FOUNDATIONS OF NURSING RESEARCH Sixth Edition CHAPTER Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Descriptive Statistics 14

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Learning Objectives 1.Recognize Statistical Symbols For Population Parameters And Sample Statistics 2.Identify The Two Broad Classifications Of Statistics 3.Discuss Four Major Groups Of Descriptive Statistics

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Learning Objectives 4.Compare Categories Within Each Of The Four Major Groups Of Descriptive Statistics 5.Determine Appropriate Descriptive Statistics To Use In Presenting Selected Data 6.Construct Graphs To Present Selected Descriptive Statistics

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Learning Objectives 7.Critique Descriptive Statistics Presented In Research Reports

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Learning Objective One Learning Objective One Recognize Statistical Symbols For Population Parameters And Sample Statistics

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Statistical Terms Parameters used when discussing populations Statistics used when discussing samples

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Determining Type of Statistical Data Greek letter mu (μ)—population parameters English letters s or SD—sample statistics

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Trends in Literature Words instead of symbols –mean or standard deviation

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Learning Objective Two Learning Objective Two Identify The Two Broad Classifications Of Statistics

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Descriptive Statistics Organize and summarize numerical data collected from samples Allows examination of study participants’ –Characteristics –Behaviors –Experiences

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Inferential Statistics Concerned with populations Use sample data to make inferences about a population Help determine real differences versus chance differences

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Descriptive Versus Inferential Statistics Descriptive—examine characteristics of study participants Inferential—determine if sample is representative of population

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Learning Objective Three Learning Objective Three Discuss Four Major Groups Of Descriptive Statistics

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Descriptive Statistics Measures to condense data Measures of central tendency Measures of variability Measures of relationships

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Measures to Condense Data Summarize data Frequency distributions Graphic presentations Percentages

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Measures of Central Tendency Average distribution or most common value for a group of data Mean Mode Median

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Measures of Variability Describe how spread out the values are in a distribution Range Percentile Standard deviation Variance Z scores

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Measures of Relationships Concern the correlations between variables Correlation coefficients Scatter plots Contingency tables Correlational procedures

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Learning Objective Four Learning Objective Four Compare Categories Within Each Of The Four Major Groups Of Descriptive Statistics

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Measures to Condense Data Frequency distribution –All values or scores are listed. –Number of times each one appears is recorded.

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Measures to Condense Data— Frequency Distribution Distribution is small. –Score listed individually Range of scores is large. –Group the scores before counting frequencies –The groups of scores are called class intervals.

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Measures to Condense Data— Frequency Distribution (cont’d) Symmetrical distributions Skewed, or nonsymmetrical, distributions –Positively skewed –Negatively skewed

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Measures to Condense Data— Frequency Distribution (cont’d) Normal distribution –Symmetrical distribution –One set of values in the middle of the distribution –Bell-shaped curve

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Measures to Condense Data— Graphic Presentations Data may be presented in a graphic form. –Visually appealing –According to the level of measurement of the variable to be presented

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Measures to Condense Data— Graphic Presentations (cont’d) Bar graph –Represents frequency of occurrence –Illustrates distribution of nominal data and some types of ordinal data Histogram –Graph that uses bars to represent the frequency distribution of a variable –Illustrates variables measured at the ordinal, interval, or ratio level

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Measures to Condense Data— Graphic Presentations Frequency polygon –Graph using dots connected with straight lines –Represents frequency distribution of ordinal, interval, or ratio data

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Measures to Condense Data— Percentages Number of parts per hundred that a certain portion of the whole represents Statistic representing the proportion of a subgroup to a total group Expressed as a percentage ranging from 0 to 100

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Measures of Central Tendency Mode (Mo) –Category or value that occurs most often Modal class –Category with the greatest frequency –Unimodal –Bimodal –Multimodal

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Measures of Central Tendency (cont’d) Median (Md or Mdn) –Middle score or value Mean (M or ˆ “x-bar”) –Average sum of a set of values x

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Measures of Variability Range –Distance between highest and lowest value Interquartile range (IQR) –Middle half of the values Semiquartile range (SQR) –Half the interquartile range

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Measures of Variability (cont’d) Percentile –Datum point below which lies a certain percentage of the values –Common statistic used to compare performance with others

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Measures of Variability (cont’d) Standard deviation (SD or s) –Measurement that indicates the average variation of all the values in a set from the mean value

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Measures of Variability (cont’d) Variance –Measure used in several inferential statistical tests Z score –Score indicating how many standard deviations from the mean a value lies –Interpreted in relation to SD units above or below the mean

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Measures of Relationships Correlation coefficient (r) –Magnitude and direction of relationship between two variables –Can vary between –1.00 and –Zero (0) indicates the absence of any relationship.

