5.1: Basics of Statistics

Like most people, you probably feel that it is important to "take control of your life." But what does this mean? Partly it means being able to properly evaluate the data and claims that bombard you every day. If you cannot distinguish good from faulty reasoning, then you are vulnerable to manipulation and to decisions that are not in your best interest. Statistics provides tools that you need in order to react intelligently to information you hear or read. In this sense, statistics is one of the most important things that you can study.

Here are some claims that you may have heard on several occasions. (We are not saying that each one of these claims is true!)

• 4 out of 5 dentists recommend Dentyne.

• Almost 85% of lung cancers in men and 45% in women are tobacco-related.

• Condoms are effective 94% of the time.

• Native Americans are significantly more likely to be hit crossing the streets than are people of other ethnicities.

• People tend to be more persuasive when they look others directly in the eye and speak loudly and quickly.

• Women make 75 cents to every dollar a man makes when they work the same job.

• A surprising new study shows that eating egg whites can increase one's life span.

• People predict that it is very unlikely there will ever be another baseball player with a batting average over 400.

• There is an 70% chance that in a room full of 30 people that at least two people will share the same birthday.

• 79.48% of all statistics are made up on the spot.

Before going further, however, two distinct meanings of the word “statistics” should be clarified. First, “statistics” could mean the academic discipline, a field of study, involving the collection, presentation, interpretation, and use of data. When used in this sense, the word is considered singular (though it looks plural). Second, in a narrower sense, a number collected in a survey or study is referred to as a “statistic.” For instance, the average height of a sample of 100 people would be a (one) statistic. This is a singular word (of course, two or more of these numbers would be referred to as “statistics”). Be aware of the difference when you encounter this word.

All of these claims are statistical in character. We suspect that some of them sound familiar; if not, we bet that you have heard other claims like them. Notice how diverse the examples are; they come from psychology, health, law, sports, business, etc. Indeed, data and data-interpretation show up in discourse from virtually every facet of contemporary life.

Statistics are often presented in an effort to add credibility to an argument or advice. You can see this by paying attention to television advertisements. Many of the numbers thrown about in this way do not represent careful statistical analysis. They can be misleading and push you into decisions that you might find cause to regret. For these reasons, learning about statistics is a long step towards taking control of your life. (It is not, of course, the only step needed for this purpose.) This chapter will help you learn statistical essentials. It will make you into an intelligent consumer of statistical claims.

You can take the first step right away. To be an intelligent consumer of statistics, your first reflex must be to question the statistics that you encounter. The British Prime Minister Benjamin Disraeli famously said, "There are three kinds of lies -- lies, damned lies, and statistics." This quote reminds us why it is so important to understand statistics. So let us invite you to reform your statistical habits from now on. No longer will you blindly accept numbers or findings. Instead, you will begin to think about the numbers, their sources, and most importantly, the procedures used to generate them.

We have put the emphasis on defending ourselves against fraudulent claims wrapped up as statistics. Just as important as detecting the deceptive use of statistics is the appreciation of the proper use of statistics. You must also learn to recognize statistical evidence that supports a stated conclusion. When a research team is testing a new treatment for a disease, statistics allows them to conclude based on a relatively small trial that there is good evidence their drug is effective. Statistics allowed prosecutors in the 1950’s and 60’s to demonstrate racial bias existed in jury panels. Statistics are all around you, sometimes used well, sometimes not. We must learn how to distinguish the two cases.

Populations and samples

Before we begin gathering and analyzing data, we need to characterize the population we are studying. If we want to study the amount of money spent on textbooks by a typical first-year college student, our population might be all first-year students at your college. Or it might be:

• All first-year community college students in the state of California.

• All first-year students at public colleges and universities in the state of California.

• All first-year students at all colleges and universities in the state of California.

• All first-year students at all colleges and universities in the entire United States.

• And so on.

Definition: Population

The population of a study is the group the collected data is intended to describe.

Sometimes the intended population is called the target population since the collected data might not actually be representative of the intended population if we design our study badly.

