1. Quantitative Data Analysis
Chapter 16
Quantitative Data Analysis
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2. Learning Outcomes
Differentiate between descriptive and inferential statistics.
State the purposes of descriptive statistics.
Identify the levels of measurement in a research study.
Describe frequency distribution.
List measures of central tendency and their use.
List measures of variability and their use.
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3. Learning Outcomes (Cont.)
Identify the purpose of inferential statistics.
Distinguish between a parameter and a statistic.
Explain the concept of probability as it applies to the analysis of sample data.
Distinguish between type I and type II errors and their effects on a study’s outcome.
Distinguish between parametric and nonparametric tests.
List the commonly used statistical tests and their purposes.
Critically analyze the statistics used in published research studies.
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4. Descriptive Data Analysis
Define
State the purpose
Frequency distribution
Levels of measurement
Central tendency
Variability
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5. What Is Descriptive Statistics?
Description and/or summarization of sample data
Allow researchers to arrange data visually to display meaning and to help in understanding the sample characteristics and variables under study.
In some studies, descriptive statistics may be the only results sought from statistical analysis.
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6. Purposes of Descriptive Statistics
Reduce data to manageable proportions by summarizing them
Measure of central tendency
Scatter plot
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7. Levels of Measurement Nominal Ordinal Interval Ratio
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8. Nominal Measurement Classify objects or events into categories
Examples
Gender
Marital status
Religious affiliation
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9. Ordinal Measurement
Shows relative ranking of objects; numbers assigned to each category can be compared, and a member of a higher category is said to have more of a certain attribute than one in a lower category
Intervals are not necessarily equal
Examples
Class ranking
Likert scale responses
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10. Interval Measurement
Shows rankings of events or objects on a scale with equal intervals between the numbers
Zero point is arbitrary.
Examples
Temperature scales
Beck depression inventory
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11. Ratio Measurement
Shows rankings of events or objects on scales with equal intervals and absolute zeros
Highest level of measurement—usually only achieved in physical sciences
Examples
Weight
Blood pressure
Height
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12. Frequency Distribution
Common basic way to organize data
Summarizes the occurrences of events under study; tallies the frequency of events
Cohort groups are sometimes created to investigate the frequencies of certain data.
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13. Central Tendency Summarizes the middle of the group
Each measure has specific uses and is most appropriate to select types of distribution and measurement.
An “average”
Mode: most frequent score
Median: middle score
Mean: average score
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14. Normal Distribution
A theoretical concept that observes that interval or ratio data group themselves about a midpoint in a distribution closely approximating the normal curve.
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15. Skewness Not all data follow a normal curve.
Positive skew equals low range mean.
Example: world income
Negative skew equals high range mean.
Example: age at death
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16. Variability or Dispersion
Relates to spread of data
Enables you to evaluate homogeneity or heterogeneity
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17. Standard Deviation Most frequently used measure of variability
Average deviation of scores from mean
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18. Range Simplest but most unstable measure of variability
To what extent are the variables related?
Difference between the highest and lowest scores
Always reported with other measures of variability
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19. Percentile The percentage of cases a given score exceeds
Median is the 50th percentile
A score in the 90th percentile is exceeded by only 10% of scores
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20. Inferential Statistics
Combines mathematical processes and logical; allow researchers to test hypotheses about a population using data obtained from probability and nonprobability samples
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21. Hypothesis Testing Answers questions such as
How much of this effect is a result of chance?
How strongly are these two variables associated with each other?
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22. Hypothesis Testing (Cont.)
Scientific or alternative hypothesis (H1): Is what the researcher believes the outcome will be, that the variables will interact in some way
Null hypothesis (H0): Is the hypothesis that can actually be tested by statistical methods; states that no difference exists between the groups under study
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23. Probability
Support for the scientific hypothesis by rejecting the null hypothesis
This is done by applying probability theory.
Definition: An event’s long-run relative frequency in repeated trials under similar conditions
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24. Type I and Type II
Type I: Rejection of the null hypothesis when it is actually true
Type II: Accepting the null hypothesis when it is false
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25. Level of Significance (Alpha Level)
Probability of making type I error = 0.05
The researcher is willing to accept the fact that if the study was done 100 times, the decision to reject the null hypothesis would be wrong 5 times out of those 100 trials.
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26. Level of Significance (Alpha Level) (Cont.)
Can set probability at 0.01 if one wants a smaller risk of reflecting a true null hypothesis (the decision to reject the null hypothesis would be wrong 1 time out of 100 trials)
Selected alpha level depends on how important it is not to make an error.
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27. Practical versus Statistical Significance
A statistically significant hypothesis = finding unlikely to have occurred by chance
Magnitude of significance is important to the outcome of data analysis.
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28. Parametric versus Nonparametric
Parametric: More powerful and more flexible than nonparametric; used with interval and ratio variables
Nonparametric: Not based on the estimation of population parameters; used with nominal or ordinal variables
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29. Tests of Difference
Chi-square: Uses nominal data to determine whether frequencies in each group are different from what would be expected by chance
The t statistic: Tests whether the means of two groups are different
ANOVA: Tests variations between and within multiple groups
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30. Tests of Difference (Cont.)
