Chapter 1Part 3 – or I promise I’ll figure out how to use PowerPoints better someday!

Frequency• Twenty students were asked how many hours they worked per day.• Their responses, in hours, are as follows:• 5; 6; 3; 3; 2; 4; 7; 5; 2; 3; 5; 6; 5; 4; 4; 3; 5; 2; 5; 3

• A frequency is the number of times a value of thedata occurs• Relative frequency is the ratio (fraction or proportion)

of the number of times a value of the data occurs in theset of all outcomes to the total number of outcomes.• To find the relative frequencies, divide each frequency by the total

number of students in the sample – in this case 20.• Note that the sum of the relative frequency is 20/20, or 1.

Data Value Frequency

2 33 54 35 66 27 1

Data Value Frequency

Relative Frequency

2 3 3/20 or 0.153 5 5/20 or 0.254 3 3/20 or 0.155 6 6/20 or 0.306 2 2/20 or 0.107 1 1/20 or 0.05

Frequency• Cumulative relative frequency is the accumulation of the

previous relative frequencies• To find the cumulative relative frequencies, add all the

previous relative frequencies to the relative frequency for the current row• The last row should

be 1, unless of course rounding causes it to beslightly off of 1

Data Value Frequency Relative Frequency Cumulative Relative Frequency2 3 3/20 or 0.15 0.153 5 5/20 or 0.25 0.15 + 0.25 = 0.404 3 3/20 or 0.15 0.40 + 0.15 = 0.555 6 6/20 or 0.30 0.55 + 0.30 = 0.856 2 2/20 or 0.10 0.85 + .010 = 0.957 1 1/20 or 0.05 0.95 + 0.05 = 1.00

Experimental Design• The purpose of any study is to investigate the relationship between

two variables• If we notice something, or observe something, we are doing an

observational study• Even if we are asking someone a question or measuring them or having them fill

out a survey – we’re not altering the information; just collecting it• A research study comparing the risk of developing lung cancer, between

smokers and non-smokers, would be one example• This type of research draws a conclusion by comparing subjects against a

control group, in cases where the researcher has no control over the experiment• One of the main reasons for performing any observational research is due to

ethical concerns

Experimental Design• Sometimes researchers need to manipulate things a little to

see what effects are produced• When you do that, manipulate things, you’re conducting an experimental

study.• There is a lot of terminology, protocols, and ethics associated with doing

experimental studies• Suppose there are trials of a new drug meant to reduce blood

pressure• The drug (and the dosage) is the independent or explanatory variable• You want to see if it has an effect on blood pressure

• The blood pressure readings are the dependent or outcome variable

Experimental Design

You then give some patients the drugAnd you would give some patients a placebo

This is the treatment group This is the control group

Experimental Design• It is possible that someone’s blood pressure might well drop

just because they believe that the new medicine will be effective.• The placebo (Latin for “I will please”) is a fake pill to try and

control for this possibility.• The volunteers do not know which group they are in (blind

study)• If you do not tell the people taking their blood pressure which

patients are which, you now have a double blind study• This way, you eliminate the power of suggestion on both sides

Experimental Design• You look for a difference in the average blood pressure of the

treatment group compared to the control group after the drug has been taken for a suitable amount of time• If the difference is big enough, you declare that your drug

works• We’ll spend a lot of time in this course talking about how to

find out if it IS big enough

Experimental Design• Even with all of these precautions, it might turn out that the

drug “worked”, not because of the specially developed chemical you put in, but because of some supposedly unimportant substance you used to fill up space in the pill• This might be discovered some time later when the drug stops

working because you started using some other filler• When something else besides the independent variable is

responsible for a difference in the dependent variable between the control group and the treatment group, we call that something else a confounding variable• It confounds, or confuses, the analysis of the effect

Ethics• The widespread misuses and misrepresentation of statistical

information often gives the field a bad name.• The book discusses Diederik Stapel, please read for your own

edification• He was accused of:• Creating datasets, which largely confirmed the prior expectations• Altering data in existing datasets• Changing measuring instruments without reporting the change• Misrepresenting the number of experimental subjects

• The Vaccine War (Please see alternate link on Canvas if this does not work)

Ethics• Many types of statistical fraud are difficult to spot• Some researches simply stop collecting data once they have just enough

to prove what they had hoped to prove• They don’t want to take the chance that a more extensive study would

complicate their lives by producing data contradicting their hypothesis• Professional organizations, like the American Statistical

Association, clearly define expectations for researchers• There are even laws in the federal code about the use of

research data

Ethics – Human Participant• Ethics and Law dictate that researchers should be mindful of

the safety of their research subjects.• U.S. Dept. of Health and Human Services oversees federal

regulations of research studies with the aim of protecting participants.• Research institutions, to ensure the safety of all human

subjects, establish oversight committees known as Institutional Review Boards (IRB)

Ethics – Human Participant• All planned studies must be approved in advance by the IRB• Key protections that are mandated by law include:• Risks to participants must be minimized and reasonable with respect to

projected benefits• Participants must give informed consent• The risks of participation must be clearly explained to the subjects of the study• Subjects must consent in writing, and researches are required to keep documentation

of the consent• Data collected from individuals must be guarded carefully to protect their

privacy• Understanding these safeguards and protections is important so that you

can recognize proper data analysis

Homework Problem Set• Chapter 1• Starts on page 51• Problems 43, 46, 51, 52, 63, 64, 65, 73, 80• Due next Wednesday• Do your best to avoid…