Why is it important to specify the population? We might get different answers to our question as we vary the population we are studying. First-year students at a large university might take slightly more diverse courses than those at your college, and some of these courses may require less popular textbooks that cost more; or, on the other hand, the University Bookstore might have a larger pool of used textbooks, reducing the cost of these books to the students. Whichever the case (and it is likely that some combination of these and other factors are in play), the data we gather from your college will probably not be the same as that from a large university. Particularly when conveying our results to others, we want to be clear about the population we are describing with our data.

Example \(\PageIndex{1}\)

A newspaper website contains a poll asking people their opinion on a recent news article. What is the population?

Solution

While the target (intended) population may have been all people, the real population of the survey is readers of the website.

If we were able to gather data on every member of our population, say the average (we will define "average" more carefully in a subsequent section) amount of money spent on textbooks by each first-year student at your college during the 2009-2010 academic year, the resulting number would be called a parameter.

Definition: Parameter

A parameter is a value (average, percentage, etc.) calculated using all the data from a population

We seldom see parameters, however, since surveying an entire population is usually very time-consuming and expensive unless the population is very small or we already have the data collected.

Definition: Census

A survey of an entire population is called a census.

You are probably familiar with two common censuses: the official government Census that attempts to count the population of the U.S. every ten years, and voting, which asks the opinion of all eligible voters in a district. The first of these demonstrates one additional problem with a census: the difficulty in finding and getting participation from everyone in a large population, which can bias, or skew, the results.

There are occasionally times when a census is appropriate, usually when the population is fairly small. For example, if the manager of Starbucks wanted to know the average number of hours her employees worked last week, she should be able to pull up payroll records or ask each employee directly.

Since surveying an entire population is often impractical, we usually select a sample to study;

Definition: Sample

A sample is a smaller subset of the entire population, ideally one that is fairly representative of the whole population.

We will discuss sampling methods in greater detail in a later section. For now, let us assume that samples are chosen in an appropriate manner. If we survey a sample, say 100 first-year students at your college, and find the average amount of money spent by these students on textbooks, the resulting number is called a statistic.

Definition: Statistic

A statistic is a value (average, percentage, etc.) calculated using the data from a sample.

Example \(\PageIndex{2}\)

A researcher wanted to know how citizens of Los Angeles felt about a voter initiative. To study this, she goes to a large shopping mall and randomly selects 500 shoppers and asks them their opinion. 60% indicate they are supportive of the initiative. What is the sample and population? Is the 60% value a parameter or a statistic?

Solution

The sample is the 500 shoppers questioned. The population is less clear. While the intended population of this survey was LA citizens, the effective population was mall shoppers. There is no reason to assume that the 500 shoppers questioned would be representative of all LA citizens.

The 60% value was based on the sample, so it is a statistic. (Note that this is singular).

Try it Now 1

The U.S. federal debt at the end of 2001 was $5.77 trillion and grew to $6.20 trillion by the end of 2002. At the end of 2005 it was $7.91 trillion and grew to $8.45 trillion by the end of 2006.² Calculate the absolute and relative increase for 2001-2002 and 2005-2006. Which year saw a larger increase in federal debt?

Try it Now 2

A college reports that the average age of their students is 28 years old. Is this a statistic or a parameter?

Categorizing data

Once we have gathered data, we might wish to classify it. Roughly speaking, data can be classified as categorical data or quantitative data.

Definition: Quantitative and Categorical Data

Categorical (qualitative) data are pieces of information that allow us to classify the objects under investigation into various categories.

Quantitative data are responses that are numerical in nature and with which we can perform meaningful arithmetic calculations.

Example \(\PageIndex{3}\)

We might conduct a survey to determine the name of the favorite movie that each person in a math class saw in a movie theater.

Solution

When we conduct such a survey, the responses would look like: Finding Nemo, The Avengers, or Dunkirk. We might count the number of people who give each answer, but the answers themselves do not have any numerical values: we cannot perform computations with an answer like "Finding Nemo." This would be categorical data.

