Chapter 16 Descriptive Statistics Copyright 2012 Wolters Kluwer

Chapter 16 Descriptive Statistics Copyright © 2012 Wolters Kluwer Health | Lippincott Williams & Wilkins

Question 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