Measurement and statistical analysis in quantitative studies Flashcards
Advantages of measurement
- X guesswork and ambiguity in gathering and communicating information
- helps obtain objective information,which can be independently verified (as measurement is based on explicit rules)
- Helps obtain reasonably precise information
- Helps distinguish among subjects who possess different amounts/levels of an attribute
- Acts as a language of communication and helps communicate information clearly (numbers are less vague than words)
Levels of Measurement
❖Ratio: highest level; ratio scales, unlike interval scales, have a meaningful zero and provide information about the absolute magnitude of the attribute.
❖Interval: ranks people on an attribute and specifies the distance between them
❖Ordinal: ranks people on an attribute
❖Nominal: lowest level; involves using numbers simply to categorize attributes
Descriptive statistics
Used to describe and synthesize data
▪ Parameters: descriptor for a population
▪ Statistics: descriptive index from a sample
Frequency Distributions
❖A systematic arrangement of numeric values on a variable from lowest to highest
❖ count of the number of times (and/or percentage) each value was obtained
❖Frequency distributions can be described in terms of:
o Shape
o Central tendency
o Variability
❖Can be presented in a table (Ns and percentages) or graphically (e.g., frequency polygons)
Bivariate Descriptive Statistics
❖Used for describing the relationship between two variables
❖Two common approaches
o Crosstabs (contingency tables)
o Correlation coefficients
t-Test
❖Tests the difference between two means
❖t-Test for independent groups: between-subjects test
o For example, means for men vs. women
❖t-Test for dependent (paired) groups:within- subjects test
o For example, means for patients before and after surgery
Analysis of Variance (ANOVA)
❖Tests the difference between more than two means
❖Sorts out the variability of an outcome variable into two components: variability due to the independent variable and variability due to all other sources
❖Variation between groups is contrasted with variation within groups to yield an F ratio statistic.
o One-way ANOVA (e.g., three groups)
o Multifactor (e.g., two-way) ANOVA
o Repeated measures ANOVA (RM-ANOVA): within subjects
Chi-Squared Test
❖Tests the difference in proportions in categories within a contingency table
❖Compares observed frequencies in each cell with expected frequencies—the frequencies expected if there was no relationship
Correlation Coefficients
❖Pearson’s r is both a descriptive and an inferential statistic.
❖Tests that the relationship between two variables is not zero
Correlation Coefficients
❖Pearson’s r is both a descriptive and an inferential statistic.
❖Tests that the relationship between two variables is not zero
Errors in Statistical Decisions
❖Type I error: rejection of a null hypothesis when it should not be rejected; a false-positive result
o Risk of error is controlled by the level of significance (alpha), e.g., =.05 or .01.
o P sets as 0.05: Accept the risk that out of 100 samples from a population, a true null hypothesis would be wrongly rejected 5 times (p < 0.05, i.e. statistically significant)
❖Type II error: failure to reject a null hypothesis when it should be rejected; a false-negative result
o The risk of this error is a false-negative conclusion.
o Power is the ability of a test to detect true relationships. o By convention, power should be at least .80.
o Larger samples = greater power
Effect Size Indexes
❖Effect size is an important concept in power analysis.
❖Effect size indexes summarize the magnitude of the effect of the independent variable on the dependent variable.
❖In a comparison of two group means (i.e., in a t-test situation), the effect size index is d.
❖By convention:
o d ≤ .20, small effect
o d = .50, moderate effect o d ≥ .80, large effect