Example \(\PageIndex{4}\)

A survey could ask the number of movies they have seen in a movie theater in the past 12 months (0, 1, 2, 3, 4, ...)

Solution

This would be quantitative data.

Other examples of quantitative data would be the running time of the movie you saw most recently (104 minutes, 137 minutes, 104 minutes, ...) or the amount of money you paid for a movie ticket the last time you went to a movie theater ($5.50, $7.75, $9, ...).

Sometimes, determining whether or not data is categorical or quantitative can be a bit trickier.

Example \(\PageIndex{5}\)

Suppose we gather respondents' ZIP codes in a survey to track their geographical location.

ZIP codes are numbers, but we can't do any meaningful mathematical calculations with them (it doesn't make sense to say that 98036 is "twice" 49018 — that's like saying that Lynnwood, WA is "twice" Battle Creek, MI, which doesn't make sense at all), so ZIP codes are really categorical data.

Example \(\PageIndex{6}\)

A survey about the movie you most recently attended includes the question "How would you rate the movie you just saw?" with these possible answers:

1. it was awful
2. it was just OK
3. I liked it
4. it was great
5. best movie ever!

Solution

Again, there are numbers associated with the responses, but we can't really do any calculations with them: a movie that rates a 4 is not necessarily twice as good as a movie that rates a 2, whatever that means; if two people see the movie and one of them thinks it stinks and the other thinks it's the best ever it doesn't necessarily make sense to say that "on average they liked it."

However, it DOES make sense to discuss the average rating and other statistics in this case. For instance, a movie whose average rating is a 1.8 is clearly different from one whose average is a 4.2. Also, it would mean something if the maximum rating of another movie was a 2. So, in a sense, this data can be considered quantitative.

As we study movie-going habits and preferences, we shouldn't forget to specify the population under consideration. If we survey 3-7 year-olds the runaway favorite might be Finding Nemo. 13-17 year-olds might prefer The Avengers. And 33-37 year-olds might prefer...well, Finding Nemo.

Try it Now 3

Classify each measurement as categorical or quantitative

1. Eye color of a group of people
2. Daily high temperature of a city over several weeks
3. Annual income

Sampling methods

As we mentioned in a previous section, the first thing we should do before conducting a survey is to identify the population that we want to study. Suppose we are hired by a politician to determine the amount of support he has among the electorate should he decide to run for another term. What population should we study? Every person in the district? Not every person is eligible to vote, and regardless of how strongly someone likes or dislikes the candidate, they don't have much to do with him being re-elected if they are not able to vote.

What about eligible voters in the district? That might be better, but if someone is eligible to vote but does not register by the deadline, they won't have any say in the election either. What about registered voters? Many people are registered but choose not to vote. What about "likely voters?"

This is the criteria used in much political polling, but it is sometimes difficult to define a "likely voter." Is it someone who voted in the last election? In the last general election? In the last presidential election? Should we consider someone who just turned 18 a "likely voter?" They weren't eligible to vote in the past, so how do we judge the likelihood that they will vote in the next election?

In November 1998, former professional wrestler Jesse "The Body" Ventura was elected governor of Minnesota. Up until right before the election, most polls showed he had little chance of winning. There were several contributing factors to the polls not reflecting the actual intent of the electorate:

• Ventura was running on a third-party ticket, and most polling methods are better suited to a two-candidate race.

• Many respondents to polls may have been embarrassed to tell pollsters that they were planning to vote for a professional wrestler.

• The mere fact that the polls showed Ventura had little chance of winning might have prompted some people to vote for him in protest to send a message to the major-party candidates.

But one of the major contributing factors was that Ventura recruited a substantial amount of support from young people, particularly college students, who had never voted before and who registered specifically to vote in the gubernatorial election. The polls did not deem these young people likely voters (since in most cases young people have a lower rate of voter registration and a turnout rate for elections) and so the polling samples were subject to sampling bias: they omitted a portion of the electorate that was weighted in favor of the winning candidate.

