distribution (graph is flattened)
• light-tailed = lack of outliers creates a narrow distribution (graph is steepened)

Question 15

Definition of unpaired/independent and paired/dependent data/groups and an example of a study employing this?

Answer 15

Paired/dependent = when two (or more) sets of data have come from the same individual e.g. same subject at different points of the day
- longitudinal study

Question 16

Definition of unpaired/independent data/groups and an example of a study employing this?

Answer 16

Unpaired/independent = comparing data from two groups with no common factors (two independent groups)
- cross-sectional study

Question 17

Which statistical tests will you use for parametric data and what are their individual constraints?

Answer 17

Paired t-test = parametric, 2 groups, paired

Unpaired t-test = parametric, 2 groups, independent

Repeated measures, one-way ANOVA = parametric, 3 groups or more, paired

One-way ANOVA = parametric, 3 groups or more, unpaired

Question 18

Which statistical tests will you use for non-parametric data?

Answer 18

Wilcoxon (signed rank) test = non-parametric, 2 groups, paired

Mann-Whitney U test = non-parametric, 2 groups, unpaired

Kruskal-Willis test = non-parametric, 3 or more groups (paired)

(Friedman test = non-parametric, 3 or more groups, unpaired)
- medlearn tree only has K-W test for 3 or more groups

Question 19

When testing for correlation, which statistical tests would you use and when?

Answer 19

Pearson’s test - data is continuous and follows a normal distribution

Spearman’s rank test - data is continuous but does not follow a normal distribution

Chi-squared test - data is discrete

Question 20

What is the range of resulting values from Pearson’s/Spearman’s rank tests and what symbol indicates them?

Answer 20

Pearson’s - r - from -1 to 1, perfect negative to perfect positive correlation (strong and weak in between)

Spearman’s rank - rho (looks like p) - from -1 to 1, perfect negative to perfect positive correlation (strong and weak in between)

Question 21

Which type of data, parametric or non-parametric, is better to use and why?

Answer 21

PARAMETRIC

• easier to understand
• more powerful as LESS LIKELY TO incorrectly reject/fail to reject the hypothesis

Question 22

What are descriptive statistics?

Answer 22

Descriptive statistics are used to categorise large data-sets into a tangible format
Raw data is usually presented in the form of descriptive statistics e.g. provide mean +/- SD/SEM of a collection of data points

Question 23

What are measures of central tendency?

Answer 23

Mean, mode, median

Question 24

What are measures of data dispersion?

Answer 24

Variance, standard deviation (SD), standard error/standard error of the mean (SE/SEM)

Question 25

How do you calculate variance and standard deviation of a sample and a population?

Answer 25

Variance - sum the squared differences between each data value and the mean. divide all of this by the number of values (n)
- here for population, use n on the bottom of the fraction, for sample use n-1

Standard deviation - for both, this is the square root of the variance so calculate it as such

Question 26

How do you calculate the standard error of the mean?

Answer 26

This is standard deviation divided by square root (n) (square root of the number of values)

Question 27

Which measure of central tendency should you use in cases where the data is normally distributed and not normally distributed?

Answer 27

Normally distributed = mean

Not normally distributed = median

Question 28

What is the standard error used for and hence, when can it only be used?

Answer 28

Standard error is used as a measure of how well the sample data reflects the population
- can only, therefore, be used with sample SD/variance