Statistical Measurements

Question 1

BELL CURVE

Answer 1

34% (68%) - 13.5% (95%) - 2% (99%)

The normal, or bell-shaped, curve distributes scores into six equal parts. Three of these parts are below the mean and three of these parts are above the mean. Sixty-eight percent (34% and 34%) comprise one standard deviation; 95% (13.5% and 13.5%) comprise two standard deviations; and 99% (2% and 2%) comprise three standard deviations.

Question 2

KUDER-RICHARDSON FORMULA

Answer 2

DICHOTOMOUS RELIABILITY (KR-20)

Measures internal consistency reliabilty. Can be used when the test contains dichotomous items, such as true-false questions

Question 3

ALPHA ERROR

Answer 3

TYPE I ERROR

A Type I error, also known as an alpha error, refers to the researchers’ rejection of the null hypothesis when it is correct. If the significance level is changed, such as .05 to .01, the probability of a Type I error changes as well.

Question 4

SPEARMAN-BROWN FORMULA

Answer 4

RELIABILITY OF SPLIT TEST

Sometimes it is useful to measure the internal consistency of a study by splitting the test into two halves. This reduces the test’s measured reliability, so researchers may use the Spearman-Brown formula to calculate the reliability of the test if it had not been split in two.

Question 5

MULTIVARIATE ANOVA (MANOVA)

Answer 5

GROUP DIFFERENCES ON DVs

A statistical procedure for assessing possible group differences on a set of dependent variables. For example, a researcher could conduct a MANOVA to assess whether a group of participants who receive a new educational method differ significantly from another group of participants who are taught with a traditional method on a set of achievement variables, such as quiz scores, homework scores, exam scores, and project scores.

Question 6

CONVERGENT VALIDITY

Answer 6

CORRELATION

Refers to two separate tests that measure the same attributes that are correlated. Convergent validation refers to times when there is a high correlation between the concept the test is meant to study and other constructs.

Question 7

T-TEST

Answer 7

COMPARE MEAN SCORES

When there are two groups, and therefore two mean scores, researchers can use the t-test. This test compares the t value from the first calculation to the t value in the second calculation to find whether the mean scores of the two groups are significantly different from each other.

Question 8

FACTORIAL ANOVA

Answer 8

CATEGORICAL IVs ON QUANTITATIVE DV

A statistical procedure to understand the effect on a dependent variable that is quantitative in nature of two or more independent variables that are categorical in nature. For example, a health researcher may use a factorial analysis of variance to examine the effects of diet (e.g., high vs. low carbohydrates) and exercise (e.g., 3 hours per week vs. 1 hour per week) on weight.

Question 9

PEARSON PRODUCT-MOMENT CORRELATION COEFFICIENT

Answer 9

PEARSON’S r

An index of the degree of linear relationship between two variables. Devised by Karl Pearson, it is often known as the Pearson product-moment correlation coefficient (Pearson’s r) and is one of the most commonly used sample correlation coefficients.

Question 10

PARAMETRIC STATISTICS

Answer 10

T-TEST & ANOVA

Statistical procedures that are based on assumptions about the distribution of the attributes in the population being tested (e.g., that there is a normal distribution of values). Parametric statistics, such as the t-test and analysis of variance, can be used when samples are randomly drawn from the population and results are distributed along a normal curve.

Question 11

SCHEFFÉ TEST

Answer 11

IV DIFFERENCES

A post hoc test used after a researcher obtains a significant F ratio in an analysis of variance that has more than two levels (i.e., more than two conditions of an independent variable that are being examined for differences among their mean values).

Question 12

NONPARAMETRIC STATISTICS

Answer 12

CHI-SQUARE & MANN-WHITNEY U

Statistical procedures in which the nature of the data being analyzed is such that certain common assumptions about the distribution of the attribute(s) in the population being tested (e.g., normality, homogeneity of variance) are not necessary or applicable. Nonparametric statistics, such as chi-square and the Mann-Whitney U test, are used when data is not normally distributed and variances are inconsistent. Nonparametric statistical measures, which are often used with descriptive data, should be used with nominal data.

Question 13

COEFFICIENT OF DETERMINATION

Answer 13

COMMON VARIANCE (r²)

Obtained by multiplying the value of the correlation coefficient (r) by itself, the coefficient of determination ranges in value from 0 to 1. Low values indicate the outcome is relatively unrelated to the predictor, whereas values closer to 1 indicate that the two variables are highly related. For example, if r = .30, then the squared correlation coefficient is .302 = .09 and interpreted to mean 9% of the variance between the two variables is common or overlapping.

