Behavioral Statistics

For each problem, Download the data from the Problem Description (see below).  Calculate all appropriate descriptive statistics and test the hypothesis with an appropriate alpha (α) level.  Also draw a bar or line graph.  Don't forget an APA-style write up of your results. APA-style examples are located here.

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Class Interactive Portion

Printouts of Interactive Problems.

As you read the following story, identify the dependent variable and the two independent variables (factors).
 

This story establishes the conditions for a 2 x 2 factorial ANOVA. One of the factors is area of interest; the two levels are natural science and humanities. The other factor is previous experience in college; the two levels are none and some. The dependent variable is hours of study for a final examination.
 

Here's a question for you. Read the question, take 10 seconds, and compose an answer. Who is taller, boys or girls? A halfway good answer is “It depends.” A completely good answer gives the other variable that the answer depends on; for example, “It depends on the age of the boys and girls.”

Factorial ANOVA designs are often used when a researcher thinks that the answer to a question about the effect of variable A is “It depends on variable B.” As you may have already anticipated, the way to express this idea statistically is to talk about significant interactions.

The analysis that follows is for a 2 X 3 factorial design. The factor with two levels is gender: males and females. The second factor is age: 6, 12, and 18 years old. The dependent variable is height in inches.

I've constructed data that mirror fairly closely the actual situation for Americans (Berk, 1998).
 

For a bit of help on the results, click here.

The conditions that make for happy people have been researched by psychologists for a long time. The data that follow are based on a review of the literature by Diener and colleagues (1999). Participants were asked their marital status and how often they engaged in religious behavior. They also indicated how happy they were on a scale of 1 to 10. Analyze the data with a factorial ANOVA and, if appropriate, Tukey HSD tests.
 

A popularly held belief about university professors is that they don’t work very hard, and that the higher their rank, the less work they do. A statistics student decided to determine whether the belief is true. She took a random sample of 20 university instructors in each of the faculties of business, engineering, arts, and sciences. In each sample of 20, five were instructors, five were assistant professors, five were associate professors, and five were full professors. Each professor was surveyed and asked to report confidentially the number of weekly hours of work. 
What do the test results tell you?
 

Each year billions of dollars are lost because of worker injuries on the job. Costs can be decreased if injured workers can be rehabilitated quickly. As part of an analysis of the amount of time taken for workers to return to work, a sample of male blue-collar workers aged 35 to 45 who suffered a common wrist fracture was taken. The researchers believed that the mental and physical condition of the individual affects recovery time. Each man was given a questionnaire to complete, which measured whether he tended to be optimistic or pessimistic. Physical condition was also evaluated and categorized as very physically fit, average, or in poor condition. The number of days until the wrist returned to full function was measured for each individual. These data are stored in the file.

a What are the factors in this experiment? What are the levels of each factor?
b Can we conclude that pessimists and optimists differ in their recovery times?
c Can we conclude that physical condition affects recovery times?
           

At PBA, a study was undertaken to investigate whether different training programs and software packages offered by the school were more effective than others. The study recorded the number of words per minute typed by six groups of 40 students who completed the training programs. The training program and software packages assigned to each group are as described below.

                Group 1: hands-on training/MS Word software
                Group 2: computer tutorial/MS Word software
                Group 3: hands-on training/WordPerfect software
                Group 4: computer tutorial/WordPerfect software
                Group 5: hands-on training/AmiPro software
                Group 6: computer tutorial/AmiPro software
 

The typing speeds for each student were recorded and placed in the data file. Can we conclude that the typing speeds differ among the six groups of students?

           

We dealt with a one-way analysis of variance in which we had only one independent variable. Here, we’ve extended the analysis of variance to the treatment of experimental designs involving two or more independent variables. For purposes of simplicity, we will be concerned primarily with experiments involving two variables, although the extension to more complex designs should be apparent.

Eysenck’s study was pretty complex. He was interested in whether level-of-processing notions could explain differences in recall between older and younger subjects. If older subjects do not process information as deeply, they might be expected to recall fewer items than would younger subjects, especially in those conditions that entail greater processing. This study now has two independent variables, which we shall refer to as factors: Age and Recall Condition. The experiment thus is an instance of what is called a two-way factorial design.

An experimental design in which every level of every factor is paired with every level of every other factor is called a factorial design. In other words, a factorial design is one in which we include all combinations of the levels of the independent variables. In the factorial designs discussed in our class, we will consider only the case in which different subjects serve under each of the treatment combinations. For instance, in our example, one group of younger subjects will serve in the counting condition, a different group of younger subjects will serve in the rhyming condition, and so on. However, for now we will look at a 2 X 2 factorial design.  Later, since we have 10 combinations of our two factors (5-Recall Conditions x 2-Ages), we would have 10 different groups of subjects. When the research plan calls for the same subject to be included under more than one treatment combination, we will speak of repeated-measures designs.

Independent Homework Portion

In Homework 5, we considered an example of actual data on maternal adaptation for mothers of LBW (Iow-birthweight) infants from Experimental and Control groups and Full-Term infants (Nurcombe et al,, 1984). We saw there that mothers in the Experimental (Intervention) and Full-Term treatment groups adapted better than those in the LBW—Control group. A more complete analysis of those data might involve breaking down the treatment groups by Maternal Education (High School or Less versus More Than High School). The authors of the study thought that the mothers with less education might benefit more from the Experimental program than would more highly educated mothers. If this were true, the LBW—Control versus LBW—Experimental differences would be larger for the Low Education group than for the High Education group, giving a significant interaction.  What say you?

