Statistics

What is the range for the following set of scores? Scores: 5, 7, 9, 15

10 or 11 points

EX

sum of scores. summation occurs after parentheses, exponents, and multiplying/dividing have been completed.

n

symbol for the number of scores in a sample

The Greek letter sigma

used for summation

range

which is the distance covered by the scores in a distribution, from the smallest score to the largest score.

A deviation or deviation score is the difference between a score and the mean, and is calculated as:

x- μ

EF=

N

If the mean, median, and mode are all computed for a distribution of scores, which of the following statements cannot be true?

No one had a score equal to the mode.

fact

With an ordinal, interval, or ratio scale, the categories are listed in order (usually highest to lowest)For a nominal scale, the categories can be listed in any order.

Statistical methods can be classified into two broad categories

descriptive statistics, which organize and summarize data, and inferential statistics, which use sample data to draw inferences about populations.

mode

discrete variables, nominal scale

deviation

distance from the mean. A deviation or deviation score is the difference between a score and the mean, and is calculated as: x- mean

bimodal

distribution with two modes

control condition

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.

Variance

equals the mean of the squared deviations.

variance

equals the mean of the squared deviations. Variance is the average squared distance from the mean.

mean

for a distribution is the sum of the scores divided by the number of scores.

The population is too large

for every individual to participate in the research study

continuous variable

here 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.

Population variance

is represented by the symbol σ and equals the mean squared distance from the mean. Population variance is obtained by dividing the sum of squares (SS) by N.

Population standard deviation

is represented by the symbol σ and equals the square root of the population variance.

sample variance

is represented by the symbol and equals the mean squared distance from the mean. Sample variance is obtained by dividing the sum of squares (SS) by n − 1.

Sample standard deviation

is represented by the symbol s and equals the square root of the sample variance.

Sample standard deviation

is simply the square root of the variance.

Standard deviation

is the square root of the variance and provides a measure of the standard, or average distance from the mean.

standard deviation

is the square root of the variance and provides a measure of the standard, or average distance from the mean.

SS, or sum of squares

is the sum of the squared deviation scores.

letter X

is used to represent scores for a variable

An operational definition

measures and defines a construct in terms of external behaviors that are representative of the construct.

A researcher is measuring problem-solving times for a sample of laboratory rats. However, one of the rats fails to solve the problem so the researcher has an undetermined score. What is the best measure of central tendency for these data?

median

What is the best measure of central tendency for an extremely skewed distribution of scores?

median

median

median is the preferred measure of central tendency when extreme scores exist.ordinal

median

midpoint number middle number

One item on a questionnaire asks students to identify their preferred costume for the school mascot from three different choices. What is the best measure of central tendency for the data from this question?

mode

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.

What is SS, the sum of the squared deviations, for the following population of scores? Scores: 1, 9, 0, 2, 3

50

Describe the difference in appearance between a bar graph and a histogram and describe the circumstances in which each type of graph is used.

A bar graph leaves a space between adjacent bars and is used with data from nominal or ordinal scales. In a histogram, adjacent bars touch at the real limits. Histograms are used to display data from interval or ratio scales.

What is an operational definition?

A method for measuring and defining a hypothetical construct.

For the following scores, which of the following actions will increase the range? Scores: 3, 7, 10, 15

Add 4 points to the score

academic major

Bar graph (nominal scale)

registered voter (yes/no)

Bar graph (nominal scale)

For a positively skewed distribution with a mode of and a median of , what is the most likely value for the mean?

Greater than 25

experimental condition

Individuals in the experimental condition do receive the experimental treatment.

For a negatively skewed distribution, what is the most probable order for the three measures of central tendency from smallest to largest?

Mean, median, mode

For a distribution of scores, the mean is equal to the median. What is the most likely shape of this distribution?

Symmetrical

Which of the following is a consequence of increasing variability?

The distance from one score to another tends to increase and a single score tends to provide a less accurate representation of the entire distribution.

Standard deviation

The standard deviation is the most commonly used and the most important measure of variability. Standard deviation uses the mean of the distribution as a reference point and measures variability by considering the distance between each score and the mean.

