stat methods - ch. 1,2,3,4

Nominal scale

• consists of a set of categories that have different names

• measurements on this scale label and categorize observations

Ordinal scale

• consists of set of categories that are organized in an ordered sequence

• measurements on this scale ran observations in terms of size or magnitude

Interval scale

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

Equal differences between numbers on an interval scale reflect what?

equal differences in magnitude

Ratio scale

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

With a ratio scale, ratio of numbers do reflect:

ratios of magnitude

A researcher studies the factors that determine the length of time a consumer stays on a website before clicking off. The variable, length of time, is an example of a ___ variable.

continuous

A researcher records the number of bites a goat takes of different plants. The variable, number of bites, is an example of a ___ variable.

discrete

When measuring height to the nearest inch, what are the real limits for a score of 68.0 inches?

67.5 and 68.5

The professor in a communications class asks students to identify their favorite reality television show. The different television shows make up a ___ scale of measurement.

nominal

Ranking jobs, taking into account growth potential, work-life balance, and salary, would be an example of measurement on a(n) ___ scale.

ordinal

Descriptive research / descriptive research strategy

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

Correlational method

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

Experimental method

one variable is manipulated while another variable is observed and measured

Individual differences

differences from one participant to another (age, weight, skills, motivation, and personality)

Independent variable

variable that is manipulated by the researcher

Dependent variable

variable that is observed to assess the effect of the treatment

Control condition

Individuals in this condition do not receive the experimental treatment

Experimental condition

Individuals in this condition receive the experimental treatment

Nonequivalent groups study

groups of participants not considered similar or comparable, due to the absence of random assignment to conditions.

• ex: comparing 8 year old children and 10 year old children.

Pre-post study

uses the passage of time (before/after) to create the groups of scores.

Quasi-independent variable

variable used as the independent variable in a non-experimental study

Stephens, Atkins, and Kingston (2009) found that participants were able to tolerate more pain when they shouted their favorite swear words over and over than when they shouted neutral words. For this study, what is the independent variable?

The kind of word shouted by the participants

What value is represented by the lowercase letter n?

The number of scores in a sample

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

6

What is the first step in the calculation of (∑X)²?

Add the scores

What value is represented by the letter N?

number of scores in a population

What value is represented by the letter X?

used to represent scores for a variable

Random sample

everyone in the population has an equal chance of being selected

Variable

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

Datum

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

Parameter

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

Statistic

value, usually a numerical value that describes a sample

Descriptive statistics

statistical procedures used to summarize, organize, and simplify data

Inferential statistics

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

Sampling error

natural discrepancy, or amount of error, between a sample statistic and its corresponding population parameter.

Constructs

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

Operational definition

identifies a measurement procedure (a set of operations) for measuring an external behavior and uses the resulting measurements as a definition and measurement of a hypothetical construct.

Discrete variable

• consists of separate, indivisible categories.

• No values can exist between two neighboring categories.

Continuous variable

• there are infinite number of possible values that fall between any two observed values.

• divisible into an infinite number of fractional parts.

Real limits

• boundaries of intervals for scores that are represented on a continuous number line.

• real limit separating two adjacent scores located halfway between them.

• two of these for each score

Upper real limit

at the top of the interval

Lower real limit

at the bottom of the interval

Frequency distribution

an organized tabulation of the number of individuals located in each category on the scale of measurement

Frequency distribution table

presents the measurement scale by listing the different measurement categories (X values) in a column from highest to lowest.

Proportion

measures the fraction of the total group that is associated with each score.

Percentage

% = p(100) = f/N(100)

Percentile rank

percentage of individuals in the distribution with scores at or below the particular value

Percentile

scores identified by their percentile rank are called this

Cumulative frequencies

represent accumulation of individuals as you move up the scale

Cumulative percentages

show the percentage of individuals who are accumulated as you move up the scale

Grouped frequency distribution table

presents groups of scores rather than individual values

Class intervals

Groups, or intervals, in grouped frequency distribution table.

Apparent limits

appear that they form the upper and lower boundaries for the class interval.

