Chapter 13 - Descriptive data analysis. The main contents of the chapter consist of the following: Statistics, 3 basic steps in data analysis, descriptive statistics, types of scores, scales of measurement, computer analysis,...
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 Select the appropriate statistical technique Apply the technique 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 Bellshaped curve Skewed distribution Simple Frequency Distribution Score Frequency Cumulative Freq X f cf 22 15 19 14 18 12 17 16 13 11 1 Group Frequency Distribution Class Interval f cf 66 – 68 30 63 – 65 28 60 – 62 24 57 – 59 22 54 – 56 20 51 – 53 18 48 – 50 15 45 – 47 13 Histogram Frequency 11 13 16 17 18 19 22 Frequency Polygon Frequency 11 13 16 17 18 19 22 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 andeffect relationship between the variables Correlational Techniques Pearson productmoment correlation (r) requires interval or ratio scores every subject has scores on two variables most frequently used Spearman rankorder correlation (r ) s 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 ... 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 ... 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... 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