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Measures of Relationships (cont’d) Positive relationship –Two variables tend to increase or decrease together. Negative relationship –As one variable increases, the other variable tends to decrease.

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Measures of Relationships (cont’d) Correlation does not mean causation.

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Measures of Relationships— Correlation Coefficient No set criteria to evaluate the actual strength of a correlation coefficient Nature of variables being studied help determine the strength of the relationship. Coefficient of determination –Obtained by squaring the correlation coefficient ( r 2 ) –Interpreted as percentage of variance shared by two variables

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Measures of Relationships (cont’d) Scatter plot –Graphic presentation of the relationship between two variables –Determines magnitude of the relationship and the direction of the relationship –Negative correlation –Perfect positive correlation –No relationship between the two variables

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Measures of Relationships (cont’d) Contingency table –Means of visually displaying relationship between sets of data

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Measures of Relationships (cont’d) Correlational procedures –Pearson product-moment correlation (Pearson r ) –Spearman rho ( r s, r rho, or rho)

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Learning Objective Five Learning Objective Five Determine Appropriate Descriptive Statistics To Use In Presenting Selected Data

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Frequency Distribution Appropriate measure to condense data for reporting all level of data –Nominal –Ordinal –Interval –Ratio

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Mode Only measure of central tendency appropriate for nominal data

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Median Appropriate measure of central tendency for ordinal, interval, and ratio data

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Mean Appropriate for interval and ratio data Considered the most stable measure of central tendency if distribution is normal

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Standard Deviation Most widely used measure of variability when interval or ratio data are obtained

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Variance Discussed infrequently as a measure of variability in descriptive statistics Not in the same unit of measurement as the variable that is being examined

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Z Score Useful statistic for interpreting a particular value in relation to other distribution values Allows performance comparison of someone on nonequivalent tests as a measure of variability

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Measures of Relationships— Correlational Procedures Pearson r –Used when both sets of data are at the interval or ratio level Spearman rho –Used with ordinal data

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Measures of Relationships— Correlational Procedures Correlational procedures appropriate for nominal data include –Contingency coefficient –Phi coefficient –Cramer’s V

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Learning Objective Six Learning Objective Six Construct Graphs To Present Selected Descriptive Statistics

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Measures to Condense Data— Bar Graph Data are presented on only one variable. Drawn with the bars extending horizontally or vertically with lengths representing frequency of occurrence of the category To show data being represented are separate categories, the bars do not touch each other.

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Measures to Condense Data— Histogram Data are presented on only one variable. Bars are of equal width and touch each, indicating data presented on a continuum. Width of the bar represents the size of the class interval. Height of the bar represents the frequency of occurrence of each class interval.

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Measures to Condense Data— Frequency Polygon Horizontal axis –Class intervals of the variable represented Vertical axis –Frequencies of the class intervals represented Height of each dot indicates frequency of particular class interval.

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Measures of Relationships— Scatter Plot Graph Contains variables on an X axis and a Y axis X variable –Plotted on the horizontal axis Y variable –Plotted on the vertical axis

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Measures of Relationships— Scatter Plot Graph (cont’d) Pairs of scores plotted by the placement of dots to indicate where each pair of Xs and Ys intersects Positive correlation –Lowest value for each variable is placed at the lower left corner. Values increase as they go up vertical axis and as they go right on the horizontal axis.

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Measures of Relationships— Cross-Tabulation Table Contingency table –Called 2 × 2 table if two variables and each variable has two categories –If three categories, table is called a 2 × 3 table

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Learning Objective Seven Learning Objective Seven Critique Descriptive Statistics Presented In Research Reports

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Critiquing Research Reports Difficult for beginning reader of research reports to critique the statistical content

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Guidelines for Critiquing Descriptive Statistics Identify various descriptive statistics used to analyze data Determine level of measurement of each variable by searching the researcher’s operational definitions Check descriptive data presented in the text of the report and in tables and graphs

Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research, Sixth Edition Rose Marie Nieswiadomy Guidelines for Critiquing Descriptive Statistics (cont’d) Ensure that data is presented in a manner that can be understood by average practicing nurse so study can be considered for implementation in practice