You know that women live longer than men. What about right-handed and left-handed people? Coren and Halpern’s (1991) review included data on both sex and handedness, as well as age at death. Such data are relevant to Life Insurance Companies.  An analysis of the age-at-death numbers in this problem will produce conclusions like those reached by Coren and Halpern.

Like other hallucinogenic drugs popular among teenagers and young adults who frequent the so-called club scene or raves, 5-Methoxy-N,N-di(iso)propyltryptamine hydrochloride (5-MeO-DIPT) also known as Foxy or Methoxy Foxy is rapidly gaining popularity among recreational users. The Federal Drug Enforcement Administration, reacting to the rapid increase in use and its similarity to other tryptamine compounds that have been abused, lobbied for and received approval to permanently classify MeO-DIPT as a Schedule I drug (US Drug Enforcement Administration, April, 2003). Unfortunately, with the exception of two case studies, there are apparently no systematic investigations of the consequences associated with the use of MeO-DIPT on neuropsychological development or behavior.

Adolescence in Rattus norvegicus is defined as a period consisting of the 21st postnatal day (PND) until the 60th postnatal day. According to Tirelli et al., within this period rodent adolescence can be delineated into three developmental periods consisting of early adolescence (PND 21-34), mid adolescence (PND 34-46), and late adolescence (PND 46-59). These three periods can be thought of in terms of prepubescence, periadolescence, and late adolescence/early adulthood, respectively. Spear (2000) provided support for the use of this rodent model for comparative evaluations and extrapolation to humans. Thus, the use of different adolescent age groups provides a framework for the examination of the developmental consequences associated with drugs of abuse on different stages of biological and cognitive development.

Although there are some published reports on the effects of 5-MeO-DIPT, including forensic case studies , anecdotes , and toxicological investigations, there is little published information on the specific central nervous system effects of 5-MeO-DIPT and nothing appears to be known about the long-term consequences of its use. As the availability and popularity may increase, the possible risks on development in vulnerable adolescents may be seen as an emerging societal health problem. Thus, understanding the consequences of developmental exposure to 5-MeO-DIPT on physiology, learning, and memory may be important because as the use of 5-MeO-DIPT increases so, too, will the consequences.

Greek Cross Response Testing. At the beginning of each trial, the rat was placed in the water facing the exterior wall of the start alley. One of two possible start locations were randomized and the order of the start or goal positions (see following) were determined through the use of a Fellows series (Fellows, 1967). The escape platform was located at one of two possible goal positions and the animals started at one of the two possible starting positions, depending on whether the animal was currently trained to turn right or left. Animals received 10 training trials per day, with an inter-trial interval of 15 sec between trials. The criterion was defined as 9 errorless responses within a given daily session consisting of 10 trials and an error was defined as entry of the head and abdomen into either of the current two incorrect alleys or premature exit from the correct alley. The animals were permitted to self-correct for errors and to explore the apparatus and locate the platform. On each trial, if an animal failed to locate the escape platform within 60 sec it was placed on the platform for about 15 sec. After criterion was achieved for a given turning response, either right or left, the escape platform was moved to the end of the alley 180^O (i.e., the opposite alley) from the previously correct alley. If an animal failed to achieve the criterion within 100 trials, the platform was moved to the opposite goal location. Testing continued until the animals achieved criterion on 10 response position reversals.

Thomas and Wang (1996) looked at the effects of memory on the learning of foreign vocabulary. Most of you have probably read that a good strategy for memorizing words in a foreign language is to think of mnemonic keywords. For example, in Tagalog (the official language of the Philippines), the word for eyeglasses is salamin. That word sounds much like our “salmon,” so a possible strategy would be to imagine a picture of a salmon wearing glasses. This type of encoding strategy has been recommended for years, and people who try it generally report good immediate recall of foreign vocabulary. This fits nicely with dual-coding theories, in which the word is viewed as being stored both lexically and
visually.

However, the studies that have looked at this phenomenon have generally asked the same participants to recall items at several different times. Since each recall session means an additional practice session, practice and time effects are confounded. To get around this problem, Thomas and Wang used different participants at the two recall intervals. Data with very nearly the same means and variances as theirs are presented in the file.

Thomas and Wang ran a study in which they divided participants into one of three “Strategy” groups, and then tested them at one of two times (5 minutes or 2 days). The strategies were:

      
The dependent variable was the number of English words recalled at either 5 minutes or 2 days.
 

In a study of mother—infant interaction, mothers are rated by trained observers on the quality of their interactions with their infants. Mothers were classified on the basis of whether this was their first child (primiparous versus multiparous) and whether the infant was low-birthweight (LBW) or full-term (FT). The data represent a score on a 12-point scale, on which a higher score represents better mother—infant interaction.

    Run and interpret the appropriate analysis of variance.
    Use simple effect procedures to compare low-birthweight and normal-birthweight conditions for multiparous mothers.
 

In Homework 5, we had three different examples in which we compared three groups on the basis of smoking behavior. We can set this design up as a 3 X 3 factorial by using Task as one variable and Smoking group as the other. The dependent variable was the number of errors
the participant made on that task. These data are repeated in the file.  Run the appropriate ANOVA and draw your conclusions.

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© 2008 David M. Compton, Ph.D.