Statistical models 2

Question 1

What is parametric data?

Answer 1

• Parametric data = normal data.
• Non-parametric data = not normal or non-normal
• Bell curve.
• Not too skewed (sway to left or right).
• Not too kurtotic (flat or peaky).
• No outliers (extreme values).

Question 2

Why is it important to identify parametric data

Answer 2

• Normality is an assumption of some statistical models, mathematically.
• If we violate normality and use a parametric test, we may not be able to trust the
  model estimates.

Question 3

Steps to identify if you need to use parametric test on data

Answer 3

Has an outlier?
Can outlier be removed?
Data is skewed or kurtotic?
Can the data be transformed?

Question 4

Testing for outliers

Answer 4

• Box plot, very easy in jamovi.
• The thick line in the middle of the box = median.
• The box itself spans from the 25th percentile to the
  75th percentile (or inter quartile range).
• Whiskers indicate acceptable values (not outliers).
• Any observation whose value falls outside this
  acceptable range is plotted as a dot and is not
  covered by the whiskers = outlier.
• Common alternative: 3 standard deviations
  (SD) from the mean (+/-).

Question 5

What to do when you have an outlier

Answer 5

• Run a non-parametric test.
• Commonly done if it’s a “true” value. E.g. testing went well, the participant
  understood task instructions, but scored very low; this performance represents that
  participants ability.
• Remove the value and leave as missing.
• Commonly done when working with big data sets, where you’re not going to check
  participant records and have plenty of statistical power.
• Remove the value and replace with nearest acceptable value.
• Commonly done in psychological studies.
• Remove value and replace with mean.
• Historical, not commonly done these days

Question 6

Testing skew and kurtosis

Answer 6

• Shapiro-Wilk test. Very easy in jamovi.
• Takes into account both skew and kurtosis.
• W statistic.
• Maximum value of 1 = data looks “perfectly normal”.
• The smaller the value of W the less normal the data are.
• p value (of W statistic).
• Typically, <.05 = non-normal data.
• Therefore, ≥.05 = normal data.

Question 7

Parametric tests

Answer 7

Pearson correlation
T-test
(between groups or within groups)
ANOVA
(IRM, we’ll work with between
groups)

Question 8

Non-parametric tests

Answer 8

Spearman correlation
Wilcoxon test
(2 groups/conditions)
Kruskall-Wallis test
(3 or more groups)

Question 9

Parametric v non-parametric tests

Answer 9

• There are generally non-parametric versions of all parametric tests.
• We do non-parametric tests when our data are not normally
  distributed.
• We do parametric tests when our data are normally distributed.
• Parametric tests have more statistical power, so, they are preferred
  and are generally the default set of tests.

Question 10

Degrees of freedom

Answer 10

• Important to the mathematical
  calculations of parametric and non-parametric tests.
• Based on the quantities of data in your
  model, e.g. participants or factors. In the
  models we will use in IRM, degrees of
  freedom (df) will mostly be the number of participants - 1.
• For the most part, a higher df = more statistical power.

Question 11

The independent samples t-test

Answer 11

In psychology, this tends to correspond to two different groups of participants, where each group corresponds to a different condition in your study. For each person in the study you measure some outcome variable of interest, and the research question that you’re asking is whether or not the two groups have the same population mean.

Question 12

Assumptions for the Student t-test

Answer 12

Normality (both groups are normally distributed)

Independence (we assume that the observations within each sample are independent of one another)

Homogeneity of variance (the population standard deviation is the same in both groups).