Chapter 1: Introduction to Statistics

Provide examples of nonequivalent groups study.

(i) men & women: the males automatically go in the boy group and the females go in the girl group. (ii) comparing 8-year-old children and 10-year-old children (iii) comparing people with an eating disorder and those with no disorder.

Researchers typically use 3 basic techniques to control other variables. What are they?

(i) random assignment (ii) matching (iii) holding them constant

Whenever a research study allows more than one explanation for the results, the study is said to be what? And why?

*confounded* because it is impossible to reach an unambiguous conclusion.

What are the 2 other factors that apply to continuous variables?

1. When measuring a continuous variable, it should be very rare to obtain identical measurements for two different individuals. 2. When measuring a continuous variable, each measurement category is actually an interval that must be defined by boundaries.

*1.1 Statistics, Science, and Observations*

1.1 Statistics, Science, and Observations

*1.2 Populations and Samples*

1.2 Populations and Samples

In inferential statistics, what is selected to represent the population? And by analyzing the results from the sample, what do we hope to answer?

A *sample* is selected to represent the population. By analyzing the results from the sample, we hope to answer *general questions about the population*.

What is a control condition?

A condition in which the participants do not receive the experimental treatment. Instead, they either receive no treatment or they receive a neutral, placebo treatment.

What is a nonequivalent groups study?

A research study in which the different groups of participants are formed under circumstances that do not permit the researcher to control the assignment of individuals to groups and the groups of participants are, therefore, considered nonequivalent.

What is a sample intended to be representative of? And how should it be identified?

A sample is intended to be representative of its population, and a sample should always be identified in terms of the population from which it was selected.

parameter

A value, usually a numerical value, that describes a population. It is usually derived from measurements of the individuals in the population. i.e.-The average score for the population.

statistic

A value, usually a numerical value, that describes a sample. It is usually derived from measurements of the individuals in the sample. i.e.-The average score for a sample.

Again, what does the experimental study evaluate?

An experimental study evaluates the relationship between two variables by manipulating one variable (the independent variable) and measuring one variable (the dependent variable). Note that in an experiment only one variable is actually measured.

ratio scale

An interval scale with the additional feature of an absolute zero point. With *this*, ratios of numbers do reflect ratios of magnitude.

What is another technique to summarize a set of scores?

Another common technique is to summarize a set of scores by *computing an average*.

data (plural)

Are measurements or observations.

lower real limit

At the bottom of the interval.

upper real limit

At the top of the interval.

Why are the examples just provided are not considered to be a true experiment?

Because it is impossible to use techniques like random assignment to control participant variables and ensure equivalent groups, this type of research is not a true experiment.

Is a pre-post study considered to be an experiment? If not, why?

Because the researcher cannot control the passage of time or other variables related to time, this study is not a true experiment.

ordinal scale

Consists of a set categories that are organized in an ordered sequence. Measurements on an ordinal scale rank observations in terms of size or magnitude.

What is the purpose of descriptive statistics? & What is the goal of inferential statistics?

First, descriptive statistics are used to simplify the pages of data. The goal of inferential statistics is to help researchers decide between the (two or more) interpretations that is produced from the simplified data.

What two elements are necessary for a research study to be an experiment?

First, the researcher must manipulate one of the two variables being studied. Second, all other variables that might influence the results must be controlled.

What is an example of the technique, holding them constant?

For example, if an experiment uses only 10-year-old children as participants (holding age constant), then the researcher can be certain that one group is not noticeably older than another.

Do you understand the terminology in nonexperimental research?

If you think you do then discuss it with the person next to you without using references and attempt not to use fluffy, non-descriptive language.

How is the experimental study different from a correlational study?

In an experiment only one variable is actually measured. In a correlational study, both variables are measured and the data consist of two separate scores for each individual.

In an experiment, what is created by the manipulation of the independent variable? And what is the dependent variable?

In an experiment, the *groups* are created by manipulation of the independent variable, and the participants' scores are the dependent variable. The same terminology is often used to identify the two variables in nonexperimental studies. That is, the variable that is used to create groups is the independent variable and the scores are the dependent variable.

In *behavioral research*, what does the independent variable usually consist of?

In behavioral research, the independent variable usually consists of the two (or more) treatment conditions to which subjects are exposed.

