Chapter 22

Question 1

What is descriptive statistics?

Answer 1

Used to characterize the shape, central tendency, and variability within a set of data

Question 2

What are parameters?

Answer 2

measures of population characteristics

Question 3

What is statistics?

Answer 3

descriptive index from sample data

Question 4

What is a coin rotation test?

Answer 4

frequency distribution
cumulative percent

Question 5

What are methods to display frequency distributions?

Answer 5

Grouped frequency distribution
Histogram
Line plot
Stem-and-leaf plot

Question 6

What are shapes of distributions?

Answer 6

Normal
Skewed to the right (positive)
Skewed to the left (negative)

Question 7

What are measures of central tendency?

Answer 7

mean
median
mode

Question 8

What are measures of variability?

Answer 8

range
percentiles and quartiles
box plots
variance
standard deviation
coefficient of variation

Question 9

What is a box plot?

Answer 9

Box represents the interquartile range
Horizontal line at median
“Whiskers” show minimum and maximum scores

Question 10

What is a normal distribution?

Answer 10

Also known as a bell-shaped distribution or
Gaussian distribution.
Constant and predictable characteristics:
* 68% of the scores are within 1 SD of the mean
* 95% of the scores are within 2 SD of the mean
* 99% of the scores are within 3 SD of the mean

Question 11

What is a z-score?

Answer 11

A standardized score based on the normal
distribution
* z = standard deviation units
Allows for interpretation of a score in relation to the sample mean and variance

Question 12

What are the 3 main types of descriptive statistics?

Answer 12

1.The distribution concerns the frequency of each value.
2.The central tendency concerns the averages of the values.
3.The variability or dispersion concerns how spread out the values are.

Question 13

What type of summaries do descriptive statistics provide?

Answer 13

Descriptive statistics provide simple summaries about the sample and about the observations that have been made. Such summaries may be either quantitative, i.e. summary statistics, or visual, i.e. simple-to-understand graphs. These summaries may either form the basis of the initial description of the data as part of a more extensive statistical analysis, or they may be sufficient in and of themselves for a particular investigation.

Question 14

What is a distribution?

Answer 14

total set of scores for a particular variable

Question 15

For data on the nominal scale, what measure of central tendency is meaningful?

Answer 15

mode

Question 16

For data on the ordinal scale, what measure of central tendency is meaningful?

Answer 16

median

Question 17

Which measure of central tendency is most stable?

Answer 17

mean

Question 18

Why is the mean the most reasonable estimate of population characteristics?

Answer 18

Only the mean can be subjected to arithmetic manipulations, making it the most reasonable estimate of population characteristics. For this reason, the mean is used more often than the median or mode for statistical analysis of ratio or interval data.

Question 19

The objective of the measure of dispersion or variation is to…

Answer 19

identify the extent to which the entire data set is spread from the central tendency, specifically the mean

Question 20

What does the range reflect?

Answer 20

It reflects nothing about the dispersion of scores between the two extremes. One aberrant extreme score can greatly increase the range, even though the variability within the rest of the data set is unchanged.
Although it is easily computed, the range is usually employed only as a rough descriptive measure and is typically reported in conjunction with other indices of variability.

Question 21

How is range reported?

Answer 21

Rather than reporting range as the difference between scores, research reports will usually provide the actual minimum and maximum scores, which is more useful information to characterize a sample.

Question 22

What are percentiles?

Answer 22

Percentiles are used to describe a score’s position within a distribution relative to all other scores. Percentiles divide data into 100 equal portions.
Percentiles are helpful for converting actual scores into comparative scores or providing a reference point for interpreting a particular score.

Question 23

What are quartiles?

Answer 23

Quartiles divide a distribution into four equal parts or quarters. Quartiles Q1, Q2, and Q3 correspond to percentiles at 25%, 50%, and 75% of the distribution (P25, P50, P75). The score at the 50th percentile, or Q2, is the median. The distance between the first and third quartiles, Q3 – Q1, is called the interquartile range, which represents the spread of scores within the middle 50% of the data.

Question 24

What is variance?

Answer 24

The square of the standard deviation
Helps to find the spread of the data

Question 25

What is the sum of squares and variance?

Answer 25

The sum of the squared deviation scores (SS) will be larger as variability increases.
As an index of relative variability it is limited because the sample size can influence it; that is, as n increases, the sum will also tend to increase simply because there are more scores. To eliminate this problem, the sum of squares is divided by n to obtain the mean of the squared deviation scores, shortened to mean square (MS). This value is a true measure of variability and is also called the variance.

Question 26

What is standard deviation?

Answer 26

To bring the index back into the original units of measurement, we take the square root of the variance. This value is called the standard deviation, symbolized by s.
The standard deviation of sample data is usually reported along with the mean so that the data are characterized according to both central tendency and variability.

Question 27

What is the coefficient of variation?

Answer 27

The coefficient of variation (CV) is another measure of variability that can be used to describe data measured on the interval or ratio scale.

Question 28

What are the 2 advantages of the coefficient of variation?

Answer 28

First, it is independent of units of measurement because units will mathematically cancel out. Therefore, it is a practical statistic for comparing variability in distributions recorded in different units.
Second, the coefficient of variation expresses the standard deviation as a proportion of the mean, thereby accounting for differences in the magnitude of the mean. The coefficient of variation is, therefore, a measure of relative variation, most meaningful when comparing two distributions.

Question 29

The mean of a normal distribution of z-scores will always equal __ (no deviation from the mean), and the standard deviation will always be __.

Answer 29

0; 1.0

Question 30

What tests can be applied to distributions to determine how well the data fit a normal curve?

Answer 30

goodness of fit tests