Question 14

FACE VALIDITY

Answer 14

SURFACE

In which the test looks to be valid

Question 15

TYPES OF DATA MEASUREMENT

Answer 15

NOMINAL, ORDINAL, INTERVAL, RATIO

• NOMINAL - Refers to numbers that represent categories or qualities of the variable, such as race, gender, and age. Nonparametric statistical measures, which are often used with descriptive data, should be used with nominal data.
• ORDINAL - Pertaining to rank, order, or position in a series
• INTERVAL - With interval data, the numbers on a scale have the same amount of the variable throughout the scale; for instance, degrees on the Fahrenheit temperature scale. Interval scales provide a constant and consistent unit of measurement.
• RATIO - Numerical values that indicate magnitude and have a true, meaningful zero point

Question 16

TRUE VARIANCE

Answer 16

NATURAL

Naturally occurring variability within or among research participants. This variance is inherent in the nature of individual participants and is not due to measurement error, imprecision of the model used to describe the variable of interest, or other extrinsic factors. It represents the variance of the true scores among the participants taking the measure.

Question 17

CONCURRENT VALIDITY

Answer 17

SIMULTANEOUS

In which test results are compared with other results around the same time

Question 18

CONSEQUENTIAL VALIDITY

Answer 18

SOCIETAL CONSEQUENCES

Refers to the consequences of a study on society. Some researchers believe a test must benefit society in order to be considered valid, though not all researchers agree on this point.

Question 19

Z-SCORE

Answer 19

DISTANCE FROM POPULAR MEAN SCORE

Z-Score, aka Standard Score, describes distance from the population mean of a distribution of scores. It is measured in Standard Deviations. A normal distribution ranges from -3 SDs to +3 SDs.

Question 20

CORELATION COEFFICIENT

Answer 20

LINEAR RELATIONSHIP (-1 - +1)

A numerical index reflecting the degree of linear relationship between two variables. It is scaled so that the value of +1 indicates a perfect positive relationship (such that high scores on variable x are associated with high scores on variable y), –1 indicates a perfect negative relationship (such that high scores on variable x are associated with low scores on variable y, or vice versa), and 0 indicates no relationship. The most commonly used type of correlation coefficient is the Pearson

Question 21

F RATIO

Answer 21

EXPLAINED VARIANCE / ERROR VARIANCE

In an analysis of variance or a multivariate analysis of variance, the amount of explained variance divided by the amount of the error variance; that is, the ratio of between-groups variance to within-group variance. Its value determines whether to accept the null hypothesis stating that there is no difference between the treatment and control conditions, with a large value indicating the presence of a significant effect. Ideally, a researcher prefers to have rather small variation within each group and maximal variation between the groups in order to demonstrate significant group differences.

Question 22

PREDICTIVE VALIDITY

Answer 22

FUTURE

Refers to the degree to which a measure predicts future performance

Question 23

VARIABILITY

Answer 23

SD RANGE

When measuring variability, researchers may use standard deviation (SD) to describe the variability within a distribution of scores.

Question 24

SPEARMAN’S RHO

Answer 24

CORRELATION COEFFICIENT

Spearman’s rank correlation coefficient, or Spearman’s rho, the first statistical measure for intelligence tests. It determines how well the relationship between two variables can be described.

Question 25

ANALYSIS OF COVARIANCE (ANCOVA)

Answer 25

ADJUSTS FOR NON-INVESTIGATED IV INFLUENCE

It is a statistical method of studying the responses of different groups to a dependent variable that adjusts for the influence of a variable that is not being investigated but nonetheless is related to the dependent variable and thus may influence the study results.

For example, suppose a researcher analyzes whether there is a difference in learning among three types of instruction—in-class lecture, online lecture, and textbook only. He or she divides a random selection of adult students into three groups, implements the different instruction types, and administers the same test to all participants to determine how much they learned. If the researcher knows each participant’s educational background, he or she could use an analysis of covariance to adjust the treatment effect (test score) according to educational level, which would reduce the observed variation between the three groups caused by variation in education levels rather than by the instruction itself.

Question 26

CURRICULAR VALIDITY

Answer 26

CURRICULUM

Refers to how well a test measures the curriculum being tested and is evaluated by experts.

Question 27

AD HOC TESTS

Answer 27

REPS NON-RANDOM SUB-GROUPS

Ad hoc sampling refers to non-probability sampling that is gathered with the goal of obtaining any participant that meets specific characteristics. This allows for more inclusion of individuals who may otherwise be excluded, and is often used when a group within the larger population needs representation. One drawback of this technique is that because the sample is not random, study results will not be representative of the greater population.

Question 28

INTERNAL v EXTERNAL VALIDITY

Answer 28

INTEGRITY v APPLICABILITY

While internal validity relates to how well a study is conducted (its structure), external validity relates to how applicable the findings are to the real world.

Question 29

STANDARD DEVIATION

Answer 29

MEAN OF ALL DEVIATIONS FROM THE MEAN

Measure of variability. Standard deviation (SD) is a measure of variability and describes the variability within a distribution of scores. It is the mean of all the deviations from the mean, and is a popular measure of the dispersion of scores

Question 30

ERROR VARIANCE

Answer 30

MEASUREMENT-INDUCED

The element of variability in a score that is produced by extraneous factors, such as measurement imprecision, and is not attributable to the independent variable or other controlled experimental manipulations.