What must a "real" experiment include?

In particular, a real experiment must include *manipulation of an independent variable* and *rigorous control of other, extraneous variables*. As a result, there are a number of other research designs that compare groups of scores but are not true experiments. This type of research study is classified as nonexperimental.

What is the experimental method?

In the experimental method, one variable is manipulated while another variable is observed and measured. To establish a cause-and-effect relationship between the two variables, an experiment attempts to control all other variables to prevent them from influencing the results.

experimental condition

Individuals in *this* do receive the experimental treatment.

What are individuals in the experimental condition that do receive the experimental treatment often called?

Individuals in the experimental condition do receive the experimental treatment and are often called the *experimental group*.

How can the independent variable be identified?

It can be identified as the treatment conditions to which participants are assigned.

Greek letter sigma, or Σ

It is used to stand for summation.

Some research studies are conducted simply to describe *individual variables* as they exist naturally. When the results consist of non-numerical scores, what are they typically described by?

Non-numerical scores are typically described by *computing the proportion or percentage in each category*.

What does an operational definition do?

Note that an operational definition has two components: First, it describes a set of operations for measuring a construct. Second, it defines the construct in terms of the resulting measurements. In case you forgot here is the definition: An operational definition identifies a measurement procedure (a set of operations) for measuring an external behavior and uses the resulting measurements as a definition and a measurement of an internal construct.

What do the terms continuous and discrete apply to? And what are they not applied to?

Note that the terms continuous and discrete apply to the variables that are being measured and not to the scores that are obtained from the measurement.

How are the scores often organized?

Often the scores are organized in a table or a graph so that it is possible to see the entire set of scores.

What is one problem with using samples?

One problem with using samples is that a sample provides only *limited information* about the population.

There are two general categories of variables that researchers must consider: what are they?

Participant Variables & Environmental Variables

What is a pre-post study?

Quasi-experimental and nonexperimental designs consisting of a series of observations made over time. The goal is to evaluate the effect of an intervening treatment or event by comparing observations made before versus after the treatment.

What does random assignment mean?

Random assignment means that each participant has an equal chance of being assigned to each of the treatment conditions.

What are real limits?

Real limits are the boundaries of intervals for scores that are represented on a continuous number line. The real limit separating two adjacent scores is located exactly halfway between the scores. Each score has two real limits.

What did the research start with?

Remember that the research started with a general question about the population.

How does research in the behavioral sciences typically begin?

Research in the behavioral sciences typically begins with a general question about a specific group (or groups) of individuals.

What do statistical procedures help to ensure?

Statistical procedures help to ensure that the information or observations are presented & interpreted in an accurate and informative way.

What does statistics provide to researchers?

Statistics provides researchers with a set of standardized techniques that are recognized and understood throughout the scientific community. Thus, the statistical methods used by one researcher are familiar to other researchers, who can accurately interpret the statistical analyses with a full understanding of how the analysis was done and what the results signify.

Statistics serves how many general purposes?

Statistics serve *2* general purposes

real limits

The boundaries of intervals for scores that are represented on a continuous number line. The *this* separating two adjacent scores is located exactly halfway between the scores. Each score has two *this*.

What is the complete set of scores called?

The complete set of scores is called the *data set*, or simply the *data*.

In an experiment, what is it called when participants do not receive any treatment?

The control condition

What is the dependent variable?

The dependent variable is the variable that is observed to assess the effect of the treatment.

population

The entire set of the individuals of interest for a particular research question.

What is another name for the experimental method?

The experimental research strategy.

What two general categories can statistical procedures be classified in?

The first category, *descriptive statistics*, consists of statistical procedures that are used to simplify and summarize data. The second general category of statistical techniques is called *inferential statistics*. Inferential statistics are methods that use sample data to make general statements about a population.

From the control condition the scores are compared to the participants who do receive the treatment. What is the goal of this type of study (experimental)? What is the treatment condition called?

The goal is to demonstrate that the treatment has an effect by showing that the scores in the treatment condition are substantially different from the scores in the no-treatment condition. The treatment condition is called the *experimental condition*.

When a researcher finishes examining the sample, what is the goal?

The goal is to generalize the results back to the entire population.

What is the goal of random assignment?