Sample

a relatively small group selected from individuals of interest

A researcher is curious about the average distance traveled by Canada geese during peak fall migration in the state of New York. The entire group of Canada geese in the state is an example of a

population

Variability

provides a quantitative measure of the differences between scores in a distribution and describes the degree to which the scores are spread out or clustered together.

statistics

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

upper real limit

s at the top of the interval lower real limit at bottom

What value is represented by the uppercase letter N?

the number of scores in a population

symmetrical distribution

the right-hand side of the graph is a mirror image of the left-hand side

mode

In a frequency distribution, the mode is the score or category that has the greatest frequency.possible to have more than one mode

ordinal scale

Ranking a group of cities in terms of "quality of life" would be an example of measurement on a(n)scale of measurement.

What is the last step in the calculation of(ex)2 ?

Square the sum of the scores

A researcher is interested in the texting habits of high school students in the United States. The researcher selects a group of 100 students, measures the number of text messages that each individual sends each day, and calculates the average number for the group.

The population is the entire set of high school students in the United States.The sample is the group of 100 students who were measured in the study.

What scale is used to measure the dependent variable?

The ratio scale

individuals in sample

are actual participants

results from the sample

are generalized to the population

Data (plural)

are measurements or observations

descriptive statistics

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

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

N

how many scores are in a set

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 a hypothetical construct. 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.

What term is used for the statistical techniques that use sample data to draw conclusions about the population from which the sample was obtained?

inferential statistics

central tendency

is a statistical measure to determine a single score that defines the center of a distribution. The goal of central tendency is to find the single score that is most typical or most representative of the entire group.

parameter

is a value—usually a numerical value—that describes a population. A parameter is usually derived from measurements of the individuals in the population.

statistic

is a value—usually a numerical value—that describes a sample. A statistic is usually derived from measurements of the individuals in the sample.

frequency distribution

is an organized tabulation showing the number of individuals located in each category on the scale of measurement.highest to lowest A record of the frequency, or number of individuals in each category The set of categories that make up the original measurement scale

Sampling error

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

dependent

is the one that is observed to assess the effect of the treatment.

population

is the set of all the individuals of interest in a particular study.

symmetrical distribution

it is possible to draw a vertical line through the middle so that one side of the distribution is a mirror image of the other

multimodal

more than two modes

instead of showing the actual number of individuals in each category, a population frequency distribution graph usually shows a(n).

relative frequency

ordinal scale

the categories are differentiated in terms of direction, forming an ordered series

Research begins with a question about

the population

What additional information is obtained from measurements on an interval scale compared to measurements on an ordinal scale?

An interval scale provides information about the magnitude of the difference between two measurements.

What additional information is obtained from measurements on an ordinal scale compared to measurements on a nominal scale?

An ordinal scale provides information about the direction of difference (greater or less) between two measurements.

Which of the following measuring scales are displayed by frequency distribution polygons?

Either interval or ratio scales

age

Histogram or polygon (ratio scale)

Explain why honesty is a hypothetical construct instead of a concrete variable. Describe how honesty might be measured and defined using an operational definition.

Honesty is an internal attribute or characteristic that cannot be observed or measured directly. Honesty could be operationally defined by identifying and observing external behaviors associated with being honest, such as the physiological responses to questions measured by a polygraph ("lie detector"). Or, participants could be given a questionnaire asking how they behave or feel in situations for which honesty might have an influence.

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, & Wechsler, 2002). What research design did this study use?

Nonexperimental

tail of the distribution.

The section where the scores taper off toward one end of a distribution

A recent study reports that infant rats fed a diet containing genetically modified grains reached an adult weight 10% greater than their litter-mates raised on a regular diet. For this study, what is the independent variable?

The type of diet given to the rats

A group of quiz scores is shown in a histogram. If the bars in the histogram gradually decrease in height from left to right, what can you conclude about the set of quiz scores?

There are more low scores than there are high scores.

discrete variable

consists of indivisible categories, often whole numbers that vary in countable steps

discrete variable

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

Independent

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

A researcher is interested in the fast-food eating habits of American college students. A group of 50 students is interviewed and the researcher finds that these students eat an average of 2.3 commercially prepared meals per week. For this study, the average of 2.3 meals is an example of a

statistic

correlational method

two different variables are observed to determine whether there is a relationship between them.

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.

