Statistics Proficiency Exam Chapter 1

An educational psychologist classifies students as high, medium, and low intelligence. What kind of scale is being used?

Ordinal

________ are the boundaries of intervals for scores that are represented on a continuous number line

Real limits

A ______ is a characteristic or condition that changes or has different values for different individuals

variable

The ______ is at the top of the interval, and the ______ is at the bottom

upper real limit, lower real limit

Explain the different between a discrete variable and a continuous variable. Give an example of each.

A discrete variable exists as indivisible categories such as the number of children in a family. For a continuous variable the categories are infinitely divisible such as a 1-inch interval on a ruler, which can be divided in half, in quarters, in eighths, and so on.

Calculate for the following scores: 4, 2, 5, 1 ΣX-1

11

Calculate for the following scores: 4, 2, 5, 1 ΣX

12

Calculate for the following scores: 4, 2, 5, 1 (ΣX)²

144

Calculate for the following scores: 4, 2, 5, 1 Σ(X-1)²

26

Calculate for the following scores: 4, 2, 5, 1 ΣX²

46

When measuring height to the nearest inch, what are the real limits for a score of 68 inches?

67.5 and 68.5

When measuring height to the nearest half inch, what are the real limits for a score of 68 inches?

67.75 and 68.25

Calculate for the following scores: 4, 2, 5, 1 Σ(X-1)

8

Describe the data for a correlational research study. Explain how correlational research is different from other research evaluating the relationship between two variables.

A correlational study has only one group of individuals and measures two different variables for each individual. Other research evaluating relationships between variables compares two (or more) different groups of scores.

A survey asks people to identify their age, annual income, and marital status (single, married, divorced, etc.). For each of these three variables, identify the scale of measurement that probably is used.

Age and annual income are measured on ratio scales. Marital status is measured on a nominal scale.

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

Constructs

A datum (singular) is a single measurement or observation and is commonly called a _____ or _____

score, raw score

_______ (plural) are measurements or observations

Data

_______ are statistical procedures used to summarize, organize, and simplify data

Descriptive statistics

Statistical methods are classified into two major categories: descriptive and inferential. Describe the general purpose for the statistical methods in each category.

Descriptive statistics are used to simplify and summarize data. Inferential statistics use sample data to make general conclusions about populations.

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.

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

Inferential statistics

An _______ consists of ordered categories that are all intervals of exactly the same size.

Interval scale

________ is the discrepancy, or amount of error, that exists between a sample statistic and the corresponding population parameter

Sampling error

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.

Strack, Martin, and Stepper (1988) found that people rated cartoons as funnier when holding a pen in their teeth (which forced them to smile) than when holding a pen in the lips (which forced them to frown). For this study, identify the independent variable and the dependent variable.

The independent variable is holding a pen in your teeth versus holding the pen in your lips. The dependent variable is the rating given to each cartoon.

The results from an experiment indicate that increasing the amount of indoor lighting during the winter months results in significantly lower levels of depression. Identify the independent variable and the dependent variable for this study.

The independent variable is the amount of indoor lighting, and the dependent variable is a measure of depression for each individual.

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

A researcher is interested in the relationship between caffeine consumption and activity level for elementary school children. A sample of 20 children is obtained and each child is interviewed to determine a level of caffeine consumption. The researcher then records the level of activity for each child during a 30-minute session on the playground. Is this an experimental or a correlational study? Explain your answer.

This is a correlational study. The researcher is simply observing, not manipulating, two variables.

A research study comparing college alcohol use in the United States and Canada reports that more Canadian students drink but American students drink m ore. Is this study an example of an experiment? Explain why or why not.

This is not an experiment because there is no manipulation. Instead, the study is comparing two preexisting groups (American and Canadian students).

Researchers have observed that high school students who watched educational television programs as young children tend to have higher grades than their peers who did not watch educational television. Is this study an example of an experiment? Explain why or why not.

This study could be correlational or non experimental, but it is definitely not an example of a true experiment. The researcher is simply observing, not manipulating, the amount of educational television.

