+++++Testing over 1,000 kids from a diverse variety of countries and religious backgrounds on a sharing task, the study authors found a noticeable generosity gap between those religious and nonreligious, a gap that only increased the more religious their households were. They also found that religious kids were more likely to be judgemental and to advocate harsher punishments for being wronged by others.
+++++“Some past research had demonstrated that religious people aren’t more likely to do good than their nonreligious counterparts,” said lead author Jean Decety of the University of Chicago in a statement. “Our study goes beyond that by showing that religious people are less generous, and not only adults but children too.” …
+++++Decety and his colleagues hope to continue testing their hypothesis, with efforts to test children ages 4 to 8 in 14 different countries underway.

+++++Most research is intended to examine relationships between two or more variables. For example, is there a relationship between the amount of violence that children see on television and the amount of aggressive behavior they display? To establish the existence of a relationship, researchers must make observations — that is, measurements of the two variables.
+++++The resulting measurements can be classified into two distinct data structures:

I. Measuring two variables for each individual: The correlational method

+++++One method for examining the relationship between variables is to simply measure the two variables for each individual. For example, research has demonstrated a relationship between sleep habits and academic performance for college students. The researchers used a survey to measure wake-up time and school records to measure academic performance for each student.
+++++The researchers then look for consistent patterns in the data to provide evidence for a relationship between variables. For example, as wake-up time changes from one student to another, is there also a tendency for academic performance to change?

Limitations: 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.

II. Comparing two (or more) groups of scores: Experimental and nonexperimental methods

+++++The second method for examining the relationship between two variables involves the comparison of two or more groups of scores. 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.

+++++A. The Experimental Method.

+++++The goal of an experimental study is to demonstrate a cause-and-effect relationship between two variables, by trying to show that changing the value of one variable causes changes to occur in the second variable. The experimental method has two unique characteristics:
+++++1. 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.
+++++2. Control. The researcher must exercise control over the research situation to ensure that other, extraneous variables do not influence the relationship being examined.
+++++There are two general categories of variables that researchers must consider:
+++++1. Participant Variables. These are characteristics such as age, gender, and intelligence that vary from one individual to another.
+++++2. Environmental Variables. These are characteristics of the environment such as lighting, time of day, and weather conditions.
+++++Researchers typically use three basic techniques to control other variables. First, the researcher could use random assignment, which means that each participant has an equal chance of being assigned to each of the treatment conditions. 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. Random assignment can also be used to control environmental variables. For example, participants could be assigned randomly for testing either in the morning or in the afternoon. Second, the researcher can use matching to ensure equivalent groups or equivalent environments. For example, the researcher could match groups by ensuring that every group has exactly 60% females and 40% males. Finally, the researcher can control variables by 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.
+++++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.
+++++An experimental study evaluates the relationship between two variables by manipulating one variable (the independent variable) and measuring one variable (the dependent variable). In an experiment only one variable is actually measured. This is different from a correlational study, in which both variables are measured and the data consist of two separate scores for each individual.
+++++Whenever a research study allows more than one explanation for the results, the study is said to be confounded because it is impossible to reach an unambiguous conclusion.

Control Groups in an Experiment. Often an experiment will include a control group in which the participants do not receive any treatment. The scores from these individuals are then compared with scores from participants who do receive the treatment, the experimental group. The goal is to demonstrate that the treatment has an effect by showing that the scores in the treatment group are substantially different from the scores in the control group.

+++++B. Nonexperimental methods: nonequivalent groups and pre-post studies

+++++In informal conversation, there is a tendency for people to use the term experiment to refer to any kind of research study. However, that the term only applies to studies that satisfy the specific requirements outlined earlier. 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.

+++++The top part of Figure 1.7 shows an example of a nonequivalent groups study comparing boys and girls. Notice that this study involves comparing two groups of scores (like an experiment). However, the researcher has no ability to control the assignment of participants to groups — the males automatically go in the boy group and the females go in the girl group. Because this type of research compares preexisting groups, the researcher cannot control the assignment of participants to groups and cannot ensure equivalent groups. Other examples of nonequivalent group studies include comparing 8-year-old children and 10-year-old children or comparing people with an eating disorder and those with no disorder. 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.
+++++The bottom part of Figure 1.7 shows an example of a pre–post study comparing depression scores before therapy and after therapy. The two groups of scores are obtained by measuring the same variable (depression) twice for each participant; once before therapy and again after therapy. In a pre–post study, however, the researcher has no control over the passage of time. The “before” scores are always measured earlier than the “after” scores. Although a difference between the two groups of scores may be caused by the treatment, it is always possible that the scores simply change as time goes by. For example, the depression scores may decrease over time in the same way that the symptoms of a cold disappear over time. In a pre–post study, the researcher also has no control over other variables that change with time. For example, the weather could change from dark and gloomy before therapy to bright and sunny after therapy. In this case, the depression scores could improve because of the weather and not because of the therapy. Because the researcher cannot control the passage of time or other variables related to time, this study is not a true experiment.

