Ch 1 Intro to Statistics

"In statistical notation, N is the symbol for the"

# of scores in a population

"In statistical notation, n is the symbol for the"

# of scores in a sample

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 two elements that are necessary for an experiment to achieve its goal?

1. MANIPULATION of 1 variable by changing its value 2. CONTROL over the research situation to ensure extraneous variables (confounds) do not influence the relationships being examined

What are the two types of nonexperimental methods discussed in the textbook?

1. nonequivalent groups study 2. pre-post studies

What is the value of Σ(X - 2) for the following scores: 6, 2, 4, 2?

6

nominal scale

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

statistics

A set of mathematical procedures for organizing, summarizing, and interpreting information

For the following set of scores (X=1,6,2,3), find the value of each expression: a. ΣX^2 b. (ΣX)^2 c. Σ(X-3) d. Σ(X - 3)^2

A. 50 B. 144 C. 0 D. 14

interval scale

An interval scale consists of an ordered series of categories that are all equal-sized intervals. With an interval scale, it is possible to differentiate direction and magnitude (or distance) between categories.

A tax form asks people to identify their annual income, number of dependents, and social security number. For each of these three variables, identify the scale of measurement that probably is used and identify whether the variable is continuous or discrete.

Annual income is continuous. Number of dependents and social security number are both discrete.

discrete variable

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

ordinal scale

In an ordinal scale, the categories are differentiated in terms of direction, forming an ordered series (also differ in name)

examples of nonequivalent group studies

Other examples of nonequivalent group studies include comparing girls and boys, 8-year-old children and 10-year-old children, people with an eating disorder and those with no disorder, and comparing children from a single-parent home and those from a two-parent home. 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.

independent variable

The experimental factor that is manipulated; the variable whose effect is being studied.

Knight and Haslam (2010) found that office workers who had some input into the design of their office space were more productive and had higher well-being compared to workers for whom the office design was completely controlled by an office manager. For this study, identify the independent variable and the dependent variable.

The independent variable is the amount of control over office design. The dependent variables are productivity and well-being.

dependent variable

The outcome factor; the variable that may change in response to manipulations of the independent variable.

Variable

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

ratio scale

a 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.

sample

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

parameter

a value, usually a numerical value, that describes a population

Statistic

a value, usually a numerical value, that describes a sample

For the following set of scores (X=3,2,5,1,3), find the value of each expression: a. ΣX^2 b. (ΣX)^2 c. Σ(X-1) d. Σ(X - 1)^2

a. 48 b. 196 c. 9 d. 25

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 walk- ing 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. Identify the independent and dependent variables for this study. What scale of measurement is used for the independent variable?

a. The independent variable is whether or not the motivational signs were posted, and the dependent variable is amount of use of the stairs. b. Posting vs. not posting is measured on a nominal scale.

The teacher in a communications class asks students to identify their favorite reality television show. The different television shows make up a scale of measurement. a. nominal b. ordinal c. interval d. ratio

a. nominal

What is the first step in the calculation of (ΣX)^2? a. Square each score. b. Add the scores. c. Subtract 2 points from each score. d. Add the X - 2 values.

b. add the scores

A researcher is interested in the sleeping habits of American college students.A group of 50 students is interviewed and the researcher finds that these students sleep an average of 6.7 hours per day. For this study, the average of 6.7 hours is an example of a(n) . a. parameter b. statistic c. population d. sample

b. statistic

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). What research design did this study use? a. correlational b. experimental c. nonexperimental d. noncorrelational

c. nonexperimental

A researcher is curious about the average IQ of registered voters in the state of Florida. The entire group of registered voters in the state is an example of a __________ a. parameter b. statistic c. population d. sample

c. population

nonequivalent groups

compares two groups of scores, but the researcher has no ability to control which participants go into which group because this type of research compares preexisting groups, the researcher cannot control the assignment of participants to groups and cannot ensure equivalent groups.

________________ one group with 2 variables measured for each individual ________________ one variable manipulated, one variable measured

correlational method experimental method

When measuring height to the nearest half inch, what are the real limits for a score of 68.0 inches? a. 67 and 69 b. 67.5 and 68.5 c. 67.75 and 68.75 d. 67.75 and 68.25

d. 67.75 and 68.25

the population should always be _____________ by the researcher

defined

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

correlational method

examines relationships between variables by measuring 2 different variables for each individual

t/f correlational method allows researchers to produce a cause-and-effect explanation for the relationship

false

t/f nonexperimental method allows researchers to produce a cause-and-effect explanation for the relationship

false

t/f tables, graphs, and averages are examples of inferential statistics

false; they are examples of descriptive statistics

operational definition

identifies a measurement procedure for measuring an external behavior and uses the resulting measurements as a definition of a hypothetical construct

quasi-independent variable

in a non-experimental study, the "independent variable" that is used to create the different groups of scores

What are the variables in the following researcher question?: "Does the amount of caffeine intake increase memory performance in college students?"

independent variable: amount of caffeine dependent variable: memory performance

What is the independent variable? the dependent 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.

independent: type of word shouted dependent: level of pain tolerated

constructs

internal attributes or characteristics that cannot be directly observed but are useful for describing and explaining behavior (i.e. hunger, intelligence, shyness)

examples of nominal variables

major race gender occupation

pre-post study

measures the same variable twice, comparing scores before and after treatment; researcher has no control over the passage of time

scales of measurement

nominal, ordinal, interval, ratio

Identify the population and the sample. 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. Identify the population for this study.

population: high school students in the U.S. sample: 100 students

inferential statistics must always address _____________

sample error

In statistical notation, X represents..

scores for a particular variable

the ordinal scale allows you to determine if two individuals are different and the direction of the difference, but not the ________ of the difference

size

examples of ordinal scale

small, medium, large first, second, third upper, middle, lower

descriptive statistics

statistical procedures used to summarize, organize, and simplify data

nonexperimental research

studies in which the researcher collects data without introducing an intervention; also called observational research uses a preexisting participant characteristic (i.e. male/female) or the passage of time (before/after) to create the groups being compared

inferential statistics

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

examples of interval variables

temperature calendar year IQ score

real limits of a continuous variable

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

sample error

the naturally occurring discrepancy, or error, that exists between a sample statistic and the corresponding population parameter Ex. How young is the U.S.? L.A. (sample) median age: 34.6 U.S.A. (population) median age: 38.4

what is the difference between the interval and ratio scale?

the ratio scale is anchored to a real zero, which allows you to talk about proportionality the interval scale has an arbitrary sero

population

the set of all individuals of interest in a particular study

Summation Notation Σ

the sum of

t/f correlational studies are examples of non-experimental research

true

purpose of statistics

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

continuous variable

variable for which, in theory, there are an infinite number of values between any two observed values

What are some examples of continuous variables?

weight height time

examples of ratio variables

weight, height

What are some examples of discrete variables?

whole countable #s (number of children in family) gender occupation

t/f experimental method allows researchers to produce a cause-and-effect explanation for the relationship

yes