Statistics for CSAI 1

by Albert Major

1.) Research Methods

Scales of Measurement

Scales of measurement define how variables are quantified and categorized, affecting how you analyze data:

1. Nominal scale

   • Categories without inherent order (e.g., gender: male/female/nonbinary).

   • Only labels, no numeric meaning.

2. Ordinal scale
   • Categories with a meaningful order but unequal intervals (e.g., rankings: 1st, 2nd, 3rd).
   • Indicates relative position but not exact differences.
3. Interval scale
   • Numeric scale with equal intervals but no true zero (e.g., temperature in Celsius, IQ scores).
   • Differences between values are meaningful, ratios are not.
4. Ratio scale
   • Numeric scale with equal intervals and a meaningful absolute zero point (e.g., weight, height, duration).
   • Allows meaningful computation of ratios (e.g., 20 kg is twice as heavy as 10 kg).
5. Binary (special nominal scale)

   • Only two possible categories (e.g., yes/no, pass/fail).

     ![A continuous variable is one in which, for any two values that you can think of, it’s always logically possible to have another value in between.

     A discrete variable is, in effect, a variable that isn’t continuous. For a discrete variable, it’s sometimes the case that there’s nothing in the middle.](attachment:8d3df591-ba0d-44bb-9520-08ed273dd778:Screenshot_2025-05-21_at_10.54.50.png)

     A continuous variable is one in which, for any two values that you can think of, it’s always logically possible to have another value in between.

     A discrete variable is, in effect, a variable that isn’t continuous. For a discrete variable, it’s sometimes the case that there’s nothing in the middle.

Why does it matter?

The scale determines which statistical methods are valid and appropriate. For example, means and standard deviations are appropriate for interval/ratio scales but meaningless for nominal scales.

Types of Reliability

Reliability means how consistent or repeatable a measurement is—if you measure the same thing again, do you get the same result?

So, reliability indicates consistency or repeatability of a measure. Three common types are:

1. Test-Retest Reliability
   • Stability over time: same test, same participants, different times.
   • High test-retest reliability means the measure gives consistent scores across repeated measurements.
2. Inter-Rater Reliability
   • Consistency between different observers or raters.
   • Important when subjective judgments (like clinical assessments) are involved.
3. Internal Consistency (Cronbach’s Alpha)
   • Consistency among items within a single test or measure.
   • High internal consistency means the items measure the same underlying construct.

Why does it matter?