Chapter 10 Analyzing Data

Question 1

Analysis of variance (ANOVA)

Answer 1

A parametric procedure used to test whether there is a difference among three group means.

Question 2

Chi-square

Answer 2

1. A nonparametric procedure used to assess whether a relationship exists between two nominal level variables; symbolized as χ².
2. The most commonly reported nonparametric statistic (i.e., not normally distributed) to determine whether groups are different.
3. Compares the frequency of an observed occurrence (actual number in each category) with the frequency of an expected occurrence (based on theory or past experience).

Question 3

Correlation

Answer 3

A measure that defines the relationship between two variables.

Question 4

Descriptive statistics

Answer 4

1. Statistics that describe, organize, and summarize data.

2. Based on frequency and includes measures of central tendency and measures of dispersion.

Question 5

Homogeneity of variance

Answer 5

Situation in which the dependent variables do not differ significantly between or among groups.

Question 6

Inferential statistics

Answer 6

1. Statistics that generalize findings from a sample to a population. Based on parameters.
2. Two types: Parameter estimation and hypothesis testing.

Question 7

Level of confidence

Answer 7

Probability level in which the research hypothesis is accepted with confidence. A 0.05 level of confidence is the standard among researchers (this means that researchers are willing to accept statistical significance occurring by chance 5 times out of 100).

Question 8

Mean

Answer 8

1. A measure of central tendency calculated by summing a set of scores and dividing the sum by the total number of scores; also called the average. Represented by x̄ or M.
2. The calculation takes into account each score in the distribution. Easily used in more advanced statistical analyses.
3. A precise, stable, and reliable measure, but it is sensitive to outliers (the mean will be “pulled” in the direction of extreme values).

Question 9

Measures of central tendency

Answer 9

1. Descriptive statistics that describe the location or approximate center of a distribution of data.
2. Three types: Mean, median, and mode.
3. The specific measure is chosen based on the level of measurement, shape, or form of the distribution of data and research objective.

Question 10

Measures of dispersion

Answer 10

1. Descriptive statistics that depict the spread or variability among a set of numerical data.
2. Three types: Range, variance, and standard deviation. (Also used, but less frequent: Percentile and interquartile range.)

Question 11

Median

Answer 11

1. A measure of central tendency that represents the middle score or midpoint in a distribution. Represented by Mdn; sometimes known as the 50th percentile.
2. An ordinal statistic based on ranks: Calculated by first arranging the scores in rank order. If there is an odd number of scores, the median is the middle score. If there is an even number of scores, the median is the point halfway between the two middle scores (and thus would not be a score that appears in the distribution).
3. Does not take into account each score in the distribution and is not sensitive to extreme scores.

Question 12

Mode

Answer 12

1. The score or value that occurs most frequently in a distribution; a measure of central tendency used most often with nominal-level data.
2. There may be more than one mode for any distribution of scores - data with a single mode are called unimodal and data with two modes are called bimodal.
3. Can be applied to any set of data at the nominal, ordinal, or interval/ratio level of measurement.
4. Easily identified when a frequency distribution is used.

Question 13

Negative correlation

Answer 13

Correlation in which high scores for one variable are paired with low scores for the other variable.

Question 14

Outlier

Answer 14

Data point isolated from other data points; extreme score in a data set.

Question 15

Parameter

Answer 15

Numerical characteristic of a population (e.g., population mean, population standard deviation).

Question 16

Positive correlation

Answer 16

Correlation in which high scores for one variable are paired with high scores for the other variable, or low scores for one variable are paired with low scores for the other variable.

Question 17

Probability

Answer 17

1. Likelihood that an event will occur, given all possible outcomes. Represented by 𝑝 and expressed as a decimal (e.g., 0.5 represents a 50% likelihood).
2. A system of rules for analyzing a set of outcomes and a means of predicting.
3. Helps evaluate the accuracy of a statistic and test a hypothesis, but does not represent the amount of validity associated with a research hypothesis.

Question 18

Range

Answer 18

1. A measure of variability that is the difference between the lowest and highest values in a distribution.
2. The simplest measure of dispersion - the lowest score is subtracted from the highest score.
3. Considered an unstable measure because it is based on only two values in the distribution. It is extremely sensitive to outliers and does not take into account variations in scores between extremes.

