Psychometrics

Scales of Measurement

NOIR

Nominal Ordinal Interval Ratio

Nominal

Nominal = Categories Yes-No DSM Diagnosis Red, Yellow, Blue Democrat, Republican, Independent

Ordinal

Ordinal= Categories and Rank Order

It orders along a continuum

First, Second, Third Ranks in the military Likert Scales

But the difference BETWEEN levels is NOT EQUAL

Interval

Interval- Categories, rank order, and equal intervals between numbers

Fahrenheit Scale- the difference between 20 and 30 degrees is the same as the difference between 70 and 80 degrees

However 80 degrees is not twice as hot as 40 degrees because there is no ABSOLUTE ZERO for this we need a…..

Ratio

Ratio Scales- Categories, rank order, equal intervals and Have an absolute Zero or a true zero point which represents an absence of the thing being measured

Length, Volume, Time

0 seconds, 30 seconds, 60 seconds

Why does the scale matter

In order to make accurate comparisons In order to do mathematical manipulations

So you must know about the scale to determine if the statistical analysis means anything

Which scales allow you to determine an average score?

Averages- Measures of Central Tendency Mode- the most common score

With what type of scale can you find the mode? When might it be more useful?

Median- the score at the mid point. 50% of the scores are above and 50% are below With what type of scale can you find the median? When might it be most useful?

Mean- Average With which scales can you find the mean? When might it be most useful

THE MEAN

The mean is most commonly used in statistical analysis as it can be manipulated algebraically. However it can be influenced by Extreme scores Non linear distributions

The NORMAL CURVE- most scores are likely to fall near the mean

Skewed Graphs

Positively Skewed Negatively Skewed Bimodal

Presenting Data

Frequency distribution Grouped frequency Histogram Bar graph Frequency polygon

A few other terms to know

Population: included ALL member of group Sample: subset of the target population Range- the distance from the lowest to highest score.

Can be used to compare variability between two groups. Group 1: 56- 98, Group 2: 25-69

Average deviation- a number that represents how scores arrange themselves around the mean (or deviate from the mean). Could we take the scores, subtract the mean and average them?

Variance- A way to solve the ZERO problem. We subtract the mean from the score and square it so we have all positive numbers. Then we take the average (with N-1 for population vs sample). Better, but the result is squared and squares are difficult to work with.

Standard Deviation- Take the square root of the variance. Ah…now we have a number that represents the deviation from the mean.

What the SD tells us

This figure tells us about the scores. Example- the MMPI-If a score falls within 1 SD then the client is in Normal Range and this can not be interpreted due to issues of CHANCE

Degrees of Freedom

Remember the N-1? Why did we subtract 1 from the number in the sample? Well, basically it is due to the degrees of freedom you have to change numbers. See if we have 3 scores with a mean of 5 (5, 10, 15) and are allowed to change them as long as we still get a mean of 5, we can change 2 of them and this will tell us what the third score will have to be. This is true even if you have 25 scores. The last one is determined- thus we subtract one score so that when we have new scores, this last one does not count in the statistical analysis. What if we had two separate groups, how many degrees of freedom would we have? Three groups?

One vs Two Tailed Tests

Tails are the ends of the curve. This is the area that is extreme and if relationships fall this far away from the mean, it is unlikely to have occurred by chance alone.

One tailed tests only predict one direction. This test is more powerful

Two tailed tests predict possible occurrences in both directions

Parametric vs Non Parametric tests

Parametric tests mean the data falls along the normal curve

Non Parametric tests: Data does not fall along the normal curve and different forms of calculations will be necessary to make any meaningful interpretations about the data

WE WILL FOCUS ON PARAMETRIC TESTS

Review

WOW…you’ve learned a lot in one day!! NOIR Measures of Central Tendency Ways to present Data Variance Standard Deviations Normal (bell) curve Skewed Curves One vs Two Tailed Tests Parametric vs Non Parametric Tsts Skewed graphsThese are the fundamentals you need to understand

statistics