S8 - Quantitative Research: Analyzing (Bivariate Analysis) Flashcards
What do we use bivariate analysis for?
Analyzing the links between different variables
What all are the types of bivariate analysis?
- Cross tabulations: Frequencies between variables. Nominal and ordinal.
- Correlations: Strength of a linear relationship. Scale.
- Regressions: To see trends in variables (impact/dependence). Scale.
- T-test & Anova: Comparison of means. All types of measurement scales.
Describe the bivariate analysis process
- Return to research objectives and univariate analysis
- Formulate relationships between variables (used to guide analysis)
- Determine the type of analysis needed
- Conduct the test
- Interpret and integrate
- Repeat for other relationships
What are the types of differences between responses?
- Mathematical difference: If numbers are not exactly the same, they are different. Doesn’t mean that the difference is significant or important.
- Statistical difference: If a particular difference is large enough to be unlikely to have occurred because of chance or sampling error. If we repeat the survey with another group, we will obtain the same results.
- Managerially important differences: One can argue that a difference is important from a managerial perspective only if results or numbers are sufficiently different.
Describe Hypothesis Testing.
H0: There is no difference between the two variables
H1: There is a difference between two variables
Test at .05% levels of significance
How to conduct Cross-Tabulation?
Cross tabulations: Frequencies between variables. Nominal and ordinal only.
Test = Chi-square
Analyze -> Descriptive statistics -> Cross-Tabulation
Row: Variables where we want to see if there is a difference (ex.: gender)
Columns: Choice variable.
Modifications
Cells: Observed
Statistics: Chi-square (how we want to see percentages)
Graphs we will see
Variable x and y Crosstabulation
Then, Chi-square test to see if the differences seen in the graph above are significant or not (asymptotic Significance (2-sided)).
How to conduct Correlations?
- Correlations: Strength of a linear relationship. Scale.
-1: Negative strong
1: Positive strong
Force of correlation (r)
Small: 0.1 < r < 0.29
Medium: 0.3 < r < 0.49
Large: 0.5 < r < 1
Analyze -> Correlate -> Bivariate
Put two variables of interest, select “means and standard deviations”
H0: There is no relation between the two variables.
H1: There is a relation between the two variables.
Pearson Correlation: Correlation
Sig (2 tailed): Significance
How to conduct Regressions?
Regressions: To see trends in variables (impact of x on y). Scale.
Positive inclination/slope: positive correlation
Negative inclination/slope: negative correlation
No inclination/slope: no correlation
Regression: See if there is a dependency and not just correlation.
H0: X has no impact on Y
H1: X has a positive/negative impact on Y
Analyze -> Regression -> Linear
Identify X (ex.: income) and Y (dependant, ex.: spending habits) variables.
Modifications
Statistics: Descriptives.
Analysis
Correlation tables
X variable & Y: Person Correlation
Sig. (1-tailed): Significance
Model Summary
R square: % of the variability of Y that can be explained by X
Coefficients
Significance
What are the three types of analysis that we can do with mean comparisons?
- Independent sample t-test: The comparison of two independent means. Is there a difference between two unrelated groups?
- Paired sample t-test: The comparison of two paired means. Is there a difference within the same group between 2 points in time?
- ANOVA test: One-factor analysis of the variance. Multiple variables rated by different groups. 3 or more independent groups.
H0: Both variables have the same mean/average/mode.
H1: Both variables don’t have the same mean/average/mode
How to conduct an independent sample t-test?
Independent sample t-test: The comparison of two independent means. Is there a difference between two unrelated groups?
Conditions:
- 1 non-metric variable (nominal or ordinal) and a metric variable (scale)
- Nominal/Ordinal consists of only 2 responses
- The people who respond to the scale variable are different.
Ex.: Is there a difference between male and female in the way they evaluate a certain brand on a scale from 1-5.
Analyze -> Compare Mean -> Independent sample t-test
Test variables: Scale question (Y)
Grouping variable: Nominal/Ordinal (X)
Define Group: Male=1 and Female =2
Analysis
Group Statistics: We can see the two mean
Independent sample t-test: Significance
How to conduct an paired sample t-test?
Paired sample t-test: The comparison of two paired means. Is there a difference within the same group between 2 points in time?
Conditions:
- There is one non metric variable (Nominal/Ordinal) and a metric variable (scale) OR two metric variables (scale).
- The number of possible responses to the nominal/ordinal variable doesn’t matter.
- The respondents to the scale variable are the same.
Ex.: Rate scale 1-5 flavor of ice cream before and after them trying it.
Analysis -> Compare Means -> Paired sample t-test.
Analysis
Paired Samples Statistics: Compare Means
Paired Samples Test: One-Sided p (Significance)
How to conduct an ANOVA test?
ANOVA test: one-way analysis of the variance. 3 or more independent groups.
Conditions
- There is a non-metric variable (nominal/ordinal) and a metric variable (scale)
- The number of possible responses to the nominal or ordinal variable should be bigger than two
- The respondents to the scale variable are different
Ex.: Current marital status and rate each of the following activities on a scale from 1-5.
Analyze -> Compare Means -> One-way ANOVA
Factor: X variable (marital status)
Dependant list: all the scales for each activities
Options: Descriptive statistics
Post Hoc: LSD
Analysis
Descriptives: Compare all the means
ANOVA: Significance
Multiple Comparisons: Among which groups there is a significant difference in means