Definition: Sampling Bias (selection bias)

A sampling bias is the bias caused when the sample chosen does not fairly represent the population being studied. The sampling method, therefore, must be carefully considered to avoid this type of bias.

So even identifying the population can be a difficult job, but once we have identified the population, how do we choose an appropriate sample? Remember, although we would prefer to survey all members of the population, this is usually impractical unless the population is very small, so we choose a sample. There are many ways to sample a population, but there is one goal we need to keep in mind: we would like the sample to be representative of the population.

Returning to our hypothetical job as a political pollster, we would not anticipate very accurate results if we drew all of our samples from among the customers at a Starbucks, nor would we expect that a sample drawn entirely from the membership list of the local Elks club would provide a useful picture of district-wide support for our candidate.

One way to ensure that the sample has a reasonable chance of mirroring the population is to employ randomness. The most basic random method is simple random sampling.

Definition: Simple Random Sample

A random sample is one in which each member of the population has an equal probability of being chosen. A simple random sample is one in which every member of the population and any group of members has an equal probability of being chosen.

Example \(\PageIndex{7}\)

If we could somehow identify all likely voters in the state, put each of their names on a piece of paper, toss the slips into a (very large) hat and draw 1000 slips out of the hat, we would have a simple random sample.

Solution

In practice, computers are better suited for this sort of endeavor than millions of slips of paper and extremely large headgear.

It is always possible, however, that even a random sample might end up not being totally representative of the population. If we repeatedly take samples of 1000 people from among the population of likely voters in the state, some of these samples might tend to have a slightly higher percentage of Democrats (or Republicans) than does the general population; some samples might include more older people and some samples might include more younger people; etc. In most cases, this sampling variability is not significant.

Definition: Sampling Variability

The natural variation of samples is called sampling variability.

This is unavoidable and expected in random sampling, and in most cases it is not an issue

To help account for variability, pollsters might instead use a stratified sample.

Definition: Stratified Sampling

In stratified sampling, a population is divided into a number of subgroups (or strata). Random samples are then taken from each subgroup with sample sizes proportional to the size of the subgroup in the population.

Example \(\PageIndex{8}\)

Suppose in a particular state that previous data indicated that the electorate was comprised of 39% Democrats, 37% Republicans, and 24% independents. In a sample of 1000 people, they would then expect to get about 390 Democrats, 370 Republicans, and 240 independents. To accomplish this, they could randomly select 390 people from among those voters known to be Democrats, 370 from those known to be Republicans, and 240 from those with no party affiliation.

Stratified sampling can also be used to select a sample with people in desired age groups, a specified mix ratio of males and females, etc. A variation on this technique is called quota sampling.

Definition: Quota Sampling

Quota sampling is a variation on stratified sampling, wherein samples are collected in each subgroup until the desired quota is met.

Example \(\PageIndex{9}\)

Suppose the pollsters call people at random, but once they have met their quota of 390 Democrats, they only gather people who do not identify themselves as a Democrat.

You may have had the experience of being called by a telephone pollster who started by asking you your age, income, etc. and then thanked you for your time and hung up before asking any "real" questions. Most likely, they already had contacted enough people in your demographic group and were looking for people who were older or younger, richer or poorer, etc. Quota sampling is usually a bit easier than stratified sampling but also does not ensure the same level of randomness.

Another sampling method is cluster sampling, in which the population is divided into groups, and one or more groups are randomly selected to be in the sample.

Definition: Cluster Sampling

In cluster sampling, the population is divided into subgroups (clusters), and a set of subgroups is selected to be in the sample.

Example \(\PageIndex{10}\)

If the college wanted to survey students, since students are already divided into classes, they could randomly select 10 classes and give the survey to all the students in those classes. This would be cluster sampling.

Other sampling methods include systematic sampling.

Definition: Systemic Sampling

In systematic sampling, every \(n^{th}\) member of the population is selected to be in the sample.

Example \(\PageIndex{11}\)

To select a sample using systematic sampling, a pollster calls every 100th name in the phone book.