In an experiment examining the effects of humor on memory, Schmidt (1994) showed participants a list of sentences, half of which were humorous and half were non humorous. The participants consistently recalled more of the humorous sentences than the non humorous sentences. a. Identify the independent variable for this study. b. What scale of measurement is used for the independent variable? c. Identify the dependent variable for this study. d. What scale of measurement is used for the dependent variable?

a. The independent variable is humorous or non humorous b. The independent variable is measured on a nominal scale c. The dependent variable is the number of sentences recalled d. The dependent variable is measured on a ratio scale

Research has shown that supplements high in antioxidants (strawberry, spinach, and especially blueberry) can actually reverse some effects of aging. In a typical study, one group of elderly rats receives the supplement and a second group is given an inactive placebo. Both groups are then tested on a variety of motor-behavior tasks. One common task is the Morris water maze, which measures how much time it takes for a rat to find a submerged platform in a pool of opaque water. The results generally show that the older rats receiving the supplements are able to locate the platform much faster than their peers who are not receiving supplements. a. Identify the independent and dependent variables for this study. b. What scale of measurement is used for the dependent variable?

a. The independent variable is whether the rats receive the antioxidant supplements, and the dependent variable is the amount of time needed to find the submerged platform b. Time is measured on a ratio scale

A researcher is interested in the effect of an electrolytic sports drink not he endurance of adolescent boys. A group of 30 boys is selected and half are given a treadmill endurance test while consuming the sports drink and the other half take the test while drinking water. For this study, a. Identify the population b. Identify the sample

a. The population is the entire set of adolescent boys. b. The sample is the group of 30 boys who were tested in the study.

Two scores, X and Y, are recorded for each of n=5 subjects. For these scores, find the value of each expression. Subject: X, Y A: 3, 7 B: 5, 4 C: 0, 3 D: 8, 1 E: 6, 5 a. ΣX b. ΣY c. ΣXY

a. ΣX=22 b. ΣY=20 c. ΣXY=79

For the following set of scores, find the value of each expression. X= 4, 0, 0, 8 a. ΣX² b. (ΣX)² c. Σ(X-3) d. Σ(X-3)²

a. ΣX²=80 b. (ΣX)²=144 c. Σ(X-3)=0 d. Σ(X-3)²=44

An investigator studies how concept-formation ability changes with age. Age is a ______ (discrete/continuous) variable.

continuous

For a _______, there are an infinite number of possible values that fall between any two observed values.

continuous variable

Individuals in a _______ do not receive the experimental treatment. Instead, they either receive no treatment or they receive a neutral, placebo treatment.

control condition

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

correlational method

A _______ is a collection of measurements or observations

data set

A _______ (singular) is a single measurement or observation and is commonly called a score or raw score

datum

The _____ is the one that is observed to assess the effect of the treatment

dependent variable

A researcher studies the factors that determine how many children couples decide to have. The variable, number of children, is a _______ (discrete/continuous) variable.

discrete

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

discrete variable

Individuals in the _______ do receive the experimental treatment.

experimental condition

In the _____, one variable is manipulated while another variable is observed and measured

experimental method

The ______ is the variable that is manipulated by the researcher

independent variable

In a study on perception of facial expressions, participants must classify the emotions displayed in photographs of people as anger, sadness, joy, disgust, fear, or surprise. Emotional expression is measured on a(n) _______ scale.

nominal

A ______ consists of a set of categories that have different names.

nominal scale

An ______ 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 a hypothetical construct

operational definition

An _____ consists of a set of categories that are organized in an ordered sequence.

ordinal scale

A ______ is a value, usually a numerical value, t hat describes a population

parameter

A ________ is usually derived from measurements of the individuals in the population

parameter

A researcher is interested in the reading skill of fourth-grade students in the state of Texas. The average reading score for the entire group of fourth-grade students would be an example of a _______.

parameter

A _____ is the set of all the individuals of interest in a particular study

population

In a non experimental study, the "independent variable" that is used to create the different groups of scores is often called the _______

quasi-independent variable

A _______ is an interval scale with the additional feature of an absolute zero point.

ratio scale

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

sample

A researcher is interested in the effect of humidity on the eating behavior of rats. A group of 30 rats is selected to participate in a research study. The group of 30 rats is an example of a _________.

sample

A _______ is a value, usually a numerical value, that describes a sample

statistic

A _______ is usually derived from measurements of the individuals in the sample

statistic

A researcher is interested in the effect of humidity on the eating behavior of rats and selects a group of 30 rats to participate in a research study. The amount of food eaten in one day is measured for each rat and the researcher computes the average score for the 30 rats. The average score is an example of a _______.

statistic

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

statistics

Use summation notation to express the following calculation. Add 2 points to each score, then add the resulting values

Σ(X+2)²

For the following set of scores, find the value of each expression. X= 2, 5, 0, 4 ΣX ΣX² Σ(X+1) Σ(X+1)²

ΣX=11 ΣX²=45 Σ(X+1)=15 Σ(X+1)²=71

Use summation notation to express the following calculation. Square each score, then add the squared values.

ΣX²