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**Summary of Quantitative Analysis Neuman and Robson Ch. 11**

Data Analysis Summary of Quantitative Analysis Neuman and Robson Ch. 11

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**Analyzing Quantitative Data (for brief review only)**

Parametric Statistics: -appropriate for interval/ratio data -generalizable to a population -assumes normal distributions Non-Parametric Statistics: -used with nominal/ordinal data -not generalizable to a population -does not assume normal distributions

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Tables and Graphs Frequency tables with percentages give a numerical description of the cases on a variable. Graphs like bar or pie graphs are used to display nominal or ordinal data Histograms and line graphs (frequency polygons) can display interval/ratio level data. Bivariate relationships can be displayed using contingency tables (nominal or ordinal) Relationships at the interval/ratio level are displayed using a scatterplot.

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**Basic Descriptive Statistics**

Use summary measures such as mean (interval), median (ordinal), or mode (nominal) to describe central tendency of a distribution For dispersion (variability) use standard deviation, variance, and range to tell you how spread out the data are about the mean. Can use z-scores to compare scores across two distributions

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**Contingency (Cross-Tabs) Analysis and Related Statistics**

- for non-parametric (non-normal distributions) statistics Assumptions Nominal or ordinal (categorical) data Any type of distribution The hypothesis test: The null hypothesis: the two (or more) samples come from the same distribution

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**Contingency (cont.) Conducting the Analysis: **

a. calculate percentages within the categories of the IV and compare across the categories of the DV. Are there differences in the outcomes? b. for nominal Chi-square statistic: is the relationship (the above differences) real? Phi, Cramer's V, etc.: how strong is the relationship? c. for ordinal t-test for gamma: is the relationship (the above differences) real? Gamma: how strong and what direction?

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**T-Tests (parametric) for Means and Proportions**

The t-test is used to determine whether sample(s) have different means. Essentially, the t-test is the ratio between the sample mean difference and the standard error of that difference. The t-test makes some important assumptions: Interval/Ratio level data one or two levels of one or two variables normal distributions equal variances (relatively).

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**T-tests (cont.) a. The one sample t-test:**

tests a sample mean against a known population mean b. The independent samples t-test: tests whether the mean of one sample is different from the mean of another sample. c. The paired group t-test (dependent or related samples) tests if two groups within the overall sample are different on the same dependent variable.

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ANOVA (parametric) Analysis of Variance, or ANOVA, is testing the difference in the means among 3 or more different samples. One-way ANOVA Assumptions: One independent variable -- categorical with two+ levels Dependent variable -- interval or ratio ANOVA is testing the ratio (F) of the mean squares between groups and within groups. Depending on the degrees of freedom, the F score will show if there is a difference in the means among all of the groups.

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ANOVA (cont.) One-way ANOVA will provide you with an F-ratio and its corresponding p-value. If there is a large enough difference between the between groups mean squares and the within groups mean squares, then the null hypothesis will be rejected, indicating that there is a difference in the mean scores among the groups. However, the F-ratio does not tell you where those differences are, only that one group mean is significantly different from the others.

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**Correlation (parametric)**

Used to test the presence, strength and direction of a linear relationship among variables. Correlation is a numerical expression that signifies the relationship between two variables. Correlation allows you to explore this relationship by 'measuring the association' between the variables. Correlation is a 'measure of association' because the correlation coefficient provides the degree of the relationship between the variables. Correlation does not infer causality! Typically, you need at least interval and ratio data. However, you can run correlation with ordinal level data with 5 or more categories.

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Correlation (cont.) The Correlation Coefficient : Pearson's r, the correlation coefficient, is the numeric value of the relationship between variables. The correlation coefficient is a percentage and can vary between -1 and +1. If no relationship exists, then the correlation coefficient would equal 0. Pearson's r provides an (1) estimate of the strength of the relationship and (2) an estimate of the direction of the relationship. If the correlation coefficient lies between -1 and 0, it is a negative (inverse) relationship, 0 and +1, it is a positive relationship and is 0, there is no relationship The closer the coefficient lies to -1 or +1, the stronger the relationship.

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Correlation (cont.) Coefficient of determination: provides the percentage of the variance accounted for both variables (x & y). To calculate the determination coefficient, you square the r value. In other words, if you had an r of 90, your coefficient of determination would account for just 81 percent of the variance between the variables.

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Regression Regression is used to model, calculate, and predict the pattern of a linear relationship among two or more variables. There are two types of regression -- simple & multiple a. Assumptions Note: Variables should be approximately normally distributed. If not, recode and use non-parametric measures. Dependent Variable: at least interval (can use ordinal if using summated scale) Independent Variable: should be interval. Independent variables should be independent of each other, not related in any way. You can use nominal if it is binary or 'dummy' variable (0,1)

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**Regression (cont.) b. Tests c. Statistics d. Limitations**

Overall: The null tests that the regression (estimated) line no better predicting dependent variable than the mean line Coefficients (slope "b", etc.): That the estimated coefficient equals 0 c. Statistics Overall: R-squared, F-test Coefficient: t tests d. Limitations Only addresses linear patterns Variables should be normally distributed

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**Using Computer Software to Analyze Quantitative Data**

Special statistical software is available to analyze large quantities of data and to do more complex analyses The most common computer software used in sociology are SPSS and SAS SPSS is available at both the King’s and Brescia computer labs and as well in various computer labs on main campus.

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