Question 19

Robust

Answer 19

Referring to results from statistical analyses that are close to being valid, even though the researcher does not rigidly adhere to assumptions associated with parametric procedures.

Question 20

Skewed distribution

Answer 20

1. A distribution of scores with a few outlying observations in either direction.
2. Has an off-centered peak and a longer tail in one direction.
3. The mean, median, and mode have constant positions: The mode is closest to the peak of the curve; the mean is closest to the tail; the median falls somewhere between the mean and the mode.

Question 21

Standard deviation (SD)

Answer 21

1. The most frequently used measure of variability; the distance a score varies from the mean.
2. The square root of the variance - summarizes data in the same unit of measurement as the original data.
3. The most stable measure of variability; it takes into account each score in the distribution, and is sensitive to outliers.

Question 22

Symmetrical distribution

Answer 22

A distribution of scores in which the mean, median, and mode are all the same.

Question 23

𝑡-test

Answer 23

A popular parametric procedure for assessing whether two group means are significantly different from one another.

Question 24

Variance

Answer 24

1. Measure of variability, which is the average squared deviation from the mean (i.e., the sum of all squared deviations divided by the number of scores).
2. Not widely used because it cannot be employed in many statistical analyses.

Question 25

Parametric vs. nonparametric procedures

Answer 25

1. Parametric procedures: Require certain assumptions to be met for statistical findings to be valid - the dependent variable is measured on an interval/ratio scale that is *normally distributed* in the population, and groups are mutually exclusive. 2. Nonparametric procedures: Make no assumptions about the shape of the distribution; usually used when data represent an ordinal or nominal scale; easier to calculate but less powerful than parametric procedures.

Question 26

The research design and type of data collected determine selection of appropriate _

Answer 26

Statistical procedures.

Question 27

When data represent either an interval or ratio scale, the preferred measure of central tendency is the _

Answer 27

Mean. (The mean is also sometimes appropriate for ordinal data.)

Question 28

When data represent a skewed distribution, the appropriate measure of central tendency is the _

Answer 28

Median. (Provides a balanced picture of the extreme scores or outliers.)

Question 29

When nominal data is used, the appropriate measure of central tendency is the _

Answer 29

Mode.

Question 30

Regardless of the purpose of the study, the researcher uses the _ as a preliminary indicator of central tendency.

Answer 30

Mode.

Question 31

The _ is sometimes used as a point in the distribution at which scores can be divided into two categories containing the same number of respondents.

Answer 31

Median.

Question 32

Deviated score

Answer 32

1. The difference between a raw score and the mean of that distribution (i.e., x̄ - x). 2. Forms the basis for the *variance* and the *standard deviation*. 3. The sum of the deviated scores in a distribution always equals 0.

Question 33

The standard deviation is an appropriate measure of dispersion for distributions that are _

Answer 33

Symmetrical, not skewed.

Question 34

Parameter estimation

Answer 34

Inferential statistical estimate of a characteristic of a population that is evaluated by a single number (point estimate) or an interval (interval estimate).

Question 35

Confidence interval

Answer 35

1. Confidence associated with an interval estimate. 2. A range of values that has some specified probability (e.g., 0.95 or 0.99) of including a particular population parameter.

Question 36

Hypothesis testing

Answer 36

1. Inferential statistical procedure that allows the researcher to formulate a hypothesis concerning a parameter, sample the population of interest, and make objective decisions about the sample results of the study. 2. Two types: Parametric and nonparametric procedures.

Question 37

Pearson's 𝑟

Answer 37

1. The most widely used correlation coefficient - describes the relationship between two variables. Expressed as a decimal between +1.0 and -1.0. 2. A *parametric* procedure used when both variables are *interval or ratio-level measures*.

Question 38

The _ statistic is the appropriate test when variables are measured on a nominal scale and the researcher counts the number of items in each category.

Answer 38

Chi-square.

Question 39

A statistical procedure that is appropriate even when the assumptions are violated is said to be _

Answer 39

Robust.

Question 40

Parameter vs. statistic

Answer 40

A parameter is a characteristic of a population whereas a statistic is a characteristic of a sample.

Question 41

A post-hoc test is _

Answer 41

A follow-up test to ANOVA when there are three or more groups.