Systematic sampling is not as random as a simple random sample (if your name is Albert Aardvark and your sister Alexis Aardvark is right after you in the phone book, there is no way you could both end up in the sample), but it can yield acceptable samples.

Perhaps the worst types of sampling methods are convenience samples and voluntary response samples.

Definition: Convenience Sampling and Voluntary Response Sampling

Convenience sampling is the method of choosing a sample based on what is convenient or easy.

Voluntary response sampling is allowing the sample to volunteer.

Example \(\PageIndex{12}\)

A pollster stands on a street corner and interviews the first 100 people who agree to speak to him. This is a convenience sample.

Example \(\PageIndex{13}\)

A website has a survey asking readers to give their opinion on a tax proposal. This is a self-selected sample, or voluntary response sample, in which respondents volunteer to participate.

Usually voluntary response samples are skewed towards people who have a particularly strong opinion about the subject of the survey or who just have way too much time on their hands and enjoy taking surveys.

Try it Now 4

In each case, indicate what sampling method was used:

1. Every 4th person in the class was selected
2. A sample was selected to contain 25 men and 35 women
3. Viewers of a new show are asked to vote on the show’s website
4. A website randomly selects 50 of their customers to send a satisfaction survey to
5. To survey voters in a town, a polling company randomly selects 10 city blocks and interviews everyone who lives on those blocks.

How to mess things up before you start

There are number of ways that a study can be ruined before you even start collecting data. The first we have already explored – sampling or selection bias, which is when the sample is not representative of the population. One example of this is voluntary response bias, which is bias introduced by collecting data from only those who volunteer to participate. This is not the only potential source of bias.

Note

Sampling bias – when the sample is not representative of the population

Voluntary response bias – the sampling bias that often occurs when the sample is volunteers. (This is also called “participation bias.”)

Self-interest study – bias that can occur when the researchers have an interest in the outcome

Response bias – when the responder gives inaccurate responses for any reason

Perceived lack of anonymity – when the responder fears giving an honest answer might negatively affect them

Loaded questions – when the question wording influences the responses

Non-response bias – when people refusing to participate in the study can influence the validity of the outcome

Example \(\PageIndex{14}\)

Consider a recent study which found that chewing gum may raise math grades in teenagers. This study was conducted by the Wrigley Science Institute, a branch of Wrigley, a chewing gum company. This is an example of a self-interest study; one in which the researches have a vested interest in the outcome of the study. While this does not necessarily ensure that the study was biased, it certainly suggests that we should subject the study to extra scrutiny.

Example \(\PageIndex{15}\)

A survey asks people “when was the last time you visited your doctor?” This might suffer from response bias, since many people might not remember exactly when they last saw a doctor and give inaccurate responses.

Sources of response bias may be innocent, such as bad memory, or as intentional as pressuring by the pollster. Consider, for example, how many voting initiative petitions people sign without even reading them.

Example \(\PageIndex{16}\)

A survey asks participants a question about their interactions with members of other races. Here, a perceived lack of anonymity could influence the outcome. The respondent might not want to be perceived as racist even if they are and give an untruthful answer.

Example \(\PageIndex{17}\)

An employer puts out a survey asking their employees if they have a drug abuse problem and need treatment help. Here, answering truthfully might have consequences; responses might not be accurate if the employees do not feel their responses are anonymous or fear retribution from their employer.

Example \(\PageIndex{18}\)

A survey asks “Do you support funding research of alternative energy sources to reduce our reliance on high-polluting fossil fuels?” This is an example of a loaded or leading question – questions whose wording leads the respondent towards an answer.

Loaded questions can occur intentionally by pollsters with an agenda or accidentally through poor question wording. Also a concern is question order, where the order of questions changes the results. A psychology researcher provides an example:

“My favorite finding is this: we did a study where we asked students, 'How satisfied are you with your life? How often do you have a date?' The two answers were not statistically related - you would conclude that there is no relationship between dating frequency and life satisfaction. But when we reversed the order and asked, 'How often do you have a date? How satisfied are you with your life?' the statistical relationship was a strong one. You would now conclude that there is nothing as important in a student's life as dating frequency.”

