Chapter 11: Analysis Of Quantitative Data

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codebook

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A document that describes the procedure for coding variables and their location in a format for computers

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Code sheet

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Paper with a printed grid on which a researcher records information so that it can be easily entered into a computer . It is an alternative to the direct-entry method and using optical-scan sheets

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Direct -entry methods

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A method of entering data into a computer by typing data without code or optional -scan sheets

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Possible Code Cleaning

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Cleaning data using a computer in which the researcher looks for responses or answer categories that cannot have cases

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Contingency Cleaning

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Cleaning data using a computer in which the researcher looks at the combination of categories for two variables for logically impossible cases

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Descriptive Statistics

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A general type of simple stats used by researchers to describe basic patterns in the data

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Univariate Statistics

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Statistical measures that deal with one variable only

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Frequency distribution

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A table that shows the distribution of cases into the categories of one variable (i.e. the number or percent of cases in each category)

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histogram

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A type of bar chart used to visually display the distribution of a continuous variable

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bar chart

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A display of quantitative data for one variable in the form of rectangles where longer rectangles indicate more cases in a variable category. Usually , it is used with discrete data and there is a small space between rectangles. Rectangles can have a horizontal or vertical orientation. Also called a bar graph

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Pie chart

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A display of numerical information on one variable that divides a circle into fractions by lines representing the proportion of cases in the variable's attributes

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Mode

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A measure of central tendency for one variable that indicates the most frequent or common score

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bimodal

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A distribution with two modes

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Multimodal

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A distribution with more than one mode

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Median

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A measure of central tendency for one variable indicating the point or score at which half the cases are higher or lower

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Mean

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A measure of central tendency for one variable that indicates the arithmetic average (i.e. the sum of all scores divided by the total number of scores)

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Normal Distribution

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A "bell shaped" frequency polygon for a distribution of cases, with a peak in the centre and identical curving slopes on either side of the centre. It is the distribution of many naturally occurring phenomena and is the basis for much statistical theory.

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Skewed distribution

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A distribution of cases among the categories of a variable that is not normal (i.e. not a "bell shape"). Instead of an equal number of cases on both ends, more are at one of the extremes.

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range

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A measure of dispersion for one variable indicating the highest and lowest scores .

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Percentile

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A measure of dispersion for one variable that indicates the percentage of cases at or below a score or point

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Standard Deviation

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A measure of dispersion for one variable that indicates an average distance between the scores and the mean

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Bivariate statistics

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Statistical measures that involve two variables only

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Correlation

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The idea that two variables vary together , such that knowing the values in one variable provides information about values found in another variable

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Independence

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The absence of a statistical relationship between two variables (i.e. when knowing the values on one variable provides no information about the values that will be found on another variable). There is no association between them.

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Scattergram

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A diagram to display the statistical relationship between two variables based on plotting each case's values for both of the variables.

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linear relationship

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An association between two variables that is positive or negative across the attributes or levels of the variables. When plotted in a scattergram , the basic pattern of the association forms a straight line, not a curve or other pattern.

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Curvilinear relationship

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A relationship between two variables such that as the values of one variable increase, the values of the second show a changing pattern (e.g. first decrease then increase then decrease) . It is not a linear relationship

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Precision

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The amount of spread in the points on the graph. A high level of precision occurs when the points hug the line that summarizes the relationship. A low level occurs when the points are widely spread around the line

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Cross-tabulation

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Placing data for two variables in a contingency table to show the number or percentage of cases at the intersection of categories of the two variables

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Contingency Table

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A table that shows the cross tabulation of two or more variables . It is usually shows bivariate quantitative data for variables in the form of percentages across rows or down columns for the categories of one variable

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marginals

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The totals in a contingency table , outside the body of a table

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Measure of association

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A single number that expresses the strength , and often the direction, of a relationship . It condenses information about a bivariate relationship into a single number

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Control Variable

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A "third" variable that shows whether a bivariate relationship holds up to alternative explanations. It can occur before or between other variables.

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Partials

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In contingency tables for three variables , tables that show the association between the independent and dependent variables for each category of a control variable.

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Statistical Significance

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A way to discuss the likelihood that a finding or statistical relationship in a sample is due to random factors rather than due to the existence of an actual relationship in the entire population

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Level of Statistical Significance

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Set of numbers researchers use as a simple way to measure the degree to which a statistical relationship results from random factors rather than the existence of a true relationship among variables

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Type I error

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The logical error of falsely rejecting the null hypothesis

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Type II error

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The logical error of falsely accepting the null hypothesis