IDE 620 Week 2

Question 1

A way of depicting frequency distributions for categorical (nominal) variables, such as religious affiliation, ethnic group, or state of residence

Answer 1

Bar Graph

Note that the bars do not touch in a bar graph, as they do in a histogram.

Question 2

A distribution having two modes or peaks.

Answer 2

Bimodal Distribution

Strictly speaking, for a distribution to be called bimodal, the peaks should be the same height. However, it is quite common to call any two-humped distribution bimodal, even when the high points are not exactly equal.

Question 3

Any of several methods, pioneered by John Tukey, of discovering unanticipated patterns and relationships, often by presenting quantitative data visually. The stem-and-leaf display and the box-and-whisker diagram are well-known examples.

Answer 3

Exploratory Data Analysis (EDA) `

Question 4

A tally of the number of times each score occurs in a group of scores. More formally, a way of presenting data that shows the number of cases having each of the attributes of a particular variable.

Answer 4

Frequency Distribution

Question 5

A graph with frequency shown by the height of contiguous bars, used for variables measured at the interval and ratio levels.

Answer 5

Histograph

Because the data in a histogram are interval or ratio, the bars should touch; in a bar graph for nominal or ordinal data, the bars do not touch.

Question 6

A graphic depiction of data relying on one or more lines.

Answer 6

Line graph

The lines can be linear or curvilinear. For example, a line graph of the business cycle over the past 50 years might be plotted on a line graph.

Question 7

The most common (most frequent) score in a set of scores.

Answer 7

Mode

Question 8

A distribution of scores or measures that, when plotted on a graph, produce a nonsymmetrical curve.

Answer 8

Skewed Distribution 

A positively (or upward or right) skewed distribution is one in which the infrequent scores are on the high or right side of the x-axis, such as the scores on a difficult test. A left (or downward or negatively skewed) distribution is one in which the rare values are on the low or left side of the x-axis, such as the scores on an easy test. One way to sort out which is which is to remember that a skewer is a pointy thing; when the pointy end of the distribution is on the right, it is right skewed, and conversely for left skewed

Question 9

The points falling between half a measurement unit below and half a unit above the number.

Answer 9

Real Limits (of a Number)  

Question 10

The degree to which measures or scores are bunched on one side of a central tendency and trail out (become pointy, like a skewer) on the other.

Answer 10

Skewness

The more skewness in a distribution, the more variability in the scores.

Computer programs often compute indexes of skewness. Positive values indicate a positive or right skew. Negative values indicate a negative or left skew.

Question 11

A way of recording the values of a variable, created by John Tukey, that presents raw numbers in a visual, histogram-like display. It is a histogram in which the bars are built out of numbers.

Answer 11

Stem-and-Leaf Display

Question 12

A distribution with only one mode

Answer 12

Unimodal

Question 13

Any of several statistical summaries that, in a single number, represent the typical or average number in a group of numbers. Examples include the mean, mode, and median.

Answer 13

Measures of central tendency

A batting average is a well-known measure of central tendency in the United States. A grade point average might be a more important example for many college students.

Question 14

A variable that can take on many possible values

Answer 14

Continuous variable

Question 15

A variable that takes on only a few possible values

Answer 15

Discrete variable

Question 16

The variable you are measuring

Answer 16

Dependent variable

Question 17

The variable that you manipulate

Answer 17

Independent variable

Question 18

Person who created stem-and-leaf display and EDA (exploratory data methods)

Answer 18

John Tukey

Question 19

Leftmost digits of a number

Answer 19

Leading digits (most significant digits)

Question 20

Vertical axis of na stem-and-leaf display

Answer 20

Stem

Question 21

Digits to the right of the leading digits

Answer 21

Trailing digits (less significant digits)

Question 22

Horizontal axis of display containing the trailing digits

Answer 22

Leaves

Question 23

Average; most popular measure of location or central tendency; has the desirable mathematical property of minimizing the variance.

Answer 23

Mean

Question 24

computed by taking the nth root of the product of n scores (e.g., the square root of 2 scores, the cube root of 3, etc.).

