Copyright © 2011, 2005, 1998, 1993 by Mosby, Inc., an affiliate of Elsevier Inc. Chapter 19: Statistical Analysis for Experimental-Type Research

Copyright © 2011, 2005, 1998, 1993 by Mosby, Inc., an affiliate of Elsevier Inc. Objectives Define statistical analysis Discuss three levels of statistical analysis Compare and contrast procedures in descriptive statistics, inferential statistics, and associational statistics Utilize logic in choosing a statistical approach

Copyright © 2011, 2005, 1998, 1993 by Mosby, Inc., an affiliate of Elsevier Inc. What is Statistical Analysis? Statistical analysis is concerned with the organization and interpretation of data according to well-defined, systematic, and mathematical procedures and rules.  Data refers to information obtained through data collection.  In statistical analysis, data are represented by numbers.

Copyright © 2011, 2005, 1998, 1993 by Mosby, Inc., an affiliate of Elsevier Inc. r ea f648_804gy_324.jpg

Copyright © 2011, 2005, 1998, 1993 by Mosby, Inc., an affiliate of Elsevier Inc. Three Categories of Analysis 1.Descriptive 2.Inferential 3.Associational  Each level of statistical analysis corresponds to the particular level of knowledge about the topic  Corresponds to the specific type of question asked  Whether the data are derived from the population as a whole or are a subset or sample

6 Copyright © 2011, 2005, 1998, 1993 by Mosby, Inc., an affiliate of Elsevier Inc. Descriptive Statistics  Make up 1 st level of statistical analysis  Used to reduce large sets of observations into more compact and interpretable forms  First step of any analytical process  Typically involves counting occurrences, proportions, or distribution of phenomena

7 Copyright © 2011, 2005, 1998, 1993 by Mosby, Inc., an affiliate of Elsevier Inc. Univariate, Bivariate, Multivariate Analysis Univariate: The analysis of a single variable Bivariate: The analysis of two variables simultaneously Multivariate: the analysis of multiple variables simultaneously

8 Copyright © 2011, 2005, 1998, 1993 by Mosby, Inc., an affiliate of Elsevier Inc. Descriptive Statistics: Univariate  Frequency: how many of each score?  Percentage: what proportion of each score?  Measures of central tendency: mean, median, mode  Important information regarding the most typical or representative scores in a group

9 Copyright © 2011, 2005, 1998, 1993 by Mosby, Inc., an affiliate of Elsevier Inc. Frequency Distribution  Refers to both the distribution of values for a given variable and the number of times each value occurs.  Reflects a simple tally or count of how frequently each value of the variable occurs in the set of measured objects  Usually arranged in table format

10 Copyright © 2011, 2005, 1998, 1993 by Mosby, Inc., an affiliate of Elsevier Inc. Descriptive Stats: Univariate Measures of Dispersion or Variability  How diverse are scores?  Types of statistics that measure variability  Range  Interquartile Range  Sum of squares  Variance  Standard deviation

11 Copyright © 2011, 2005, 1998, 1993 by Mosby, Inc., an affiliate of Elsevier Inc.

12 Copyright © 2011, 2005, 1998, 1993 by Mosby, Inc., an affiliate of Elsevier Inc. Descriptive Stats: Univariate Measures of Dispersion or Variability (continued)  Standard deviation  m = 5m = 5  sd =.5sd = 2

13 Copyright © 2011, 2005, 1998, 1993 by Mosby, Inc., an affiliate of Elsevier Inc. Bivariate Descriptive Stats  Contingency table  Correlation  Pearson r  Spearman rho  Chi square

14 Copyright © 2011, 2005, 1998, 1993 by Mosby, Inc., an affiliate of Elsevier Inc. Inferential Statistics  2 nd level of statistics  Used to draw conclusions about population parameters based on findings from a sample  Concerned with tests of significance  Used to examine group differences within a sample  No need to use inferential stats when analyzing results from an entire population (purpose of inferential stats is to estimate population characteristics and phenomena from the study of a smaller group or sample)

15 Copyright © 2011, 2005, 1998, 1993 by Mosby, Inc., an affiliate of Elsevier Inc. Inferential Tests of Group Difference  To what extent are my sample statistics accurate for my population?  t-test  ANOVA and its variations  ANCOVA  MANOVA  Factorial ANOVA

16 Copyright © 2011, 2005, 1998, 1993 by Mosby, Inc., an affiliate of Elsevier Inc. Associational Statistics  3 rd level of statistics  Refers to a set of procedures designed to identify relationships between and among variables and determine whether knowledge of one set of data allows the investigator to infer or predict the characteristics of another set

17 Copyright © 2011, 2005, 1998, 1993 by Mosby, Inc., an affiliate of Elsevier Inc. Associational  Multiple regression: what factors predict a continuous score?  Discriminant function analysis: what factors predict a category?

18 Copyright © 2011, 2005, 1998, 1993 by Mosby, Inc., an affiliate of Elsevier Inc. Use of Images in Statistical Analysis  Geostatistical analysis: locating data within the confines of specified geography  Other forms of visual analysis (e.g., graphics, three-dimensional figures, timelines)