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 technique 2.Apply the technique 3.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 ScoreFrequencyCumulative Freq. Xfcf

Group Frequency Distribution Class Intervalfcf 66 – – – – – – – – 47113

Histogram

Frequency Polygon

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 (r s )  nonparametric technique for use with ordinal scores  every subject has scores on two variables

Interpretation of Correlation  Coefficient of determination (r 2 )  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 r 2 =.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