OJNI

Statistics 1.1

 

 

 

 

 

Home

 

In order to take the first statistics course, read the course content below, then click on "Take The Test", follow the directions, take the test, have it graded, and print your certificate upon successful completion. Please feel free to contact the author, he is hyperlinked below! Remember, as an OJNI subscriber, you do not have to pay for this course, however, this offer is only valid until the next edition of OJNI is released and Statistics 1.2 will be available.

Statistics 1.1

Author: Arthur Johnson, PhD    


1 contact hour

Course posted July 30, 1999
Course expires July 30, 2001



Learning Objectives
Upon completion of this 1 unit course, the learner should be able to:
  1. State the goal of statistical analysis.
  2. Describe the difference between variability and cause.
  3. State to purpose of an experimental study.
  4. Describe how bias affects the results of a study.
  5. Describe why statistics is important when choosing sample size.

Introduction
Apart from the fact that statistics is a required course for a nursing degree, why should we be bothered with this bugbear of the medical profession? Taking care of a patient relies on your ability to draw on experience to ask questions and find an appropriate response. In this section we will look at what statistics can do to assist us in asking and answering questions.

The assessment of a specific medical therapy is a task that requires more than just experience and judgement to reach a valid conclusion. Such assessment requires the medical practitioner to evaluate a wide range of patients and must take into account patient variability. Statistics is a tool that helps to distinguish between those events that simply reflect variability and those events that are of medical interest.

Looking at Variability
If we were to take a random sampling of 50 people we would probably expect the group to breakdown by gender into two groups of roughly 25 men and 25 women. We would expect a result somewhere in this neighborhood but would not be surprised to find some variability from one sample to another. We would think nothing if 23 men and 27 women were found in a second sample. We might wonder if there was a reason for 20 men and 30 women in a third sample and we would certainly question a sample of 50 people that contains 10 men and 40 women. We would want to know the circumstances that caused the imbalance in the last sample.

The field of statistics attempts to quantify or put a number to the inherent variability in measurement. Statistics allows us to formulate rules and helps us to decide whether the observed results of a sampling are due to normal variation or whether there is an underlying cause at work. Such rules are generally accepted by the scientific community and allow agreement in the interpretation of data. In this course we will be discussing a number of accepted statistical rules and looking at examples of how these rules are applied for analysis of medical studies and clinical trials.

The recent events in Yugoslavia provide a good example. It has been reported that groups of refugees arriving at the borders contain many more women than men. Under the circumstances it might be expected that the groups would be evenly divided between men and women. Statistical analysis confirmed the imbalance and representatives from the United Nations began to look for the cause. In this case the question is whether the variability is normal or due to some underlying cause. Upon closer examination it was revealed that male refugees were being separated from female refugees before reaching the border and possibly taken to detention camps or even murdered.


Variability vs. Cause

 
Statistical Rule
As long as the observed number is at or within the given limits then the result is due to a variation in the sampling and not to some underlying cause.

In the above example statistics tells us that when we expect a 0.5 (50%) proportion of men to women that in 19 of the 20 samples we will find between 18 and 32 women. One out of the 20 samples will be outside these limits. Statistical rule number one is that as long as the observed number is at or within the given limits then the result is due to a variation in the sampling and not to some underlying cause. If the observed number is outside the given limits then we should look for an underlying cause. Keep in mind that an outlying sample may indeed be due to chance and our search for an underlying cause will go unrewarded. This is the risk we accept when using the statistical rule.

Calculations of this sort can easily be used to analyze other proportions and other sample sizes. For example, you may want to compare two drugs used for the treatment of hypertension. Statistical analysis allows us to compare the proportion of hypertensive subjects becoming normotensive with the usual treatment versus the new treatment. The argument also extends to other measures such as sample means and the comparison of means.

Looking for Answers
Here is an example of how we would use statistical analysis to understand the results of an experimental study. In this study of the effects of an accepted and a new anti-hypertensive drug, the investigator assigns medication to the subjects as if they were participating in a clinical trial. The results compare possible improvement with a new medication to improvement with the usual medication. The sample size contains 100 subjects.


Table A

Usual

New

Total

Same

40

40

80

Improved

10

10

20

Total

50

50

100


The results of the above sampling show no evidence that there is any benefit from the new treatment compared to the old treatment.


Table B

Usual

New

Total

Same

40

10

50

Improved

10

40

50

Total

50

50

100



The results of the second sampling show clear evidence that the new treatment is superior to the usual treatment. However, results from studies are rarely as clear as the above tables indicate. Consider the following table:


Table C

Usual

New

Total

Same

40

30

70

Improved

10

20

30

Total

50

50

100


In the third sampling, the new treatment appears to be superior to the usual treatment. However, perhaps the apparent improvement is really only due to chance variation rather than a genuine treatment effect. The variation in sample three may be within the limits of the sampling variation. Statistical analysis is able to determine the inherent variability in the data and decide whether the results are due to chance or if there is evidence of genuine improvement. Applying a statistical test to the data in Table C shows that there is indeed evidence that the new treatment is superior.

