8. Statistical Validity (Pearson Assumptions)

1. Construct validity - how well are variables measured?

2. Internal validity - was the goal to find a causal relationship?

3. External validity - is the sample random? Can we generalize?

4. Statistical validity

• Significance - det. by p-value

• Suitability - checking assumptions and execution of test

• Relevance - effect size

• Accuracy - confidence interval

Assumptions Pearson's r

1. Sample is random

2. Both variables are interval/ratio measurement level

3. Rel. is linear

2. a. variables are ordinal

Spearman correlation = special correlation which measures the strength and direction bet. 2 ordinal variables (can be measured at ordinal lvl or made ordinal using rank score to straighten out non-linear rel.)

b. variables are categorical (nominal)

Chi-square test of interdependence = test that determines the degree to which distribution of 2 categ. variables is dependent on one another

Frequencies = numbers in each categ. in the table

Contingency table = table used in Chi-square test

• need to look at row percentages

Chi-square test - compares observed frequencies to expected frequency

Variables are independent/ have no rel —> rel./proportion would hold regardless of categ. (similar results)

3. Rel. is not linear

• quadratic rel (parabola)

• monotone increasing/decreasing curvilinear rel. (= non-linear rel. that is only increasing/ decreasing) -> Spearman correlation

  

Suitability

Suitability-check if test suits the data (is data of correct measurement lvl? Is the rel. linear when correlation is tested? Etc)

Statistical hypotheses

H₀: ρ = 0 H_A: ρ > 0 -> expects positive rel. -> one sided hypothesis

One-sided hypothesis - the direction is assumed from the get-go

(+) theory-driven

(-) if rel turns out to be in opposite direction, you can't reject H₀

H_A: ρ =/= 0 -> two sided hypothesis

Two-sided hypothesis - simply says there is a rel. bet. variables, but can't specify direction

(+) looks at all possibilities (poz and neg)

(-) does not match expectations

(-) less likely to adopt new theory