The goal of random assignment is to distribute the participant characteristics evenly between the two groups so that neither group is noticeably smarter (or older, or faster) than the other.

What are the two variables that are studied by the experimental method?

The independent variable & the dependent variable.

What does the independent variable consist of?

The independent variable consists of the antecedent conditions that are manipulated prior to observing the dependent variable. antecedent (def): preceding in time or order; previous or preexisting

Stephens, Atkins, and Kingston (2009) conducted an experiment in which participants were able to tolerate more pain when they shouted their favorite swear words over and over than when they shouted neutral words. Identify the independent and dependent variables for this study.

The independent variable is the type of word being shouted and the dependent variable is the amount of pain tolerated by each participant.

What is the independent variable?

The independent variable is the variable that is manipulated by the researcher.

For an experiment with an experimental group and a control group, what is the independent variable? *Hint*: treatment

The independent variable is treatment versus no treatment.

control group

The individuals in the control condition are often called *this*.

What are the individuals in the control condition often called?

The individuals in the control condition are often called the control group.

What does the matching technique ensure?

The matching technique ensures equivalent groups or equivalent environments.

What is a sampling error?

The naturally occurring discrepancy, or error, that exists between a sample statistic and the corresponding population parameter.

Whom should identify the population?

The population being studied should always be identified by the researcher & need NOT consist of people.

What is the purpose of a control condition?

The purpose of a control condition is to provide a baseline for comparison with the experimental condition.

What is control?

The researcher must exercise control over the research situation to ensure that other, extraneous variables do not influence the relationship being examined.

Is the same terminology often used to identify the two variables in nonexperimental studies? If so, can you elaborate?

The same terminology is often used to identify the two variables in nonexperimental studies. That is, the variable that is used to create groups is the independent variable and the scores are the dependent variable.

statistics

The term refers to a set of mathematical procedures for organizing, summarizing, and interpreting information.

What is the basic concept of sampling error?

The the basic concept of sampling error: sample statistics vary from one sample to another and typically are different from the corresponding population parameters.

What are the two characteristics that differentiate experiments from other types of research studies?

The two characteristics are *manipulation* and *control*.

The real limit separating two adjacent scores is located exactly halfway between the scores. Each score has two real limits. What are they?

The upper real limit is at the top of the interval, and the lower real limit is at the bottom.

What is the variable that is manipulated by the experimenter called?

The variable that is manipulated by the experimenter is called the *independent variable*.

What is the variable that is observed and measured to obtain scores within each condition?

The variable that is observed and measured to obtain scores within each condition is the *dependent variable*.

What are environmental variables?

These are characteristics of the environment such as lighting, time of day, and weather conditions.

What are participant variables?

These are characteristics such as age, gender, and intelligence that vary from one individual to another.

A research study comparing alcohol use for college students in the United States and Canada reports that more Canadian students drink but American students drink more (Kuo, Adlaf, Lee, Gliksman, Demers, and Wechsler, 2002). Is this study an example of an experiment? Explain why or why not.

This study is nonexperimental. The researcher is simply observing, not manipulating, two nonequivalent groups of participants.

True or False: Something must have at least two different values before you can say that it is "variable."

True

What are the *two things* researchers are typically interested in?

Typically, researchers are interested in *specific characteristics* of the individuals in the population (and in the sample), or they are interested in *outside factors* that may influence the individuals.

What do researchers use as the basis for drawing conclusions about population parameters?

Typically, researchers use *sample statistics* as the basis for drawing conclusions about population parameters.

Researchers use sample statistics as the basis for drawing conclusions about what?

Typically, researchers use sample statistics as the basis for drawing conclusions about *population parameters*.

Where does the research process begin?

Typically, the research process begins with a *question* about a population parameter.

What are examples of constructs?

Variables like intelligence, anxiety, and hunger are called constructs, and because they are intangible and cannot be directly observed, they are often called hypothetical constructs.

Do nonexperimental studies produce the same kind of data as true experiments? What should you notice?

Yes, although the nonexperimental studies are not true experiments, you should notice that they produce the same kind of data that are found in an experiment. One variable is used to create groups, and a second variable is measured to obtain scores within each group.

Are correlational studies examples of nonexperimental research?

Yes, they are.