Question 31

CONTENT VALIDITY

Answer 31

DOMAIN-SPECIFIC

in which the test material comes from a certain domain

Question 32

CHI-SQUARE TEST

Answer 32

RELATIONSHIP OF CATEGORIES

Used to determine whether there is a relationship between two variables whose values are categories. For example, it may be used to test whether sex (male vs. female) is unrelated to having a household pet (yes vs. no).

Question 33

VARIANCE

Answer 33

SD²

A measure of variability. Also of the spread, or dispersion, of scores within a sample or population, whereby a small variance indicates highly similar scores, all close to the sample mean, and a large variance indicates more scores at a greater distance from the mean and possibly spread over a larger range. When measuring variability, researchers may use standard deviation (SD) to describe the variability within a distribution of scores. Variance is the square of the standard deviation and is used when conducting statistical analyses.

Question 34

EX POST FACTO RESEARCH DESIGN

Answer 34

AFTER-THE-FACT VARIABLES

Also known as a causal-comparative design, is a non-experimental quantitative design that examines variables after the fact (ex post facto). The researcher can then draw several conclusions about why these relationships occur. The analysis of variance and the t-test are frequently used in ex post facto designs.

Question 35

COEFFICIENT OF NONDETERMINATION

Answer 35

UNEXPLAINED VARIANCE

The Coefficient of Non-Determination explains the amount of unexplained, or unaccounted for, variance between two variables, or between a set of variables (predictors) in an outcome variable.

Question 36

CONSTRUCT VALIDITY

Answer 36

DO YOUR JOB!

Which refers to the degree to which a test actually measures what it is meant to measure

Question 37

DISCRIMINANT VALIDITY

Answer 37

NON-CORRELATION

Refers to two separate tests that don’t correlate

Question 38

ONE-WAY ANOVA

Answer 38

MULTI-LEVEL IVs ON SINGLE DV

An analysis of variance that evaluates the influence of different levels or conditions of a single independent variable upon a dependent variable. The mean values of two or more samples are examined in order to determine the probability that they have been drawn from the same population.

Question 39

BETA ERROR

Answer 39

TYPE II ERROR

Type II error, also known as beta error, refers to researchers’ failure to reject the null hypothesis when there is a difference between groups. Researchers can change the significance level to change the probability of Type I and Type II errors occurring. If the significance level goes down, Type I error decreases, though Type II error increases.

Question 40

BIVARIATE TABULAR ANALYSIS

Answer 40

IV PREDICTS DV

Bivariate tabular analysis can be used when the value of an independent variable can predict the value of a dependent variable. When this occurs, researchers typically plot scores along an XY plot graph to illustrate the relationship between variables.

Question 41

POST HOC TESTS

Answer 41

AFTER ANOVA

Researchers might apply a test after the analysis of variance is calculated (post hoc) if it is unclear as to which mean scores are significantly different from each other. Post hoc tests that may be able to clarify this problem include Scheffe’s method, Tukey’s HSD, Newman-Keuls, and Duncan’s new multiple range test.

Question 42

IV v DV

Answer 42

MANIPULATED v UNCHANGING

The independent variable (aka stimulus variable) is the one that is manipulated in order to observe the effects on the dependent variable, which is unchanging. The independent variable is sometimes called the stimulus variable, predictor variable, or experimental variable. Other terms for the dependent variable include the response variable, the outcome variable, and the criterion variable.

Question 43

EXPLAINED VARIANCE

Answer 43

PREDICTED - ACTUAL DATA

The discrepancy between a model and actual data.

Question 44

INCLUSIVE RANGE

Answer 44

RANGE + 1

Question 45

STANDARD ERROR OF MEASUREMENT (SEM)

Answer 45

RELIABILITY RANGE

CONFIDENCE LIMIT

The standard error of measurement (SEM) is a measure of reliability and is sometimes referred to as the confidence limit. The SEM helps researchers know that a person’s test score likely falls within a certain range of scores. The SEM is determined by assessment developers and can be found on the test’s profile. If a certain assessment has an SEM of 4.0, you first add and subtract 4 to the individual score to find the range. Therefore, because the score in this question is 82, there is a 2 out of 3 chance that the individual’s score falls between 78 and 86.

Question 46

MULTIPLE REGRESSION

Answer 46

MULTIPLE IVs ON A DV

Multiple regression is able to add together the predictive power of many independent variables. It is often used to predict a single outcome variable (DV) from a set of predictor variables (IVs).

Question 47

DUNCAN’S MULTIPLE RANGE TEST

Answer 47

DUNCAN’S MULTIPLE RANGE TEST

Duncan’s MRT. A multiple comparisons test used to follow up on an analysis of variance that yields significant results. After obtaining a significant F ratio, a researcher could conclude that at least one pair of samples is significantly different on the dependent variable and then conduct a Duncan multiple range test on pairs of samples to identify that specific pair. The overall Type I error rate would be protected, which would not be the case if separate t tests were conducted on all possible pairs.