Example \(\PageIndex{19}\)

A telephone poll asks the question “Do you often have time to relax and read a book?”, and 50% of the people called refused to answer the survey. It is unlikely that the results will be representative of the entire population. This is an example of non-response bias, introduced by people refusing to participate in a study or dropping out of an experiment. When people refuse to participate, we can no longer be so certain that our sample is representative of the population.

Try it Now 5

In each situation, identify a potential source of bias:

1. A survey asks how many sexual partners a person has had in the last year.
2. A radio station asks readers to phone in their choice in a daily poll.
3. A substitute teacher wants to know how students in the class did on their last test. The teacher asks the 10 students sitting in the front row to state their latest test score.
4. High school students are asked if they have consumed alcohol in the last two weeks.
5. The Beef Council releases a study stating that consuming red meat poses little cardiovascular risk.
6. A poll asks “Do you support a new transportation tax, or would you prefer to see our public transportation system fall apart?”

Experiments

So far, we have primarily discussed observational studies – studies in which conclusions would be drawn from observations of a sample or the population. In some cases these observations might be unsolicited, such as studying the percentage of cars that turn right at a red light even when there is a “no turn on red” sign. In other cases the observations are solicited, like in a survey or a poll.

In contrast, it is common to use experiments when exploring how subjects react to an outside influence. In an experiment, some kind of treatment is applied to the subjects, and the results are measured and recorded.

Definition: Observational Studies and Experiments

An observational study is a study based on observations or measurements.

An experiment is a study in which the effects of a treatment are measured.

Here are some examples of experiments:

Example \(\PageIndex{20}\)

1. A pharmaceutical company tests a new medicine for treating Alzheimer’s disease by administering the drug to 50 elderly patients with recent diagnoses. The treatment here is the new drug.
2. A gym tests out a new weight loss program by enlisting 30 volunteers to try out the program. The treatment here is the new program.
3. You test a new kitchen cleaner by buying a bottle and cleaning your kitchen. The new cleaner is the treatment.
4. A psychology researcher explores the effect of music on temperament by measuring people’s temperament while listening to different types of music. The music is the treatment.

Try it Now 6

Is each scenario describing an observational study or an experiment?

1. The weights of 30 randomly selected people are measured
2. Subjects are asked to do 20 jumping jacks, and then their heart rates are measured
3. Twenty coffee drinkers and twenty tea drinkers are given a concentration test

When conducting experiments, it is essential to isolate the treatment being tested.

Example \(\PageIndex{21}\)

Suppose a middle school (junior high) finds that their students are not scoring well on the state’s standardized math test. They decide to run an experiment to see if an alternate curriculum would improve scores. To run the test, they hire a math specialist to come in and teach a class using the new curriculum. To their delight, they see an improvement in test scores.

The difficulty with this scenario is that it is not clear whether the curriculum is responsible for the improvement or the improvement is due to a math specialist teaching the class. This is called confounding – when it is not clear which factor or factors caused the observed effect. Confounding is the downfall of many experiments though sometimes it is hidden.

Definition: Confounding

Confounding occurs when there are two potential variables that could have caused the outcome and it is not possible to determine which actually caused the result.

Example \(\PageIndex{22}\)

A drug company study about a weight loss pill might report that people lost an average of 8 pounds while using their new drug. However, in the fine print you find a statement saying that participants were encouraged to also diet and exercise. It is not clear in this case whether the weight loss is due to the pill, to diet and exercise, or a combination of both. In this case confounding has occurred.

Example \(\PageIndex{23}\)

Researchers conduct an experiment to determine whether students will perform better on an arithmetic test if they listen to music during the test. They first give the student a test without music and then give a similar test while the student listens to music. In this case, the student might perform better on the second test, regardless of the music, simply because it was the second test and they were warmed up.

There are a number of measures that can be introduced to help reduce the likelihood of confounding. The primary measure is to use a control group.

