Descriptive Statistics

Histogram

graphic showing distribution of quantitative variable. Looks like bar graph except there is no space between the bars.

Range

is a crude indicator of variability. Difference between highest and lowest numbers. Example: range in Set A just shown is 7; range in Set B is 90.

Descriptive Statistics- definition

is the application of statistical techniques to summarize and make sense of a particular set of data.

Scatter plot

depict relationship between two quantitative variables. IV or predictor variable placed on X axis (horizontal axis) and DV on Y axis (vertical axis).

Percentile rank

percentage of scores in reference group falling below particular score. Example: percentile rank of 93 means 93% of scores in reference group fall below raw score.

Measures of relative standing

provide information about a particular score in relation to other scores. Commonly used measures: percentile ranks and z scores.

Data set

set of data with the cases in rows and variables in columns). Example shown in Table 17.1. A statistical program (such as SPSS) is typically used to obtain descriptive statistics.

Standard deviation

square root of the variance (converts squared units to regular units).

Measures of central tendency

a numerical value is obtained that is considered typical of the quantitative variable. Most common measures: Mode- most frequently occurring number Median- center point in set of numbers Mean- arithmetic average

Variance

average deviation from the mean (in squared units).

Grouped frequency distribution

data are grouped into intervals and frequency of each interval shown

Frequency distribution

frequency of each unique data value are shown. Example is shown in Table 17.2. In the example, the frequency distribution is shown in the second column; the third column shows the "percentage distribution"

z score

shows how many standard deviations (SD) raw score falls from mean. z score of 2: score falls two standard deviations above mean. z score of -3.5: score falls three and a half standard deviations below mean.

Measures of Variability

tells how "spread out" or amount of variability present in set of numbers. Greater variability means numbers very different. Less variability means numbers not very different.

Line graph

use line(s) to depict information about variable(s). Simple line graph can show trend.

Regression analysis

used to explain or predict values of quantitative dependent variable based on values of one or more independent or predictor variables. Simple regression - one quantitative DV and one IV. Multiple regression - one quantitative DV and two or more IVs. Regression equation - defines regression line (see Figure 17.9 for depiction of reg. line).

Bar Graph

uses vertical bars to represent data. Height of bars shows frequencies of categories. Used for categorical variables.

Comparison of Mean, Median, Mode (Skew)

If normally distributed, no skew. When variable skewed to left (negatively skewed), mean shifts to left the most, median shifts second most, and mode least affected. When data are negatively skewed: mean < median < mode. When variable skewed to right (positively skewed): mean > median > mode. Resulting rules: Rule One. If mean less than median, data are skewed to the left. Rule Two. If mean greater than median, data are skewed to the right.

Contingency Tables

Displays information in cells formed by the intersection of two or more categorical variables.

Graphical representations of data

Graphical representations of data are pictorial representations of data. Common representations: bar graphs Histograms line graphs scatter plots.

Normal Curve

Has a bell shape. If data normally distributed then "68, 95, 99.7 percent rule" applies. Approximately 68% of cases fall within 1 standard deviation of mean. Approximately 95% of cases fall within 2 standard deviations. Approximately 99.7% fall within 3 standard deviations.