Looking for Questions
An observational program is necessary to look for questions. An experimental program is necessary to answer questions. In the next example we have a group of subjects, probably normal to whom we assign a set of characteristics - demographic, physiologic parameters, behavior patterns, presence or absence of medical events, etc. Once we determine the set of characteristics, we can analyze the database in a number of different ways. Consider Table D, which compares cholesterol levels with the occurrence of cardiac events:



Table D

Low Chol

High Chol

Total

No Event

40

30

70

Event

10

20

30

Total

50

50

100



The numbers in Table D indicate that subjects with high cholesterol are more likely to experience cardiac events than persons with low cholesterol. Application of a statistical test allows us to see that the difference cannot be reasonably attributed to chance variation. This observation leads us to an important question - will a decrease in cholesterol lead to a decrease in cardiac events? The question helps us to design an experiment to determine whether reducing cholesterol with diet or drugs will lead to a reduction of cardiac events. It is important to accept that the observational data does not justify or endorse a specific intervention.

Can observational data ever justify or endorse an intervention? The answer is a qualified yes. The relationship of smoking to health is a good example. Setting up a study composed of one group of smokers and one group of non-smokers would not be ethically acceptable. However, a variety of observational studies have been conducted that clearly indicate that smoking is deleterious to health. Using the data collected from these observational studies it is possible to make a good case for intervention.

Looking for Bias
Statistics allows us to create questions from observational data and to find answers from planned experiments. In both instances we seek to understand whether chance or cause is responsible for the behavior of the data. But chance and cause are not the only factors at work in statistical analysis. A third factor called bias can blur the interpretation of the data beyond chance or cause. Bias is defined as unrecognized factors that influence the results so that cause can appear as chance and chance can appear as cause.

A properly conducted experimental program in which the investigator assigns a treatment to a specific group is less likely to be affected by bias. The key component is how the assignment of the treatment is carried out. Statistics provides an assignment procedure that assures that each subject has an equal chance of being assigned to one of the two treatment groups. This type of assignment procedure is called random assignment and is similar to flipping a coin for each subject. If the coin comes up heads, the subject is placed in one group and if the coin comes up tails the subject is placed in a second group. This is the only assignment procedure that protects against bias.

In an observational study, the subjects in effect assign themselves by the traits they possess to a specific group. In this type of study the possibility of bias is always present. This is the main reason why observational studies are used to suggest a question rather than provide an answer.

You may read that more elaborate statistical analysis can adjust (at least for know variables) against any biasing influences. Be assured that this is only possible because such analyses minimize the influence of subjects whose characteristics vary appreciably from the rest of the group by simply ignoring them.

Looking for an Appropriate Number of Subjects
Common sense tells that if we have developed a breakthrough drug we should be able to demonstrate its effectiveness by designing a small study. A less effective drug would require a larger group of subjects to demonstrate the effectiveness of a particular drug. Often the number of subjects in a study will be based on the number of available subjects or on the number of subjects the researchers were able to afford. Studies of this sort are quite likely to have too small a sample size.

Studies with too large a sample size are seldom an issue. However, if a study is too small we might conclude that the results are due to chance when a larger study might show the drug to be effective. Apart from the consequences of failing to find a useful drug the small study raises a critical ethical problem. The participants who give their informed consent to participate in a study are defrauded if the study is too small to yield useful results.

Statistics can be helpful in determining the correct sample size. In order for statistics to be helpful however, the investigator must have a working idea of the magnitude of difference between the new treatment and the usual treatment. If the goal of the study is to determine which drug treatment is better (how much improvement does the new drug provide compared to the usual drug) then how much improvement does the new drug have to provide to be clinically significant.

If the usual drug causes decreased blood pressure or decreased cholesterol levels in 20% of the subjects, how much more improvement does the new drug have to provide to justify a change to the new drug? How much greater a percent resolution would be of clinical importance - 25%, 30%? For example, if the investigator were interested in distinguishing a 20% improvement rate from a 30% improvement rate then the number of subjects per group would be 400. Once the investigator makes a commitment to the magnitude of difference, the statistician can easily calculate the sample size for the study.


Recap

  1. Statistics quantifies variability and aids the researcher in distinguishing between chance and cause.
  2. Observational studies suggest questions.
  3. Planned experimental studies answer questions.
  4. Bias can enhance or diminish the real differences between treatments.
  5. The proper study size is fixed if there is an understanding of the magnitude of difference between two treatment options.

Copyright 1999-2000 Wild Iris Medical Education    Reprinted here with permission.

Take the Test                Note: You will go to NursingCEU's site for the test.