ANCOVA: Measures differences among group means on an important variable
MANOVA: Measures differences in group means when there is more than one dependent variable
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31. Nonparametric Chi-square Fisher’s exact probability test
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32. Tests of Relationship
Exploring the relationship between two or more variables reflecting interval data
Determining the correlation, the degree of association (ranges from −1.0 to +1.0)
Most common (three names for same test)
Pearson product moment correlation coefficient
Pearson r
Pearson correlation coefficient
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33. Correlation Coefficients Range from
−1.0 to +1.0
Negative correlation
r = −0.38
Positive correlation
r = 0.65
Perfect correlation
r = +1.0 (positive) or –1.0 (negative)
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34. Nominal and Ordinal Data Tests of Relationships
Phi coefficient (dichotomous variables (e.g. M/F, yes/no))
Point-biserial correlation (relationship between nominal variable and interval variable)
Spearman’s rho- correlation between two sets
of ranks
Kendall’s tau-correlation between two sets
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35. Studying Complex Relationships among More than Two Variables
Multiple regression
One dependent variable
Multiple independent variables
Used to determine what variables contribute to change in the dependent variable and to what degree
Types of multiple regression
Forward solution-independent variable that has the highest correlation with the dependent variables is entered first and the next variable is the one that will increase the explained variance the most
Backward solution-all variables are entered into the solution and each variable is deleted to determine whether the explained variance drops significantly
Stepwise solution-combination of forward and backward solutions
Hierarchical solution
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36. Studying Complex Relationships among More than Two Variables.
Studying Complex Relationships among More than Two Variables
Hierarchical regression, on the other hand, deals with how predictor (independent) variables are selected and entered into the model. Specifically, hierarchical regression refers to the process of adding or removing predictor variables from the regression model in steps. For instance, say you wanted to predict college achievement (your dependent variable) based on high school GPA (your independent variable) while controlling for demographic factors (i.e., covariates). For your analysis, you might want to enter the demographic factors into the model in the first step, and then enter high school GPA into the model in the second step. This would let you see the predictive power that high school GPA adds to your model above and beyond the demographic factors. Hierarchical regression also includes forward, backward, and stepwise regression, in which predictors are automatically added or removed from the regression model in steps based on statistical algorithms. These forms of hierarchical regression are useful if you have a very large number of potential predictor variables and want to determine (statistically) which variables have the most predictive power ( 36

37. Studying Complex Relationships among More than Two Variables
Types of multiple regression-further explanation
Forward selection begins with an empty equation.  Predictors are added one at a time beginning with the predictor with the highest correlation with the dependent variable.  Variables of greater theoretical importance are entered first.  Once in the equation, the variable remains there.
Backward elimination (or backward deletion) is the reverse process.  All the independent variables are entered into the equation first and each one is deleted one at a time if they do not contribute to the regression equation.
Stepwise selection is considered a variation of the previous two methods.  Stepwise selection involves analysis at each step to determine the contribution of the predictor variable entered previously in the equation.  In this way it is possible to understand the contribution of the previous variables now that another variable has been added.  Variables can be retained or deleted based on their statistical contribution.
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38. Confidence Intervals
An estimated range of values that provides a measure of certainty about the sample findings
Most commonly reported in research is a 95% degree of certainty, meaning 95% of the time, the findings will fall within the range of values given as the CI.
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39. Odds Ratio
Used in harm studies to estimate if a participant has been harmed by being exposed to a particular event
Calculated by dividing the odds in the treatment or exposed group by the odds of the control group
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40. Meta-Analysis
Method that statistically combines findings from multiple studies focused on similar variables
Is usually a complex project, entailing an interdisciplinary team
Odds ratios often used
Provides the highest level of evidence in the evidence-informed hierarchy
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41. Advanced Statistics
Path analysis-
Structural equation modelling
Hz0
Factor analysis 41

42. Critical Thinking Decision Path: Descriptive Statistics
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43. Critical Thinking Decision Path: Inferential Statistics—Difference Questions
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44. Critical Thinking Decision Path: Inferential Statistics—Relationship Questions
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45. Critiquing Descriptive Statistics
Are appropriate descriptive statistics used?
What level of measurement is used?
Is the sample size large enough?
What descriptive statistics are reported?
Are these appropriate to the level of measurement used?
Are appropriate summary statistics provided for each major variable?
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46. Critiquing Inferential Statistics
Does the hypothesis reflect if differences or relationships are being tested?
Is the level of significance indicated?
Does the measurement level permit parametric testing?
Is the sample size large enough for parametric testing?
Is there enough information given to assess appropriateness of parametric use?
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47. Critiquing Inferential Statistics (Cont.)
Do the statistics used match the problem, hypothesis, method, sample, and level of measurement?
Are hypothesis results clearly presented?
Do tables and graphs enhance text?
Are the results understandable?
Are practical and statistical significance distinguishable?
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48. Take-Home Message?
Science and research prove nothing in isolation—research evidence only provides support for a theory.
One study’s findings are rarely sufficient to support a major practice change.
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