Chapter 13

Descriptive Data Analysis

Statistics

Science is empirical in that knowledge is acquired by observation

Data collection requires that we make measurements of our observations

Measurements then yield data Statistics are used for analyzing data

3 Basic Steps in Data Analysis

1. Select the appropriate statistical technique2. Apply the technique3. Interpret the result

Descriptive statistics

Used to organize, simplify, and summarize the collected data

Data typically consist of a set of scores called a distribution. These scores result from the measurements taken

The original measurements or values in a distribution are called raw scores

Types of Scores

Continuous a continuous progression from the smallest possible

amount to the largest possible amount, with measurement theoretically possible at any point along the continuum; may be expressed as a fraction (e.g., height, weight, temperature, strength)

Discrete measurement and classification are possible only in

whole units; no fractional units (e.g., size of family, number of schools in country)• Dichotomous – 2 category variable (yes/no;

alive/dead)

Scales of Measurement

Nominal Ordinal Interval Ratio

Nominal

Merely classifies objects in accordance with similarities and differences with respect to some property; no hierarchy of scores

Examples • color of hair• gender• response to a yes/no question• shoe preference

Ordinal

Type of data that is characterized by the ability to rank order on the basis of an underlying continuum

No common unit of measurement Examples

• class ranks• place of finish in a race

Interval

Data having known and equal distances between score units, but having an arbitrary zero point

Example• temperature on Fahrenheit scale

Ratio

Possesses same properties of interval data, but does have a true zero point

Examples• height or weight• distance measurement

Computer Analysis

Variety of computer programs for statistical computations; mainframe and desktop SPSS

• See Appendix A in textbook for more information SAS Statview Excel

Fast, easy to use, widely available

Organizing and Graphing Scores

Frequency distributions Simple frequency distribution Group frequency distribution

Graphing techniques Histogram Frequency polygon

Normal curve Bell-shaped curve Skewed distribution

Simple Frequency Distribution

Score Frequency Cumulative Freq.

X f cf

22 1 15

19 2 14

18 3 12

17 5 9

16 2 4

13 1 2

11 1 1

Group Frequency Distribution

Class Interval f cf

66 – 68 2 30

63 – 65 4 28

60 – 62 2 24

57 – 59 2 22

54 – 56 2 20

51 – 53 3 18

48 – 50 2 15

45 – 47 1 13

Histogram

0

1

2

3

4

5

6

11 13 16 17 18 19 22

Fre

quen

cy

Frequency Polygon

0

1

2

3

4

5

6

11 13 16 17 18 19 22

Fre

quen

cy

Normal Curve

Symmetrical Curves

Distribution Shapes

Types of Descriptive Statistics

Measures of Central Tendency mean median mode

Measures of Variability standard deviation variance range minimum/maximum

Measuring Group Position

Percentile ranks and percentile Standard scores

z score T score

Relationships Among Variables

Correlational Statistics Correlation is a family of statistical techniques

that is used to determine the relationship between 2 or more variables• correlation coefficient ranges from -1.0 to +1.0• scatterplot is a graphic illustration of the

relationship between 2 variables• correlation provides information about the

magnitude and direction of a relationship, but does not imply a cause-and-effect relationship between the variables

Correlational Techniques

Pearson product-moment correlation (r) requires interval or ratio scores every subject has scores on two variables most frequently used

Spearman rank-order correlation (rs) nonparametric technique for use with ordinal

scores every subject has scores on two variables

Interpretation of Correlation

Coefficient of determination (r2) Portion of the total variance in a variable that

can be explained or accounted for by the variance of the other variable

Square of the correlation coefficient

If r = .70 … then r2 = .49

Question of Accuracy

Linear relationship Curvilinear relationship Reliability of test scores

Low reliability reduces correlation Range of scores

Correlation will be smaller for a homogeneous group than a heterogeneous group