Is validity coefficient the same as correlation coefficient?

Type of Reliability Application Test-retest Use this type of reliability estimate whenever you are measuring a trait over a period of time.
Example: teacher job satisfaction during the school year Parallel forms Use this type of reliability estimate whenever you need different forms of the same test to measure the same trait.
Example: multiple forms of the SAT Internal consistency Use this type of reliability estimate whenever you need to summarize scores on individual items by an overall score.
Example: combining the 20 items on a statistics test to represent level of knowledge about a particular aspect of statistics Interrater Use this type of reliability estimate whenever you involve multiple raters in scoring tests.
Example: AP essay test grading

Validity tells you how useful your experimental results are; a validity coefficient is a gauge of how strong (or weak) that “usefulness” factor is. For example, let’s say your research shows that a student with a high GPA should perform well on the SAT and in college. A validity coefficient can tell you more about the strength of that relationship between test results and your criterion variables.

Example (for testing concurrent validity): you want to design an instrument that measures “success in college.” You design a scale called the SUCCESS scale which measures how well students will do in their first year of college based on GPA, social skills, extra-curricular interests and other criteria. The score ranges from 0 to 10, with career counselors grading students on a 5-point item for each set of criteria. As a criterion, you have a second set of college advisers grade the students at the end of their first year. You correlate your SUCCESS rankings with the rankings obtained from the college advisers. This gives you a validity coefficient.

In general, validity coefficients range from zero to .50, where 0 is a weak validity and .50 is moderate validity. The possible range of the validity coefficient is the same as other correlation coefficients (0 to 1) and so, in general, validity coefficients tend not to be that strong; this means that other tests are usually required. It’s not unusual for validity coefficients to max out at around .30. For the above example, this low correlation means that some students with GPAs may not perform well on standardized tests or in college.

How to find Validity Coefficients

The validity coefficient is just another type of correlation coefficient. Therefore, you can use any statistical software to find validity correlation.

You can use the Excel CORREL function to find correlation coefficients:

1. Type your data into a worksheet. Your independent variables should be on one column and your dependent variables should be in a second column.
2. Click the function button on the toolbar (fx).
3. Type “Correl” to find the Correl function. Click on “Correl.”
4. Type the cell locations of your independent variables into the array 1 box. For example, A1:A30.
5. Type the cell locations of your dependent variables into the array 2 box. For example, B1:B30.
6. Click “OK.”

Click one of the links below to see directions for finding validity correlations in different software programs:

• Correlation Coefficient SPSS
• Minitab Correlation Coefficient

References

Neil J. Salkind. Tests & Measurement for People Who (Think They) Hate Tests & Measurement

CITE THIS AS:
Stephanie Glen. "Validity Coefficient: Definition and How to Find it" From StatisticsHowTo.com: Elementary Statistics for the rest of us! https://www.statisticshowto.com/validity-coefficient-definition-and-how-to-find-it/

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Linear regression methods aim to determine the linear relationship between two sets of variables. In the assessment of reliability, two variables come from replicate measures of the same phenomenon using the same method. For validity, they are from two different methods measuring the same phenomenon.

General principle

Two variables can be displayed as a scatterplot: one on the x-axis against one (from either replicate measures or another method) on the y-axis. Figure C.7.1 is an example of a scatterplot and regression equation.

The relationship between the two sets of paired scores is shown by the regression line with the equation y = mx + c, where m is the slope and c is the y intercept. The slope represents the average increase in y if x were to increase by one unit, the intercept is the y value when x = 0.

• The correlation coefficient ‘r’, describes the closeness of the data to the regression line, or, the linear association between the two measurements
• r2 provides a measure of how much of the variability in one set of measurements is explained by the variability in the other set of measurements
• 1 - r2 is the proportion that remains unexplained by the relationship

Figure C.7.1 Example of scatterplots and regression equations. As a reference, energy expenditure from indirect calorimetry is plotted on x-axis. On the left, energy expenditure estimated from combined accelerometer and heart rate (AHR) is presented. On the right, energy expenditure from pedometer is presented.
Source: [10].

Systematic error

Suppose that validity of the variable on y-axis is of interest. Its systematic error in reference to the other on x-axis can be described using the intercept and slope of the regression line:

• The intercept ‘c’ provides a measure of the fixed systematic error between the two variables, i.e. one method provides values that are different to those from the other by a fixed amount. A value of 0 for c indicates no fixed error. Confidence intervals (e.g. 95%) can be used to examine whether c ≠ 0 and thus determine whether fixed error is statistically significant.
• The slope, m, provides a measure of the proportional error between the two variables, i.e. one method provides data that are different to those from the other by an amount that is proportional to the level of the measurement. A value of 1 for m indicates no proportional error. Confidence intervals (e.g. 95%) can be used to examine whether m ≠ 1 and thus determine whether proportional error is present.

Random error

Random error inherently exists in any measurements. The influence of random errors on the regression estimates vary whether the error is present in the variable on y-axis or the other on x-axis. If the random error were present in the variable on y-axis, estimates of the slope and intercept would become more imprecise, but estimates themselves would be unbiased. By contrast, if the error is present in the variable on x-axis, the slope would be attenuated or ‘diluted’ toward the null. Thus, effects of random errors would vary by how a regression line would be fitted.

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