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Chapter 16 Descriptive Statistics Copyright © 2012 Wolters Kluwer Health | Lippincott Williams & Wilkins Question
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Tell whether the following statement is true or false: Nominal measurement is the ranking of objects based on their relative standing on an attribute. Copyright © 2017 Wolters Kluwer Health | Lippincott Williams & Wilkins Answer False Nominal measurement: the classification of characteristics into mutually exclusive categories Ordinal measurement: the ranking of objects based on their relative standing on an attribute Copyright © 2017 Wolters Kluwer Health | Lippincott Williams & Wilkins Measurement • Nominal measurement: the classification of characteristics into mutually exclusive categories • Ordinal measurement: the ranking of objects based on their relative standing on an attribute • Interval measurement: indicating not only the ranking of objects but the amount of distance between them • Ratio measurement: distinguished from interval measurement by having a rational zero point Copyright © 2017 Wolters Kluwer Health | Lippincott Williams & Wilkins Descriptive Statistics • Summarize quantitative data • Describe quantitative data Copyright © 2017 Wolters Kluwer Health | Lippincott Williams & Wilkins Question Tell whether the following statement is true or false: Frequency distributions impose order on raw data. Numeric values are ordered from lowest to highest, accompanied by a count of the number of times each value was obtained. Copyright © 2017 Wolters Kluwer Health | Lippincott Williams & Wilkins Answer True Frequency distributions impose order on raw data. Numeric values are ordered from lowest to highest, accompanied by a count of the number (or percentage) of times each value was obtained. Copyright © 2017 Wolters Kluwer Health | Lippincott Williams & Wilkins Frequency Distributions • Impose order on raw data • Numeric values are ordered from lowest to highest, accompanied by a count of the number (or percentage) of times each value was obtained. • Common methods of display – Histograms – Frequency polygons Copyright © 2017 Wolters Kluwer Health | Lippincott Williams & Wilkins Distribution • Symmetric: two halves are mirror images of each other • Skewed: asymmetric with one tail longer than the other – Positively skewed – Negatively skewed • Modality: number of peaks – Unimodal – Multimodal • Normal distribution Copyright © 2017 Wolters Kluwer Health | Lippincott Williams & Wilkins Question What is the median? A. Average or typical value of a set of scores B. Value that occurs most frequently in a distribution C. Point above which and below which 50% of the cases fall D. Arithmetic average of all scores Copyright © 2017 Wolters Kluwer Health | Lippincott Williams & Wilkins Answer C Central tendency are indexes, expressed as a single number, that represent the average or typical value of a set of scores. The mode is the value that occurs most frequently in a distribution, the median is the point above which and below which 50% of the cases fall, and the mean is the arithmetic average of all scores. Copyright © 2017 Wolters Kluwer Health | Lippincott Williams & Wilkins Central Tendency • Central tendency are indexes, expressed as a single number, that represent the average or typical value of a set of scores. • Mode: value that occurs most frequently in a distribution • Median: point above which and below which 50% of the cases fall • Mean: arithmetic average of all scores Copyright © 2017 Wolters Kluwer Health | Lippincott Williams & Wilkins Question Tell whether the following statement is true or false: Range is the distance between the highest and lowest scores. Copyright © 2017 Wolters Kluwer Health | Lippincott Williams & Wilkins Answer True Range is the distance between the highest and lowest scores. Copyright © 2017 Wolters Kluwer Health | Lippincott Williams & Wilkins Variability • Variability: how spread out the data are • Range: distance between the highest and lowest scores • Standard deviation: indicates how much, on average, scores deviate from the mean • Calculation – Deviation scores represent the degree to which each person’s score deviates from the mean. The variance is equal to the SD squared. Copyright © 2017 Wolters Kluwer Health | Lippincott Williams & Wilkins Bivariate Descriptive Statistics • Relationships between two variables • Contingency table two-dimensional frequency distribution in which the frequencies of two nominalor ordinal-level variables are crosstabulated • Correlation coefficients describe the direction and magnitude of a relationship between two variables. – Product–moment correlation coefficient (Pearson’s r)—interval or ratio – Spearman’s rho coefficient—ordinal • Scatter plot Copyright © 2017 Wolters Kluwer Health | Lippincott Williams & Wilkins Risk Indexes • Absolute risk reduction: expresses the estimated proportion of people who would be spared from an adverse outcome through exposure to an intervention • Relative risk: estimated proportion of the original risk of an adverse outcome that persists among people exposed to an intervention • Relative risk reduction: estimated proportion of untreated risk that is reduced through exposure to the intervention Copyright © 2017 Wolters Kluwer Health | Lippincott Williams & Wilkins Risk Indexes • Odds ratio: ratio of the odds for the treated versus untreated group • Number needed to treat: estimate of how many people would need to receive the intervention to prevent one adverse outcome Copyright © 2017 Wolters Kluwer Health | Lippincott Williams & Wilkins Chapter 15 Developing and Testing Self-Report Scales Copyright © 2012 Wolters Kluwer Health | Lippincott Williams & Wilkins Question Tell whether the following statement is true or false: Scale development begins with a sound conceptualization of the construct (the latent