Definition: Control Group

When using a control group, the participants are divided into two or more groups, typically a control group and a treatment group. The treatment group receives the treatment being tested; the control group does not receive the treatment.

Ideally, the groups are otherwise as similar as possible, isolating the treatment as the only potential source of difference between the groups. For this reason, the method of dividing groups is important. Some researchers attempt to ensure that the groups have similar characteristics (same number of females, same number of people over 50, etc.), but it is nearly impossible to control for every characteristic. Because of this, random assignment is very commonly used.

Example \(\PageIndex{24}\)

To determine if a two-day prep course would help high school students improve their scores on the SAT test, a group of students was randomly divided into two subgroups. The first group, the treatment group, was given a two-day prep course. The second group, the control group, was not given the prep course. Afterwards, both groups were given the SAT.

Example \(\PageIndex{25}\)

A company testing a new plant food grows two crops of plants in adjacent fields, the treatment group receiving the new plant food and the control group not. The crop yield would then be compared. By growing them at the same time in adjacent fields, they are controlling for weather and other confounding factors.

Sometimes not giving the control group anything does not completely control for confounding variables. For example, suppose a medicine study is testing a new headache pill by giving the treatment group the pill and the control group nothing. If the treatment group showed improvement, we would not know whether it was due to the medicine in the pill or a response to have taken any pill. This is called a placebo effect.

Definition: Placebo Effect

The placebo effect refers to the effectiveness of a treatment influenced by the patient’s perception of how effective they think the treatment will be, so a result might be seen even if the treatment is ineffectual.

Example \(\PageIndex{26}\)

A study found that when doing painful dental tooth extractions, patients who were told they were receiving a strong painkiller while actually receiving a saltwater injection found as much pain relief as patients receiving a dose of morphine.

To control for the placebo effect, a placebo, or dummy treatment, is often given to the control group. This way, both groups are truly identical except for the specific treatment given.

Definition: Placebo and Placebo controlled Experiments

A placebo is a dummy treatment given to control for the placebo effect.

An experiment that gives the control group a placebo is called a placebo controlled experiment.

Example \(\PageIndex{27}\)

1. In a study for a new medicine that is dispensed in a pill form, a sugar pill could be used as a placebo.
2. In a study on the effect of alcohol on memory, a non-alcoholic beer might be given to the control group as a placebo.
3. In a study of a frozen meal diet plan, the treatment group would receive the diet food, and the control could be given standard frozen meals stripped of their original packaging.

In some cases, it is more appropriate to compare to a conventional treatment than a placebo. For example, in a cancer research study, it would not be ethical to deny any treatment to the control group or to give a placebo treatment. In this case, the currently acceptable medicine would be given to the control group, sometimes called a comparison group in this case. In our SAT test example, the non-treatment group would most likely be encouraged to study on their own, rather than be asked to not study at all, to provide a meaningful comparison.

When using a placebo, it would defeat the purpose if the participant knew they were receiving the placebo.

Definition: Blind studies

A blind study is one in which the participant does not know whether or not they are receiving the treatment or a placebo.

A double-blind study is one in which those interacting with the participants don’t know who is in the treatment group and who is in the group receiving a placebo.

Example \(\PageIndex{28}\)

In a study about anti-depression medicine, you would not want the psychological evaluator to know whether the patient is in the treatment or control group either, as it might influence their evaluation, so the experiment should be conducted as a double-blind study.

It should be noted that not every experiment needs a control group.

Example \(\PageIndex{29}\)

If a researcher is testing whether a new fabric can withstand fire, she simply needs to torch multiple samples of the fabric – there is no need for a control group.

Try it Now 7

To test a new lie detector, two groups of subjects are given the new test. One group is asked to answer all the questions truthfully, and the second group is asked to lie on one set of questions. The person administering the lie detector test does not know what group each subject is in.

Does this experiment have a control group? Is it blind, double-blind, or neither?

Reference

1. References (10)
2. www.whitehouse.gov/sites/defa...s/hist07z1.xls

Contributors and Attributions

• Saburo Matsumoto
  CC-BY-4.0