The average number that the researcher calculated is an example of a

The average number is a statistic.

limits

The boundaries that separate intervals are called real limits and are located exactly halfway between adjacent scores.

Population

The entire group of individuals of interests

Describe how the goal of an experimental research study is different from the goal for nonexperimental or correlational research. Identify the two elements that are necessary for an experiment to achieve its goal.

The goal of an experiment is to demonstrate the existence of a cause-and-effect relationship between two variables. To accomplish the goal, an experiment must manipulate an independent variable and control other, extraneous variable

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

The independent variable is the type of word being shouted. The dependent variable is pain tolerance.

Ford and Torok (2008) found that motivational signs were effective in increasing physical activity on a college campus. Signs such as "Step up to a healthier lifestyle" and "An average person burns 10 calories a minute walking up the stairs" were posted by the elevators and stairs in a college building. Students and faculty increased their use of the stairs during times that the signs were posted compared to times when there were no signs.

The independent variable is whether or not the signs were posted and the dependent variable is how much the stairs were used.What scale of measurement is used for the independent variable?Posted versus not posted is measured on a nominal scale.

There is some evidence that people with a visible tattoo are considered to be less attractive than are people without a visible tattoo. Resenhoeft, Villa, and Wiseman (2008) showed one group of students a color photograph of a 24-year-old woman with a tattoo of a dragon on her arm. A second group of students was shown the same photograph but with the tattoo removed. Each participant was asked to rate the attractiveness of the woman in the photograph.

The independent variable is whether the tattoo is present or is removed.Tattoo versus no tattoo is measured on a nominal scale. The dependent variable is the rating of attractiveness.Attractiveness is measured on a ratio scale.

Gentile, Lynch, Linder, and Walsh (2004) surveyed over 600 eighth- and ninth-grade students asking about their gaming habits and other behaviors. Their results showed that the adolescents who experienced more video game violence were also more hostile and had more frequent arguments with teachers. Is this an experimental or a nonexperimental study? Explain your answe

This is not an experiment because no independent variable is manipulated. They are comparing two preexisting groups of individuals based on their level of experiencing video game violence.

In a correlational study, how many variables are measured for each individual and how many groups of individuals are in the study?

Two variables and one group

constructs

Variables like intelligence, anxiety, and hunger are internal attributes or characteristics that cannot be directly observed but are useful for describing and explaining behavior.

Descriptive research

involves measuring one or more separate variables for each individual with the intent of simply describing the individual variables.

Variable

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

data set

is a collection of measurements or observations

sample

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

datum (singular

is a single measurement or observation and is commonly called a score or raw score.

skewed distribution,

the scores tend to pile up toward one end of the scale and taper off gradually at the other end

EX

the sum of scores

When measuring height to the nearest half inch, what are the real limits for a score of 69.0 inches?

68.75 and 69.25

birth-order position among siblings

Bar graph (ordinal scale)

inferential statistics

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

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.

measurement scale

consists of a set of categories that are used to classify individuals.

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.

interval scale

consists of an ordered series of categories that are all equal-sized intervals. it is possible to differentiate direction and distance between categories

continuous variable

consists of categories that are infinitely divisible and each score corresponds to an interval on the scale

nominal scale

consists of categories that differ only in name and are not differentiated in terms of magnitude or direction

interval scale

consists of ordered categories that are all intervals of exactly the same size. Equal differences between numbers on 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 researcher studies the factors that determine the number of jobs adults have in a lifetime. The variable, number of jobs, is an example of a(n)variable.

discrete

The experimental method

examines relationships between variables by manipulating an independent variable to create different treatment conditions and then measuring a dependent variable to obtain a group of scores in each condition

What additional information is obtained from measurements on a ratio scale compared to measurements on an interval scale?

A ratio scale provides information about the ratio of two measurements, which allow comparisons such as "twice as much."

construct

is a variable that cannot be directly observed

ratio scale

is an interval scale for which the zero point indicates none of the variable being measured. With a ratio scale, ratios of measurements reflect ratios of magnitude.

ratio scale

is an interval scale with the additional feature that a score of zero indicates none of the variable being measured. With a ratio scale, ratios of numbers do reflect ratios of magnitude.

letter N

The letter N is used as the symbol for the number of scores in a population