Relative frequencies

rather than report actual frequencies, findings reported as percentages to simplify data

Normal distribution

symmetrical, with the greatest frequency in the middle and relative frequencies decreasing as you approach either extreme.

Skewed distribution

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

Symmetrical distribution

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

Tail of the distribution

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

Positively skewed

skewed distribution with tail on the right-hand side

Negatively skewed

skewed distribution with tail on the left side

Central tendency

statistical measure to determine a single score that defines center of a distribution

Mean

• arithmetic average

• computed by adding all scores in distribution and dividing by number of scores

Population mean

µ = (∑X) ÷ N

Sample mean

M = (∑X) ÷ n

Weighted mean

Median

midpoint of the list

Interpolation

can be used to estimate an intermediate value between any two other X values

Mode

score or category that has the greatest frequency

Bimodal

distribution with two modes

Multimodal

distribution with more than two modes

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.

Range

highest score - lowest score = this

Quartiles

divide distribution into 4 equal parts each 25% of the distribution

Interquartile range (IQR)

distance between X values of 25th and 75th percentile (between Q1 and Q3)

Deviation

difference between a score and the mean

Variance

• mean of the squared deviations

• average squared distance from the mean

Standard deviation

• square root of the variance

• provides a measure of the standard, or average distance from the mean

Sum of squares

sum of squared deviation scores

Population variance

• σ²

• equals mean squared distance from mean

• SS / N

Population standard deviation

• σ

• equals square root of population variance

Degrees of freedom

• determine number of scores in the sample that are independent and free to vary

Biased statistic

average value of statistic either underestimates or overestimates the corresponding population parameter

Unbiased statistic

average value of statistic is equal to the population parameter

A researcher is curious about the average age of drivers in the city of Columbus. If he obtains a database of every driver in the city and calculates the average, this is an example of a ________.

parameter

Statistical methods are classified into which two major categories?

descriptive and inferential

A research study comparing salaries for recent college graduates in Spain versus France reports that recent graduates in France earn more than those in Spain. What research design did this study use?

nonexperimental

In what kind of study will you find a quasi-independent variable?

nonexperimental studies

What is not required for a proper experriment?

a quasi-independent variable

A researcher studies the factors that determine the number of cars owned by American families. The variable, number of cars, is an example of a ___________ variable.

discrete

When measuring weight to the nearest half ounce, what are the real limits for a score of 23 ounces?

22.75 and 23.25

A survey asked families to report on the number of cars they own. The following is the complete frequency table for the results.

X	f
1	125
2	101
3	?

If the proportion of families with 1 car is 50%, find the number of families with 3 cars.

24

The following frequency distribution table represents test scores for a class of students.

X	f
61–68	2
69–76	6
77–84	12
85–92	5
93–100	1

How many students scored less than 70?

It cannot be determined

A set of scores ranges from a high of X = 75 to a low of X = 23. If the bottom interval in a frequency table is 18–23, what is the top interval?

72-77

Four species of insects around a pond are being studied. The initial phase of the study involves capturing and counting members of the species. The four species are labeled A, B, C, and D. If these values are presented in a frequency distribution graph, what kind of graph would be appropriate?

a bar graph

What would be the most appropriate way to display a graph of a population's IQ scores?

When a population consists of numerical scores from an interval or a ratio scale, it is customary to draw the distribution with a smooth curve.

On a quiz, the possible points are 0, 1, 2, 3, and 4. The following is the classroom set of scores on the quiz:

0	0	0	1	1
1	1	2	2	2
2	2	2	3	3
3	3	4	4	4

What best describes this set of scores

symmetrical

The students in a psychology class seemed to think that the midterm exam was very easy. If they are correct, what is the most likely shape for the distribution of exam scores?

negatively skewed

A skewed distribution typically has _____ tail(s), and a normal distribution has ____ tail(s).

1; 2

In a grouped frequency distribution, one interval is listed as 50–59. Assuming that the scores are measuring a continuous variable, what are the real limits for this interval?

49.5 and 59.5