"There are three kinds of lies: Lies, damned lies, and Statistics" - Mark Twain

Why study Statistics?

We are bombarded by statistics on a daily basis. Average income, average number of children in a family, the statistics of your favorite professional sports player, probability of winning Lotto, etc. etc. The main goal of this course is to make you a better and more critical (skeptical) consumer of information. We can be lied to only if we passive accept what is presented to use or accept a statement because we simply do not understand. If you understand what underlies the statistics you are present with you will be able to make an informed decision about whether or not to accept them and be able to realize their limitations and possible "Better" or more appropriate statistics that are more "truthful".

Statistics is a tool used to organize information and to draw inferences about data. Any tool can be misused.

Social and behavioral sciences rely heavily on statistics because of the large amount of variance inherent when studying behavior and mental processes. Statistics help us make decisions when we have incomplete and possibly innaccurate data.

1. Individual Difference
2. Measurement Error
3. Unreliability

Variabilty means we have less faith in any single score when drawing inferences.

Statistics quantifies variability and takes it into account.

Two General categories of statistics and some specific statistics for each:

Descriptive:

procedures for organizing, summarizing, and describing quantative information. Also use for characterizing relationships between variables.

Inferential:

Drawing inferences about a population from a sample

Measurement scales:

Nominal Scales

naming

Labels that imply a difference but don't indicate what the difference is.

exclusive and exhaustive categories

e.g., Subject 1, Subject 2, Subjects 3

We could have just as easily called them

Can you name other examples?

 

Ordinal Scales

not only put observations in exclusive and exhaustive categories but also rank order them. That is they tell you some about the nature of the difference between groups.

e.g., finish position in a race

Here 1, 2, 3 are not assigned arbitrarily but rather indicate that 1 was faster than 2 who was faster then 3. So we can make general statements about greater than, less than or equal to.

 

Interval Scales

Includes the properties of nominal and ordinal but also tells us something about the difference between observations.

The "amount" between any two intervals of the same size is constant.

With this type of scale we can start to use mathematical operations.

For example, calendar time.

If we start at the year 1 then we know that the amount of time that passed between the year 1 and the year 2 is the same amount of time as passed between the year 1999 and 2000 or any other two years (ignoring leap years!).

Now we can add and subtract numbers! Multiplication and division can be done but this is controversial!!

Do you know why?

 

Ratio Scales

include the properties of all the other scales but allows, with out any argument, for multiplication and division.

The key is having an absolute zero. Your scale must have a Zero point that indicates the complete absence of what you are trying measure.

Weight, for example, the typical bathroom scale starts at zero (no weight, no one is standing on the scale).

Someone who 200 is twice as heavy as someone who weighs 100 pounds.

200/100 = 2

2 x 100 = 200

It all makes sense.

What abut temperature?

Do you understand why you can't get a "true" ratio with an interval scale?

Also, keep in mind that psychologist don't have direct measures. Even though our scales might have zeros they may not reflect the absence of the trait they are trying to measure (creativity, memory, etc.). Exactly what level of measurement psychological scales operate at is hotly debated!

 

Let know if this makes sense.

email me at: crawley@ac.marywood.edu

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This page was updated at 3:00 p.m. May 28, 2002