Quantitative Analysis

Define Quantitative AnalysisDescribe the coding process

Identify two functions of codebooksPractice doing a codebook format

Describe ways to enter dataGive examples of univariate analysis

Explain central tendency and issues that surround itDistinguish discrete from continuous variables

Differentiate the goals of univariate, bivariate, and multivariate analysesIdentify the goal of subgroup comparisons

Differentiate dependent from independent variablesShow how bivariate data are presented and analyzed

Show how multivariate data are presented and analyzed

Assignment for 4/1

• Qualitative Article Review• 2-3 page review describing the

relevant components of the research

• Critique of whether or not the study has been done right

• What improvements, if any, are needed? If none needed, what are the strengths of the study?

• Quantitative analysisNumerical representation and manipulation of observations for the purpose of describing and explaining the phenomena that those observations reflect.

Sources of Quantitative Data

• Questionnaires• Rating forms• Measurements• Open-ended questions• Field observations

Terminology

• Attribute – A characteristic of a person or thing.

• Variable – A logical grouping of attributes.

Variables

• Independent– Variable with values that are not

problematical in an analysis , but are simply taken as given—it causes or determines a dependent variable

• Dependent– Variable assumed to depend on or be

caused by another (D=income, I=educ)

• (Intervening)

• Continuous variableIncreases steadily in tiny fractions.

• Discrete variableJumps from category to category without intervening steps.

Levels of Data

• Nominal• Ordinal• Interval • Ratio

• Important when determining codes for independent and dependent variables

What level of data are they?

•Age•Sex•Blood pressure•IQ•Income•Job title•Finish place in race•Ethnicity

•# of work-outs per week•Test score•Job responsibility classification•Temperature•Height•Satisfaction level (Likert scale)

Developing Code Categories

Two basic approaches:• Beginning with a coding scheme

derived from the research purpose.• Generate codes from the data.

Coding:• Code categories should be

exhaustive and mutually exclusive.• Reliability

Student Responses That Can Be Coded “Financial Concerns”

Financial Concern

s

Tuition is too high x

Not enough parking spaces

Faculty don’t know what they are doing

Books cost too much x

Not enough classes offered

Not enough financial aid x

Codebook Construction

Purposes:• Primary guide used in the coding

process.• Document that describes the

locations of variables and lists the assignments of codes to the attributes composing those variables.

Entering Data

• Data entry specialists enter the data into an SPSS data matrix or Excel spreadsheet.

• Optical scan sheets.• PDAs.• Part of the process of data

collection.

Transforming and Missing Data

• Transform – A specific function in SPSS that can recode variables– Age into age categories

• Missing or misrepresented responses?

Types of Analyses

• Univariate• Bivariate• Multivariate

• Univariate analysisDescribes a case in terms of a single variable - the distribution of attributes that comprise it.

• Frequency distribution (f =)Description of the number of times that the various attributes of a variable are observed in a sample.

Descriptive Statistics

•Frequencies•Percentages•Central tendency

–Mean–Median–Mode

•Dispersion measures

–Range–Variance–Standard deviation

Graphical Representation - Frequencies

•Pie Charts•Bar Graph•Histogram

SPSS Analysis: GSS Attendance at Religious Services, 2000

Value Label Value Frequency %

Valid %

Cum%

Never 0 583 20.7 21.3 21.3

Lt Once A Year 1 219 7.8 8.0 29.3

Once A Year 2 234 11.9 12.2 41.5

Sevrl Times A

Yr 3 369 13.1 13.5 55.0

• AverageMeasure of central tendency.

• Mean (x bar)Result of diving the sum of the values by the total number of cases.

• ModeThe most frequently occurring attribute.

• MedianMiddle attribute in the ranked distribution of observed attributes.

• DispersionRefers to the way values are distributed around some central value.

• Range = X(max) – X(min)• Interquartile range

• Standard deviationIndex of the amount of variability in a set of data.

Basketball Example

•Team #101101420

•Team #28891010

Calculating Std. Deviation and Variance

1. Calculate the mean2. Subtract the mean from each score

(this is your deviation score)3. Square the deviation scores4. Add the squared deviation scores5. Divide this number by n-16. Take the sq. root of this number7. Square the number

What do the data look like?(Distribution Curves)

• Normal distribution– 68/95% rule

• Skewness– Positive– Negative

Univariate Analysis

• Describing a case in terms of the distribution of attributes that comprise it.

Example:• Gender - number of women, number

of men.

Presenting Univariate Data

Goals:• Provide reader with the fullest

degree of detail regarding the data.• Present data in a manageable from.

Subgroup Comparisons

• Describe subsets of cases, subjects or respondents.

Examples• "Collapsing" response categories.• Handling "don't knows."

• Bivariate analysisAnalysis of two variables simultaneously. Focus is on the variables and the empirical relationships.

• Descriptive, univariate• Inferential, bivariate & multivariate

Bivariate Analysis

• Describe a case in terms of two variables simultaneously.

• Example:– Gender– Attitudes toward equality for men and

women

• Contingency tablesValues of the dependent variable are contingent on values of the independent variable.

Constructing Bivariate Tables

• Divide cases into groups according to the attributes of the independent variable.

• Describe each subgroup in terms of attributes of the dependent variable.

• Read the table by comparing independent variable subgroups in terms of an attribute of the dependent variable.

Construct a contingency Table

• 150 Fathers favor year-round schools and 50 oppose it; 100 Mothers favor year-round schools and 300 oppose it

So what’s the deal on significance?

• Statistical significance = unlikeliness that relationships observed are due to chance

• Significance level= .05 (based on probability)

• Type I Error• Type II Error

**The key is how meaningful the results are- not necessarily if statistically significant.

Tests of Associations

• Chi-square (nominal, ordinal data)– Expected vs. observed– Phi (2x2)– Cramer’s V (larger tables)

• Correlations (Pearson, Spearman)– Depends on level, sample size– +1 and –1 (perfect correlations) 0= none– Used to determine reliability– Correlation does not equal to causation– Gives p value but the corr statistic more useful

Tests of Difference (Parametric)

• Parametric- compares means• Non-parametric- compares ranks (median

based)• T-test (grouped data with 2 values)

– Indep usually nominal/ordinal & dep usually interval/ratio

– Indep t-test (2 groups) – matched pairs t-test (same group at 2 times)– Reports as a t statistic (check Lavene’s)– Check means to determine differences

Tests of difference… con’t

• Analysis of variance (2+ groups on indep with nominal/ord and int/ratio dep)– Post hoc to determine which groups

differ– F statistic (like the t statistic)– Check for meaningfulness

Test of Difference (non-parametric)

• Mann-Whitney U test (like indep t-test)• Sign test (like matched t-test)• Wilcoxin Signed Ranks test- like t-test

when dependent has more than 2 ranked values

• Kruskal-Wallis (like oneway)• Friedman Analysis of variance (repeated

measures)

Multivariate Analysis

• Analysis of more than two variables simultaneously.

• Can be used to understand the relationship between two variables more fully.

Things to remember about stats…

• Pay attention to levels of your data• Identify independent and dependent

variables• Know when to choose parametrics/ non-

parametrics and the appropriate test• P< .05• Check for meaningfulness• Sometimes not finding significance is

more important

Quantitative Analysis

• Univariate - simplest form,describe a case in terms of a single variable.

• Bivariate - subgroup comparisons, describe a case in terms of two variables simultaneously.

• Multivariate - analysis of two or more variables simultaneously.