Introductory wk4-5

IRM XBPY

Parametric data

normal data

Non-parametric data

not normal or non-normal

Normality of continuous data

Bell curve, not too skewed, not too kurtotic, no outliers (extreme values).

Whiskers (lines exiting the box) 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 (+/-).

Shapiro-Wilk test considers

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).

Parametric tests

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

Non-parametric tests

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

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

they are preferred and are generally the default set of tests.

In the IRM models, degrees of freedom (df) will mostly be

the number of participants - 1. For the most part, a higher df = more statistical power.

Imagine 5 chairs amongst 5 people

the 5th person to 'choose' has no choice.

Homoscedasticity refers to homogeneity of variance

A common assumption for parametric statistical models. Most commonly tested using Levene’s test.

When you violate the assumption of homogeneity of variance

use Welch’s (t-test) Test.

In parametric tests, observations are independent

i.e. no two observations in a data set are related to each other or affect each other in any way. A common assumption for parametric statistical models.

Independence violation example

A gym manager wanted to compare the fitness levels of people who attend the gym on Mondays and Wednesdays. She collected fitness levels from 20 people on Monday and 20 people on Wednesday. Three participants were represented in both days.

Pearson correlation coefficient is referred to

as r.

Pearson assesses linear (straight line) relationships

between two variables.

Assumptions that apply to Pearson correlation

linear relationship (straight line), parametric data/normality, homogeneity of variance (homoscedasticity), independence.

At least one Pearson variable needs to be continuous

The other variable can be continuous or dichotomous.

r = 0 no relationship

r = 1 perfect positive, r = -1 perfect negative.

T-tests are for 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-test assumptions

Parametric data/normality, independence, homogeneity of variance (homoscedasticity).

T-test DV needs to be continuous

IV needs to be dichotomous (groups or time points).

T-tests are not measures of effect size

We traditionally use Cohen’s d to measure effect size for t-tests.

ANOVA (analysis of variance)

 Investigates differences in means. In this course, we will look at one-way between group

One-way refers to having

one IV/factor. Each IV/factor will have >2 levels.

between-group

each participant is represented once in one group.

within-subject factors

(same participant over time; irrelevant to this course).

key ANOVA estimate

F = (model variance) / (error variance).

The larger the F, the more variance

you are explaining in your DV by your IV

F is not an

effect size measure

Post-hoc tests tell you where the significant group difference(s) is(are).

You can only run post-doc tests if your F is statically significant (p<.05 if you have a standard alpha of 0.05)

You can only run post-doc tests if your F is

statistically significant (p<.05 if you have a standard alpha of 0.05)

Holm correction step 1

 First, you sort all of your p-values in order, from smallest to largest. For the smallest p-value all you do is multiply it by p, and you’re done

Holm correction step 2

However, for all the other ones it’s a two-stage process. For instance, when you move to the second smallest p-value, you first multiply it by p. If this produces a number that is bigger than the adjusted p-value that you got last time, then you keep it.

Key assumptions of Holm test

normality (QQ plot and Shapiro-Wilks test. When you only have two groups, use Mann-Whitney or the Wilcoxon test. Three or more, use Kruskal-Wallis in non-parametric one-way), homogeneity of variance (Levene, Brown-Forsythe, Welch one-way) and independence (there’s not an obvious or simple way to test for this, but there are some situations that are clear violations of this)

If you have a repeated measures design, where each participant in your study appears in more than one condition, then

independence doesn’t hold

Spearman correlation coefficient is referred to as

rho (ρ) or as rs. Works on ranks of data (unlike Pearson correlation)

Spearman can use same effect size cut-offs as Pearson correlation

Assesses strength of monotonic relationship between two variables, linear or non-linear

Spearman correlation assumptions

 at least one variable needs to be continuous. The other variable can be continuous or dichotomous. The relationship between the two variables is monotonic (if you order pairs of data, they constantly increase or consistently decrease)

Spearman reporting examples

rs (38) = .34, p=.009 There was a statistically significant and weak positive relationship between hours of TV watched and fatigue. rs (196) = -.75, p<.001 There was a statistically significant and strong negative relationship between hours of TV watched and sleep duration. rs (degrees of freedom) = estimate, p=x

Like the t-test, the Wilcoxon test comes in two forms

one- and two-sample

Wilcoxon can handle any data type

where you want to compare two groups

Mann-Whitney U Wilcoxon test

for between-subjects

One sample Wilcoxon test

for within-subjects

Wilcoxon reporting examples

W = 110, p<.001 Those in the heavy TV watching group were statistically significantly more fatigued than the low TV watching group W = 54, p=.037 Those in the heavy TV watching group had statistically significantly less sleep than those in the low TV watching group W = estimate, p=x

Non-parametric correlation; non-parametric T-test

Spearman; Wilcoxon

True or false: most IRM students report that the content is confusing at first, but they eventually understand it

True