Why Study Statistics?
|"One distinguishing characteristic of an educated person is that he or she can be emotionally moved by statistics."
||George Bernard Shaw
|"Mankind would rather commit suicide than learn arithmetic."
Statistics is a tool used by many disciplines. You use statistics to help you answer questions about phenomena of interest. Thus the data you collect isn't just numbers--it is information which can help you understand the phenomenon of interest. Different disciplines have different phenomena they seek to understand. As a psychologist, I'm interested in understanding particular behaviors, those are the phenomena of interest I'm going to use statistics to help understand.
In this course statistics is taught by using example of various phenomena of interest. You'll be collecting data and then using statistical procedures to help understand the phenomenon you have explored.
Statistics is power--the power to persuade*. Statistics provides a new way of marshaling information to make a decision. Those who have discovered the manner of quantitative analyses are less swayed by proficient persuasive compelling speakers who weave their charismatic magic around the issue. Its the opposite of "Don't confuse me with the facts." -- Its "Give me the facts in a way I can understand them."
Generally speaking, when we have a data set and we want to figure out what the data tells us about the phenomena, we are doing "data analysis." Statistics is only one component of data analysis.
- Descriptive Statistics and Data Analysis. Techniques and procedures to organize and summarize data. Even a small research project may generate many hundreds of numbers. The data per se are simply unorganized chaos. Descriptive statistics is the label for procedures we can use to help discover the way the data are patterned. The human perceptual system is very powerful in deriving and recognizing patterns. Descriptive statistical procedures simply help us in that task.
- Some of the procedures are calculations such as measures of central tendency (mean) and measures of dispersion (range)
- Some are graphic (frequency distributions [a table], frequency polygons, and histograms.
- Some are newly developed techniques of scientific visualization.
- Weather Radar is an example. There isn't any red or green or yellow weather. The "false" colors are indicating the amount of precipitation.
- You've all seen pictures which illustrate how brain activity will change depending on whether a person hears, says, sees, or thinks a word. Different areas of the brain are active with these different tasks. The results are being displayed as changes in the color of the graphic to allow our pattern recognition capabilities to operate. (I'm sure you realize the brain is not actually chaning color).
- Here's a really wild example of scientific visualization: projecting a representation of the human genome in 3-D.
- And here is another one I just found, the Eagle Nebula.
- Inferential Statistics. Inferential statistics is used to determine the reliability of the results of the research.
- The word "reliability" is being used in a particular way here.
- The generic meaning of the word "reliable" is when the measurement or procedure is repeated in the future you will get pretty much the same result.
- Inferential statistics are a way of deciding whether or not you would get the same result by repeating the procedure on a different group of subjects -- on a new sample of cases.
- Science is interested in the general case, but can only conduct research on particular cases.
- Descriptive statistics describe what this group of subjects did. Inferential statistics determine whether or not the result we got with these subjects will happen in the future with different subjects. If the same result is likely to happen in the future with different subjects then the result is reliable.
- For example we can measure simple visual reaction time (SVRT) in a sample of 10 males and 10 females.
- SVRT procedure: Person has finger resting on a response button. The instructions are, "As soon as the signal light above the button turns on, press the button. Do not press the button until you are sure the signal light has come on. If you respond before the signal light comes on we will have to start the measurement process from the beginning. There will be a buzzer to indicate the signal light will occur within the next 5 seconds so you can be ready.
- We will find the average SVRT of the females to be about 0.20 seconds (1/5 second; 200 milliseconds; 200 ms) and that of males, 0.18 seconds.
- The average male SVRT is shorter than the average female SVRT--this is a descriptive statistic; it is true of that sample of 20 persons.
- If I repeat the research with another sample of males and females, will I find the same results? If the results are reliable, I would expect to replicate the finding. That is, we would be describing the general case, "Males have shorter simple reaction times than females."
- We are not concluding that every male has a shorter reaction time than every female. Instead, we are saying if you were to randomly pick a male and a female from a class and measure SVRT, you'd make money (on a 1:1 odds bet) by betting the male would have the shorter RT.
- "Inferential statistics is a way of reaching a decision: should I decide the research supports theory A or not? Did the independent variable have an effect? Does it really matter whether or not children watch TV? Do elevated cholesterol levels lead to increased heart attacks?
- Be careful not to confuse the reliability issue with the "Clinical vs Scientific" prediction problem.
- Scientific predictions describe the "general case" or the underlying model. What's true in general.
- Clinical predictions attempt to predict something about an individual. To make a prediction about an individual instead of the general case probably will require additional information.
- Thus, for example, Freudian theory says that everyone goes through a series of stages in psychosexual development. That is the general case. But not everyone has the same outcome--psychosexual development depends upon the particular experiences you have with your parents/family/etc. To describe a particular person's psychosexual development (a clinical prediction), requires additional information beyond the fact of humanity.
- In the simple reaction time measurement, the general prediction is that males have shorter reaction times than females. A clinical prediction is to take a particular male and a particular female and predict whether or not this male will have a shorter reaction time than this female.
Inferential Statistical Reasoning Explored Further.
Basis of inferential statistics.
Note: An extended tutorial expanding this topic is available. Click here.
O.K. Let's pretend I have collected the data. I found the SVRT for 10 males and 10 females and found the average RT of women was 0.02 seconds longer (the difference in the means was 0.02 seconds).
Now the question is whether or not the same type of difference--the mean female SVRT is longer than the mean male SVRT--will repeat itself with a new group of subjects.
Here is how inferential statistics answers that question.
- Assume the real difference between male and female RTs is zero (0.0) seconds.
- Use computers to simulate running that experiment many thousands of times using the situation where there is NO difference between female and male reaction times.
- Where does the data I actually measured fit in the simulated data?
Here's an example of what how that kind of information might be plotted:
Each computer simulation result is plotted as a filled square. As you can see the filled squares bounce around the "no difference" value.
Where does the actual data fit in this picture? I've drawn two possibilities. It could be the open square or it could be the open triangle.
- If the actual data is located like the open square then the conclusion I would make is "The data I got (mean difference is 0.02 sec) is the kind of result I'd expect when really there is NO difference so I cannot say there is a difference."
- If the actual data is located like the open triangle then the conclusion I would make is "The data I got is NOT like the data that happens when the real difference is zero, so my data is showing there is a REAL difference between male and female reaction times."
What the open triangle illustrates is a "whopper" effect. Its an easy decision to make with data like that. But what if the triangle were closer to the filled squares? How would you make the decision then? Well, inferential statistical procedures provides some rules for reaching the decision of whether or not the "real" results is similar to the "simulated" results.
- The line of reasoning described here is an example of the "Null Hypothesis Testing Model of Inferential Statistics".
- "Null Hypothesis" is another way of saying the "No Difference Hypothesis".
- This inferential method always starts out assuming the difference between the two groups is zero and then asks how many possible samples could have produced the results we actually got.
* I was introduced to the "statistics is the power to persuade" argument many years ago and I neglected to credit the originator. Now his name is lost in the vagarities of memory. Belated thanks.
© 2002 - 2007 by BurrtonWoodruff. All rights reserved. Modified Sunday, March 25, 2007