| variable | mean | variance |
|---|---|---|
| Sepal.Length | 5.84 | 0.69 |
| Sepal.Width | 3.06 | 0.19 |
| Petal.Length | 3.76 | 3.12 |
| Petal.Width | 1.20 | 0.58 |
Scale Development
SWK 3402
OSU College of Social Work
Developing a Scale
- Operationalize Construct
- Define Variables
- Measure Variables
- Assess Scale Reliability
- Calculate Scale Scores
Research Aim
Compare the flower size of different iris species.
Operationalize Flower Size
Dimensions of flower size:
- Sepal Length
- Sepal Width
- Petal Length
- Petal Width
Operationalize the flower size
We operationalize flower size as the average of four variables.
\[ Size = \frac{Sepal\ Length + Sepal\ Width + Petal\ Width + Petal\ Length}{4} \]
Measuring the Variables
We travel to a forest with three species of irises.
Using our rulers, we measure 150 irises (50 per species).
Overall Results
Assess Scale Reliability
How are the items related to one another?
Correlation Table (standardized variance)
| Sepal.Length | Sepal.Width | Petal.Length | Petal.Width | |
|---|---|---|---|---|
| Sepal.Length | 1.00 | -0.12 | 0.87 | 0.82 |
| Sepal.Width | -0.12 | 1.00 | -0.43 | -0.37 |
| Petal.Length | 0.87 | -0.43 | 1.00 | 0.96 |
| Petal.Width | 0.82 | -0.37 | 0.96 | 1.00 |
Cronbach’s Alpha
A formal measure of variable relationships. Reflects the scale’s internal consistency.
A reliability coefficient ranging from 0 (no consistency) to 1 (perfect consistency)
Cronbach’s alpha of our 4 variables = 0.708
- At the limit of acceptability for scientific use
Modifying our Measure
Let’s drop Sepal Width, since it was negatively related to other variables.
Cronbach’s alpha of our 3 variables = 0.88
- much better!
Calculate Scale Scores
\[ Size = \frac{Sepal\ Length + Petal\ Width + Petal\ Length}{3} \]
| variable | mean | variance |
|---|---|---|
| size | 3.6 | 1.17 |
Difference in flower size
Traver| SWK 3402 | 2024