Stats 151 Notes
STAT 151
Introduction to
Applied Statistics I
Byron Schmuland
CAB 473
byrons@ualberta.ca
Why bother with statistics?
If your experiment needs statistics, you ought to have done a better experiment.
Ernest Rutherford
Uncertainty is everywhere!
Many processes in nature (chemical, physical, economic, etc.) follow laws that are not exact, but are subject to a certain amount of chance variation.
It is impossible to eliminate all sources of variation from an experiment, no matter how well planned.
Doesn’t uncertainty ruin everything?
No! Statistics is the science of dealing with uncertain situations, by facing up to chance variation and using it to your advantage.
Using statistical ideas you can extract useful information from a set of data, and use it to solve real life problems.
Problem: Tell the truth?
A sociologist is interested in the percentage of husbands who cheat on their wives. However, if you simply interview men and ask them "Did you ever cheat on your wife?", they will tend to lie.
Solution: Randomization
Interview each man and have him secretly flip a coin. If he is faithful and the coin is "heads", he says "NO". Otherwise, he says "YES". This way the sociologist is ignorant of the man’s past, so there is no motive to lie.
To find the correct estimate of faithful husbands, double the number of "NO"s.
Randomization and design of experiments is covered in the required reading Ch. 11-13.
Problem: Towards an HIV antibody?
A researcher in the department of immunology has developed a strain of the HIV virus, and he wants to know if it is infectious. The virus is applied to human cells which are stained to detect infected cells. He sees six stained cells out of 1000.
Unfortunately, even on a sample of cells to which no virus has been applied, he sees three stained cells. Is the ratio 6/1000 big enough, compared to
3/1000, to conclude that the strain is actually infectious? Comparison of two
Introduction to
Applied Statistics I
Byron Schmuland
CAB 473
byrons@ualberta.ca
Why bother with statistics?
If your experiment needs statistics, you ought to have done a better experiment.
Ernest Rutherford
Uncertainty is everywhere!
Many processes in nature (chemical, physical, economic, etc.) follow laws that are not exact, but are subject to a certain amount of chance variation.
It is impossible to eliminate all sources of variation from an experiment, no matter how well planned.
Doesn’t uncertainty ruin everything?
No! Statistics is the science of dealing with uncertain situations, by facing up to chance variation and using it to your advantage.
Using statistical ideas you can extract useful information from a set of data, and use it to solve real life problems.
Problem: Tell the truth?
A sociologist is interested in the percentage of husbands who cheat on their wives. However, if you simply interview men and ask them "Did you ever cheat on your wife?", they will tend to lie.
Solution: Randomization
Interview each man and have him secretly flip a coin. If he is faithful and the coin is "heads", he says "NO". Otherwise, he says "YES". This way the sociologist is ignorant of the man’s past, so there is no motive to lie.
To find the correct estimate of faithful husbands, double the number of "NO"s.
Randomization and design of experiments is covered in the required reading Ch. 11-13.
Problem: Towards an HIV antibody?
A researcher in the department of immunology has developed a strain of the HIV virus, and he wants to know if it is infectious. The virus is applied to human cells which are stained to detect infected cells. He sees six stained cells out of 1000.
Unfortunately, even on a sample of cells to which no virus has been applied, he sees three stained cells. Is the ratio 6/1000 big enough, compared to
3/1000, to conclude that the strain is actually infectious? Comparison of two