What should you *realize* about the tendency for people to use the term experiment to refer to any kind of research study in informal conversation?

You should realize that the term only applies to studies that satisfy the specific requirements.

Fill in the blank: Random assignment can also be used to control ____________________ variables.

environmental

What is another name for *constructs*?

hypothetical constructs

The measurement obtained for each individual, what is it called?

It is called a *datum* or, more commonly, a *score* or *raw score*.

What does the average provide?

It provides a single descriptive value for the entire set.

How is statistics often defined?

It's often defined as facts and figures, such as average income, crime rate, birth rate, baseball batting averages, and so on. These statistics are usually informative and time saving because they condense large quantities of information into a few simple figures.

Research is often intended to examine relationships between what?

Most research is intended to examine relationships between *two or more variables*.

Do you expect the statistics from a sample to be perfect? If not, why?

No, I do not expect the statistics from a sample to be perfect. There is always some margin of error when sample statistics are used to represent population parameters.

Are researchers able to measure everyone in the population? If not, why?

No, it usually is not possible to measure everyone in the population because populations are typically very large.

Populations can vary in size depending on what?

Populations can obviously vary in size from extremely large to very small, depending on *how the researcher defines the population*.

What is the 2nd method for examining the relationship between two variables? And what comparison does it involve?

The 2nd method for examining the relationship between two variables is the *experimental and nonexperimental methods*. It compares *two or more groups of scores.*

What is the goal of an experimental study?

The goal of an experimental study is to demonstrate a cause-and-effect relationship between two variables? Besides demonstrating the C&E relationship an experiment attempts to show that changing the value of one variable causes changes to occur in the second variable.

What does a population consist of?

The population need not consist of people—it could be a population of rats, corporations, parts produced in a factory, or anything else a researcher wants to study.

What is manipulation?

The researcher manipulates one variable by changing its value from one level to another. A second variable is observed (measured) to determine whether the manipulation causes changes to occur.

What are the limitations of the correlational method?

The results from a correlational study can demonstrate the existence of a relationship between two variables, but they *do not provide an explanation for the relationship*. In particular, a correlational study *cannot demonstrate a cause-and-effect relationship*.

Every population parameter has a corresponding what?

sample statistic

What is another name for statistics?

statistical procedures

order of mathematical operations

1. Any calculation contained within parentheses is done first. 2. Squaring (or raising to other exponents) is done second. 3. Multiplying and/or dividing is done third. A series of multiplication and/or division operations should be done in order from left to right. 4. Summation using the Σ notation is done next. 5. Finally, any other addition and/or subtraction is done.

What are the 2 general purposes statistics serves?

1. Statistics are used to organize and summarize the information so that the researcher can see what happened in the research study and can communicate the results to others. 2. Statistics help the researcher to answer the questions that initiated the research by determining exactly what general conclusions are justified based on the specific results that were obtained.

Although samples are generally representative of their populations, what are they NOT expected to do?

A sample is not expected to give a perfectly accurate picture of the whole population. Thus, there typically is some *discrepancy* between a sample statistic and the corresponding population parameter.

sample

A set of individuals selected from a population, usually intended to represent the population in a research study.

What is a datum (singular)?

A single measurement or observation.

datum, score, or raw score

A single measurement or observation.

nominal scale

Consists of a set of categories that have different names. Measurements on *this* label and categorize observations, but do not make any quantitative distinctions between observations.

interval scale

Consists of ordered categories that are all intervals of exactly the same size. Equal differences between numbers on the scale reflect equal differences in magnitude. However, the zero point on on *this* is arbitrary and does not indicate a zero amount of the variable being measured.

What is descriptive statistics?

Descriptive statistics are statistical procedures used to summarize, organize, and simplify data. Descriptive statistics are techniques that take raw scores and organize or summarize them in a form that is more manageable.

continuous variable

For *this*, there are an infinite number of possible values that fall between any two observed values. A *this* is divisible into an infinite number of fractional parts.

Which example is a numerical score & a non-numerical score? •A recent newspaper article reported that 61% of the adults in the United States drink alcohol. •The number of hours spent studying each day.

If you don't know, look at previous flash card.

quasi-independent variable

In a nonexperimental study, the "independent" variable that is used to create the different groups of scores is often called *this*.

