12. The Senate consists of 100 senators, of whom 34 are Republicans and 66 are Democrats. A bill to increase defense appropriations is before the Senate. Thirty-five percent of the Democrats and 70% of the Republicans favor the bill. The bill needs a simple majority to pass. Using a probability tree, determine the probability that the bill will pass.
14. A metropolitan school system consists of three districtsnorth, south, and central. The north district contains 25% of all students, the south district contains 40%, and the central district contains 35%. A minimum-competency test was given to all students; 10% of the north district students failed, 15% of the south district students failed, and 5% of the central district students failed.
a. Develop a probability tree showing all marginal, conditional, and joint probabilities.
b. Develop a joint probability table.
c. What is the probability that a student selected at random failed the test?
Chapter 19
Basic Quantitative Data Analysis
Data Cleaning
Check for odd symbols, truncated or overlong times
Recheck scoring
Recheck coding categories
Compare one variable value with value in second variable
Look for outliers
2
Reasons for Missing Data
Participant skipped item or questionnaire, purposely or inadvertently
Participant withdrew, became ill, or died
Had to omit all or part of the data collection
Poor directions or poorly worded question
Data missed during data entry
3
Categorizing Missing Data
Missing completely at random (MCAR)
Missing at random (MAR)
Missing not at random (MNAR)
4
Replacing Missing Data
Complete case analysis is when you drop any participant from the analysis when they have missing data
If a lot of participants are missing data it may negatively impact the results
5
Replacing Missing Data
Principles in handling missing data are:
Some missing data cannot be replaced
Imputation uses existing information to estimate the missing values
The easiest approach is to replace missing data with the group’s mean (average) on the item
6
Replacing Missing Data
Principles in handling missing data are:
A more justifiable approach is to use the average of the individual participant’s scores or ratings on the remaining items of a multi-item scale
Missing values may be estimated from values at previous time points
7
Replacing Missing Data
Principles in handling missing data are:
Incomplete cases (participants) may be deleted and the analysis may be done on those who completed the study
A regression imputation may be done to estimate the values of the missing data
8
Replacing Missing Data
Principles in handling missing data are:
Expectation maximization uses a series of iterations to reach convergence
Multiple imputation contrasts and combines replacement values to find the best estimates
9
Visual Representations
Stem and leaf illustrates distribution of values
Box plots illustrate distribution of values
Bar and pie charts demonstrate differences between groups and subgroups
Plots can show relationships between interval level variables
10
Basic Descriptive Statistics
Normal distribution is represented by a symmetrical bell-shaped curve
Positive skew has more cases at low end of values
Negative skew has more cases at high end of values
11
Basic Descriptive Statistics
Mode is the value that occurs most often
Median is the middle score in the distribution
Mean is the average of all scores
12
Basic Descriptive Statistics
Range is the distance between the highest and lowest scores
The range or distance between these endpoints can be divided into various portions
13
Basic Descriptive Statistics
Variance is the average of the squared deviations from the mean
Standard deviation is the square root of the variance
14
Bivariate Association
Bivariate refers to relationships between a set of variables
Pearson product moment correlation coefficient represented as r is the most commonly used bivariate measure of association
15
Bivariate Association
A correlation matrix can be used to analyze multiple variables at one time to see the differences in the strengths of relationships between various pairs of variables
You may also calculate the coefficient of determination (R2)
16
Additional Measures of Association
Spearman rank-order correlation is used for ordinal data
The chi-square statistic is used for nominal data
17
Additional Measures of Association
Fisher’s Exact Test is used if there are less than five cases per cell
The Mann-Whitney U Test is used instead of chi-square if the data are ordinal
18
Chapter 18
Quantitative Data Management
Data Management
You should review data as soon as it is collected in order to check for:
Consent forms are complete and signed
No duplicate identification numbers were given
No data is missing
Scoring was done correctly
Handwriting is legible
2
Managing the Data
In order to more efficiently manage the data consider:
Setting up a tracking system
Keeping data secure
Developing a filing system for your data
Ensuring each file is complete
Coding items as needed
3
Selecting the Software for the Database
When thinking about what software you need consider:
Is your data quantitative, qualitative, or both?
How will you analyze the data?
Will the data analysis be simple or complex?
How do you want to present your results?
4
Selecting the Software for the Database
When thinking about what software you need consider:
Is there support for the software?
What is the cost of the software?
Is the software compatible with your system?
5
Database Creation
Pilot test the software if never used before
Develop a codebook
Create the database
Input the data
6
Considerations in Building a Database
Think ahead to how you will use the data
Provide meaningful names for variables
Put accuracy checks in place
Test the database with preliminary analysis
7

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