Answer 24

Geometric mean

Question 25

calculated by dividing n by the sum of the reciprocals of the numbers.

Answer 25

Harmonic mean (smaller than the arithmetic and geometric mean)

Question 26

The middle score or measurement in a set of ranked scores or measurements; the point that divides a distribution into two equal halves; the 50th percentile.

Answer 26

Median

Question 27

The most common (most frequent) score in a set of scores.

Answer 27

Mode

Question 28

A mean computed after removing the extreme observations.

Answer 28

Trimmed Mean

Thus, a trimmed mean is a measure of central tendency that allows the researcher to deal separately with a distribution’s outliers.

Question 29

Anything that produces systematic error in a research finding; causes of bias can range from poor data collection to flawed measurements to inappropriate statistical analysis. While the distortions due to systematic error continue to grow in the long run, random errors tend to balance out in the long run.

Answer 29

Bias

Question 30

The effects of any factor that the researcher did not expect to influence the dependent variable.

Answer 30

Bias `

Question 31

A type of graph in which boxes and lines show a distribution’s shape, central tendency, and variability. The “boxplot,” as it is often called, gives an informative picture of the values of a single variable and is helpful for indicating whether a distribution is skewed and has outliers.

Answer 31

Box-and-whisker diagram

Question 32

The upper and lower boundaries of each box in a box-and-whisker diagram

Answer 32

Hinges

Question 33

The number of values “free to vary” when computing an inferential statistic. It’s the number of pieces of information that can vary independently of one another or, alternatively stated, the number of unconstrained observations used in calculating an estimate

Answer 33

Degrees of freedom

Question 34

 A statistic showing the amount of variation or spread in the scores for, or values of, a variable.

Answer 34

Measure of dispersion

When the dispersion is large, the scores or values are widely scattered; when it is small, they are tightly clustered. Two commonly used measures of dispersion are the variance and the standard deviation. A measure of dispersion always implies the presence of a measure of central tendency, such as a mean. For example, the standard deviation measures deviation from the mean.

Question 35

The mean value of a variable in repeated samplings or trials

Answer 35

Expected value

Question 36

The mean of the sampling distribution of a statistic.

Answer 36

Expected value

Question 37

The middle half of a distribution. A measure of dispersion calculated by taking the difference between the first and third quartiles (that is, the 25th and 75th percentiles). Also called “midspread.”

Answer 37

Interquartile Range (IQR) 

Question 38

 A subject or other unit of analysis that has an extreme value on a variable or a combination of variables or has a large residual value.

Answer 38

Outlier

Outliers are important because they can distort the interpretation of data or make misleading a statistic that summarizes values (such as a mean). Outliers may also indicate that a sampling error has occurred by including a case from a population different than the target population.

Question 39

Divisions of the total rank-ordered cases or observations in a study into four groups of equal size. Technically, the three points that divide a series of ordered scores into four groups.

Answer 39

Quartiles

Question 40

A measure of variability, of the spread or the dispersion of values in a series of values.

Answer 40

Range

To get the range of a set of scores, you subtract the lowest value or score from the highest.

Question 41

A statistic that shows the spread, variability, or dispersion of scores in a distribution of scores. It is a measure of the average amount the scores in a distribution deviate from the mean.

Answer 41

Standard deviation

The standard deviation is the square root of the variance. As a variable, it is symbolized as SD, Sd, s, or lowercase sigma (σ).

Question 42

 A measure of the spread of scores in a distribution of scores, that is, a measure of dispersion.

Answer 42

Variance

The larger the variance, the farther the individual cases are from the mean. The smaller the variance, the closer the individual scores are to the mean.

Specifically, the variance is the mean of the sum of the squared deviations from the mean score divided by number of scores. That is, it’s the average distance from the mean in squared units. (See sum of squares for an example.) Taking the square root of the variance gives you the standard deviation (i.e., it converts the variance into regular, nonsquared units). A variance cannot be less than zero, nor can the standard deviation.