When describing data, how do you distinguish between a sample & a population? *Hint*: What must you identify?

In order to distinguish a sample from a population you must identify a characteristic. Depending on what type of characteristic it is, a parameter or a statistic, you can then distinguish between a sample & population.

What is the correlational method?

In the correlational method, two different variables are observed to determine whether there is a relationship between them.

How is the relationship between variables examined (in the experimental & nonexperimental methods)?

In this situation, the relationship between variables is examined by using one of the variables to *define* the groups, and then *measuring* the second variable to obtain scores for each group.

control condition

Individuals in *this* do NOT receive the experimental treatment. Instead, they either receive no treatment or they receive a neutral, placebo treatment. The purpose of a control condition is to provide a baseline for comparison with the experimental condition.

experimental group

Individuals in the experimental condition do receive the experimental treatment and are often called the *this*.

What is inferential statistics?

Inferential statistics consist of techniques that allow us to study samples and then make generalizations about the populations from which they were selected.

constructs (hypothetical constructs)

Internal attributes or characteristics that cannot be directly observed but are useful for describing and explaining behavior.

Where does the actual data come from? & What are the data used for?

It comes from a sample and are used to compute sample statistics.

operational definition

*This* identifies a measurement procedure (a set of operations) for measuring an external behavior and uses the resulting measurements as a definition and a measurement of an internal construct.

*Fill in the blank*: A researcher is interested in the texting habits of high school students in the United States. If the researcher measures the number of text messages that each individual sends each day and calculates the average number for the entire group of high school students, the average number would be an example of a _____________.

*parameter*

*Fill in the blank*: A researcher is interested in how watching a reality television show featuring fashion models influences the eating behavior of 13-year-old girls. A group of 30 13-year-old girls is selected to participate in a research study. The group of 30 13-year-old girls is an example of a ___________.

*sample*

*Fill in the blank*: A researcher is interested in how watching a reality television show featuring fashion models influences the eating behavior of 13-year-old girls. In the same study, the amount of food eaten in one day is measured for each girl and the researcher computes the average score for the 30 13-year-old girls. The average score is an example of a ____________.

*statistic*

discrete variable

A *this* consists of separate, indivisible categories. No values can exist between two neighboring categories.

variable

A characteristic or condition that changes or has different values for different individuals.

data set

A collection of measurements or observations.

What is a datum commonly called? *Hint*: There's two different names.

A datum is commonly called a *score* or *raw score*.

Briefly define the concept of sampling error.

Sampling error is the error, or discrepancy, between the value obtained for a sample statistic and the value for the corresponding population parameter.

Statistical techniques are classified into two general categories. What are the two categories called, and what is the general purpose for the techniques in each category?

The two categories are descriptive statistics and inferential statistics. Descriptive techniques are intended to organize, simplify, and summarize data. Inferential techniques use sample data to reach general conclusions about populations.

independent variable

The variable that is manipulated by the researcher. In behavioral research, *this* usually consists of the two (or more) treatment conditions to which subjects are exposed. *This* consists of the antecedent conditions that are manipulated prior to observing the dependent variable

dependent variable

The variable that is observed to assess the effect of the treatment.

What is the difference between the *margin of error* & the *sampling error*?

There is zero difference. The margin of error *is* the sampling error.

The difference between two groups is probably the result of random factors such as chance. The unpredictable, unsystematic differences that exist from one sample to another are an example of what?

They are an example of sampling error.

When researchers are *making observations*, to establish the existence of a relationship between two variables, they are in reality taking what?

They are taking measurements.

Some research studies are conducted simply to describe *individual variables* as they exist naturally. When the results consist of numerical scores, what are they typically described by?

They are typically described by statistical techniques

What is this discrepancy called? & What does it create?

This discrepancy is called *sampling error*, and it creates *the fundamental problem that inferential statistics must always address*.

How does the researcher answer the question?

To answer the question, a researcher studies a sample and then generalizes the results from the sample to the population.

What must researchers use to demonstrate a cause-and-effect relationship between two variables?

To demonstrate a cause-and-effect relationship between two variables, researchers must use the *experimental method*.

In order to demonstrate changes in variables, what is necessary?

To demonstrate changes in variables, it is necessary to make measurements of the variables being examined.