variable) to be measured, excluding its dimensionality. Copyright © 2017 Wolters Kluwer Health | Lippincott Williams & Wilkins Answer False Scale development begins with a sound conceptualization of the construct (the latent variable) to be measured, including its dimensionality. Copyright © 2017 Wolters Kluwer Health | Lippincott Williams & Wilkins Conceptualizing the Construct • Scale development begins with a sound conceptualization of the construct (the latent trait) to be measured, including its dimensionality. – Unobservable latent trait – Unidimensional Copyright © 2017 Wolters Kluwer Health | Lippincott Williams & Wilkins Type of Scale • Scale selection is done before items can be generated. • Two broad categories of multi-item reflective scales • Traditional summated rating (Likert) • Latent trait Copyright © 2017 Wolters Kluwer Health | Lippincott Williams & Wilkins Generating Item Pool • Sources – Existing instruments – Research literature – Concept analyses – In-depth studies – Clinical observations Copyright © 2017 Wolters Kluwer Health | Lippincott Williams & Wilkins Decisions about Item Features • Number of items • Response items • Positive and negative stems • Item intensity • Item time frames Copyright © 2017 Wolters Kluwer Health | Lippincott Williams & Wilkins Number of Items • Domain sampling model: homogeneous set of items from a hypothetical universe of items • Goal is to provide appropriate redundancy so idiosyncrasies can be cancelled out. • Recommends starting with 3 to 4 times as many items as you will have in your final scale Copyright © 2017 Wolters Kluwer Health | Lippincott Williams & Wilkins Response Options • Scale items contain: – A stem – Response options • For example, strongly disagree, disagree, agree, strongly agree Copyright © 2017 Wolters Kluwer Health | Lippincott Williams & Wilkins Positive and Negative Stems • The objective was to include items that would minimize the possibility of an acquiescence response set—the tendency to agree with statements regardless of their content. • Many experts currently advise again including negative and positive items on a scale. Copyright © 2017 Wolters Kluwer Health | Lippincott Williams & Wilkins Item Intensity • The intensity of the statements (stems) should be similar and fairly strongly worded. • Statements should not be so extremely worded as to result in universal rejection. Copyright © 2017 Wolters Kluwer Health | Lippincott Williams & Wilkins Item Time Frames • A time frame should not emerge as a consequence of item development. • It should be decided upon in advance, based on the conceptual understanding of the construct and the needs for which the scale is being constructed. Copyright © 2017 Wolters Kluwer Health | Lippincott Williams & Wilkins Wording the Items—Readability • Clarity • Jargon • Length • Double negatives • Double-barreled items Copyright © 2017 Wolters Kluwer Health | Lippincott Williams & Wilkins Question Once content validity has been established at a satisfactory level, the scale must be administered to a development sample. What is the typical number of respondents who are representative of the target population? A. 100 B. 150 C. 250 D. 300 Copyright © 2017 Wolters Kluwer Health | Lippincott Williams & Wilkins Answer D Once content validity has been established at a satisfactory level, the scale must be administered to a development sample—typically 300 or more respondents who are representative of the target population. Copyright © 2017 Wolters Kluwer Health | Lippincott Williams & Wilkins Content Validity • Satisfactory level – Development sample – 300 or more respondents representative of target population Copyright © 2017 Wolters Kluwer Health | Lippincott Williams & Wilkins Field Testing the Instrument • Developing the sampling plan • Developing a data collection plan • Preparing for data collection Copyright © 2017 Wolters Kluwer Health | Lippincott Williams & Wilkins Question Tell whether the following statement is true or false: Exploratory factor analysis is used to reduce a small set of variables into a larger set of underlying dimensions, called factors. Copyright © 2017 Wolters Kluwer Health | Lippincott Williams & Wilkins Answer False Exploratory factor analysis is used to reduce a large set of variables into a smaller set of underlying dimensions, called factors. Copyright © 2017 Wolters Kluwer Health | Lippincott Williams & Wilkins Analysis of Scale Development Data Basic item analysis • Inter-item correlation • Item–scale correlations Exploratory factor analysis (EFA) • Factor extraction • Principal components analysis (PCA) • Factor rotation—orthogonal or oblique Copyright © 2017 Wolters Kluwer Health | Lippincott Williams & Wilkins Illustration of Factor Rotation Copyright © 2017 Wolters Kluwer Health | Lippincott Williams & Wilkins Scale Refinement and Validation • Revising the scale • Scoring the scale • Conducting a validation study – Confirmatory factor analysis Copyright © 2017 Wolters Kluwer Health | Lippincott Williams & Wilkins Confirmatory Factor Analysis • CFA is a second study often undertaken to validate the scale. • A subset of sophisticated statistical techniques (structural equation modeling) • Involves tests of a measurement model – Stipulates the hypothesized relationship between latent traits and manifest variables (items) Copyright © 2017 Wolters Kluwer Health | Lippincott Williams & Wilkins Interpretability of Scale Scores • Interpretability: the degree to which one can assign qualitative meaning – Percentile – Standard scores – Norms – Cutoff points Copyright © 2017 Wolters Kluwer Health | Lippincott Williams & Wilkins Critiquing Scale Development Studies • Methods used • Whether the evidence regarding the scale’s psychometric adequacy is sufficiently sound – See Box 15.1 Copyright © 2017 Wolters Kluwer Health | Lippincott Williams & Wilkins
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