Terminology in nonexperimental research Although the two research studies shown in Figure 1.7 are not true experiments, they produce the same kind of data that are found in an experiment. In each case, one variable is used to create groups, and a second variable is measured to obtain scores within each group. 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. For example, the top part of Figure 1.7, gender (boy/girl), is the independent variable and the verbal test scores are the dependent variable. However, you should realize that gender (boy/girl) is not a true independent variable because it is not manipulated. For this reason, the “independent variable” in a nonexperimental study is often called a quasi-independent variable. -ESBS

variables

constructs and operational definitions

+++++Some variables, such as height, weight, and eye color are well-defined, concrete entities that can be observed and measured directly. On the other hand, many variables studied by behavioral scientists are internal characteristics that cannot be observed or measured directly. However, we all assume that these variables exist and we use them to help describe and explain behavior. For example, we say that a student does well in school because he or she is intelligent. Or we say that someone is anxious in social situations, or that someone seems to be hungry. 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.
+++++Although constructs such as intelligence are internal characteristics that cannot be directly observed, it is possible to observe and measure behaviors that are representative of the construct. For example, we cannot “see” intelligence but we can see examples of intelligent behavior. The external behaviors can then be used to create an operational definition for the construct. An operational definition measures and defines a construct in terms of external behaviors. For example, we can measure performance on an IQ test and then use the test scores as a definition of intelligence. Or hunger can be measured and defined by the number of hours since last eating.

types of variables and scales

+++++A discrete variable consists of separate, indivisible categories. No values can exist between two neighboring categories. e.g. integers, male/female, occupation.
+++++For a continuous variable, there are an infinite number of possible values that fall between any two observed values. A continuous variable is divisible into an infinite number of fractional parts.
+++++A nominal scale consists of a set of categories that have different names. Measurements on a nominal scale label and categorize observations, but do not make any quantitative distinctions between observations.
+++++An ordinal scale consists of a set of categories that are organized in an ordered sequence. Measurements on an ordinal scale rank observations in terms of size or magnitude.
+++++An 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 an interval scale is arbitrary and does not indicate a zero amount of the variable being measured.
+++++A ratio scale is an interval scale with the additional feature of an absolute zero point. With a ratio scale, ratios of numbers do reflect ratios of magnitude. – ESBS

A population is the entire set of the individuals of interest for a particular research question.
A sample is a set of individuals selected from a population, usually intended to represent the population in a research study.
A variable is a characteristic or condition that changes or has different values for different individuals.
To demonstrate changes in variables, it is necessary to make measurements of the variables being examined. The measurement obtained for each individual is called a datum or, more commonly, a score or raw score. The complete set of scores is called the data set, or simply the data.
When describing data, it is necessary to distinguish whether the data come from a population or a sample. A characteristic that describes a population — for example, the average score for the population — is called a parameter. A characteristic that describes a sample is called a statistic. – ESBS

Variance has several different symbols when it’s calculated from a sample, including , , and . and come from the words standard deviation squared. MS comes from the words mean square. When variance is calculated from a population, it typically has just one symbol, (pronounced “sigma squared”), and is a parameter. (Remember, Latin letters are used for statistics, which are calculated from samples, and Greek letters are used with parameters, which are calculated from or hypothesized for populations.) – SBS

+++++Bessel’s correction…is the use of instead of in the formula for the sample variance and sample standard deviation, where is the number of observations in a sample. This corrects the bias in the estimation of the population variance, and some (but not all) of the bias in the estimation of the population standard deviation, but often increases the mean squared error in these estimations. …This correction is so common that the term “sample variance” and “sample standard deviation” are frequently used to mean the corrected estimators (unbiased sample variation, less biased sample standard deviation), using . However caution is needed: some calculators and software packages may provide for both or only the more unusual formulation. – wikipedia

Over the years there has come to be a slow movement away from that position and toward the use of the un-squared . That is the position that I think is the better one, but, as you will see when we come to the analysis of variance, I am not always consistent myself. For a more extensive discussion of this issue, see Grissom and Kim (2012, p. 140). – FSBS p243

Matthews (2000)…compiled data from 17 countries on the number of breeding pairs of storks and the number of live human births to explore the notion that storks deliver babies. He found a positive correlation, = .62

+++++The advantage of a correlation coefficient is that it is a single number that allows you to quickly characterize the degree to which two variables are related. When you can say that a specific test of manual skills is correlated .85 with performance on the job, you are saying something important. In that example I imagine that I would be saying something much less useful if I said that an increase of 10 points on the test is associated with a 5-point difference in job performance. On the other hand, when you are interested in speaking about the magnitude of change, a regression coefficient is useful. If I could tell you that making birth control information available to an additional 10% of a population of women at high risk of producing a child that will not live for a year will decrease infant mortality by 9.7 percentage points, I am telling you something that is probably far more useful than telling you that the correlation between contraception and infant mortality in sub-Saharan Africa is .44. Both statistics have their uses, and you can choose the one that best serves your needs. – FSBS p254-5

+++++We use a distribution instead of a distribution when sampling requires us to estimate the population standard deviation from the sample standard deviation, [and] when we don’t know the population standard deviation or when we compare two samples to each other. …There are many distributions — one for each possible sample size. As the sample size gets smaller, we become less certain about what the population distribution really looks like, and the distributions become flatter and more spread out. However, as the sample size gets larger, the distributions begin to merge with the distribution because we gain confidence as more and more participants are added to our study.

Estimating Population Standard Deviation from a Sample

+++++Before we can conduct a single-sample test, we have to estimate the standard deviation. To do this, we use the standard deviation of the sample data to estimate the standard deviation of the entire population. Estimating the standard deviation is the only practical difference between conducting a test with the distribution and conducting a test with a distribution. Here is the standard deviation formula that we have used up until now with a sample:
+++++We need to make a correction to this formula to account for the fact that there is likely to be some level of error when we’re estimating the population standard deviation from a sample. Specifically, any given sample is likely to have somewhat less spread than does the entire population. One tiny alteration of this formula leads to the slightly larger standard deviation of the population that we estimate from the standard deviation of the sample. Instead of dividing by , we divide by .