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

Shapiro-Wilk test: 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 - 2 groups
(between groups or within groups)
ANOVA - >2 groups
(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

Homoscedastic

Answer 12

Even distribution/variance across correlation line
Homogenous or equal variance.

• Refers to homogeneity of variance.
• A common assumption for parametric statistical models.
• Most commonly tested using Levene’s test (F):
• p<.05 (less than) violated homogeneity of variance.
• p≥.05 (greater than) all is fine, you have not violated homogeneity of variance.
• When you violate the assumption of homogeneity of variance, use
  Welch’s (t-test) Test.

Question 13

Heteroscedastic

Answer 13

Uneven distribution/variance across correlation line
Heterogenous or unequal variance.

Question 14

Independence (in context of parametric tests)

Answer 14

• Observations are independent, i.e. no two observations in a dataset
  are related to each other or affect each other in any way.
• A common assumption for parametric statistical models.
• You need to check this using logic. There’s no test for it.

Question 15

Pearson correlation

Answer 15

• Pearson correlation coefficient is referred to a as r.
• Assesses linear (straight line) relationships between two variables.

r = 0 no relationship
r = 1 perfect positive relationship
r = -1 perfect negative relationship

Correlations are also measures
of effect size!

Question 16

Pearson correlation Assumptions

Answer 16

• Linear relationship (straight line).
• Parametric data/normality.
• Homogeneity of variance (homoscedasticity).
• Independence.
• At least one variable needs to be continuous.
• The other variable can be continuous or dichotomous.

Question 17

T-tests

Answer 17

• When you want to compare two means.
• If “group 1” is larger than “group 2” the t statistic will be positive; if
  “group 2” is larger then the t statistic will be negative.
• T-tests are not measures of effect size.
• We traditionally use Cohen’s d to measure effect size for t-tests.

p value less than 0.05 is statistically significant

T value:
This is the result of the t-test formula, which compares the means of two groups (or a sample mean to a population mean) relative to the variability in the data (standard error).
A higher absolute t-value indicates a larger difference between groups (or means) relative to the variance, which suggests a stronger deviation from the null hypothesis.

Question 18

Assumptions of t-test

Answer 18

• Parametric data/normality.
• Independence.
• Homogeneity of variance (homoscedasticity).
• DV needs to be continuous.
• IV needs to be dichotomous (groups or time points).

Question 19

Between group (independent) t-tests

Answer 19

If the two means are from different people.

Question 20

Within group (dependent or paired) t-tests

Answer 20

if the two means are from the same people at different times.

Question 21

Spearman’s rank order correlation

Answer 21

Treat data as an ordinal scale and rank each variable in order. e.g. That is, student 1 did the least work out of anyone (2 hours) so they get the lowest rank (rank = 1). Student 4 was the next laziest, putting in only 6 hours of work over the whole semester, so they get the next lowest rank (rank = 2).

Question 22

Cohen’s d

Answer 22

effect size that tells us how large the difference between groups of data. The strength of the effect.

A d of 0.5 indicates that the two group means differ by 0.5 standard deviations.
A d of 1 indicates that the group means differ by 1 standard deviation.
A d of 2 indicates that the group means differ by 2 standard deviations.

A value of 0.2 represents a small effect size.
A value of 0.5 represents a medium effect size.
A value of 0.8 represents a large effect size.

Question 23

Error in statistical models…

Answer 23

Is important to measure, report and interpret

Question 24

Data = x + y, where x and y are…

Answer 24

Model and error

Question 25

Statistical significance is not…

Answer 25

A measure of effect size

Question 26

What three factors affect statistical power?

Answer 26

Sample size, effect size, type 1 error rate