Analysis & Presentation of Quantitative Data PDF

ANALYSIS & PRESENTATION OF QUANTITATIVE DATA PREPARED BY: YVETTE M. BATAR, RN, MAN,DM Sources: Polit, E. & Beck C., Essentials of Nursing Research, 10th Edition 2022. Tan, Crestita B., A Research Guide in Nursing Education: Building an Evidence-based...

ANALYSIS & PRESENTATION OF QUANTITATIVE DATA PREPARED BY: YVETTE M. BATAR, RN, MAN,DM Sources: Polit, E. & Beck C., Essentials of Nursing Research, 10th Edition 2022. Tan, Crestita B., A Research Guide in Nursing Education: Building an Evidence-based Practice, 4th Edition 2006.  LEARNING OBJECTIVES ON COMPLETING THIS C HAPTER, S TUDENT NURSES WILL BE ABLE TO: Describe the characteristics of Specify the appropriate applications for t- frequency distributions, and identify tests, analysis of variance, chi-squared and interpret various descriptive tests, and correlation coefficients and statistics. interpret the meaning of the calculated statistics. Describe the logic and purpose of Describe the applications and principles of parameter estimation, and interpret multiple regression and analysis of confidence intervals. covariance. Describe the logic and purpose of tests Understand the results of simple statistical of statistical significance, describe procedures described in a research report. hypothesis testing procedures, and interpret p values. Define new terms in the chapter  4 MAIN PURPOSES OF 4 MAJOR LEVELS OF STATISTICAL ANALYSIS MEASUREMENTS 1. Nominal Measurement - the lowest level, 1.To describe data. involves using numbers to categorize attributes. 2.To estimate population 2. Ordinal Measurement - ranks people on an values. attribute. 3.To test hypothesis. 3. Interval Measurement - occurs when researchers can rank people on an attribute 4.To provide evidence & specify the distance between them. regarding measurement 4. Ratio Measurement - the highest level, properties of quantified have a meaningful zero & provide variables. information about the magnitude of the attribute.  TYPES OF ORDINAL MEASUREMENT OR SCALE 1. Likert Scale 2. Graphic Rating Scale Respondents are asked to Respondents are asked to indicate the degree to which respond a bipolar continuum they agree or disagree with such as from “highest” to the ideas expressed by the “lowest” or “most” to “least”. indicator. A simple line on which one Used to assess the attitude marks an X anywhere of respondents towards the between the extremes with an variables being investigated. infinite number of places where the X can be placed.  TYPES OF ORDINAL MEASUREMENT OR SCALE 3. Guttman Scale 4. Semantic Differential Used to assess the attitudes Scale of respondents, using a Use to measure the meaning continuum of cumulative of concepts to determine the statements. emotional-evaluative component of the respondent’s attitude.  STATISTICS A branch of Mathematics used to summarize, organize, present, analyze and interpret numerical data such as the numerical characteristics of sample parameters and the numerical characteristics of a population. DESCRIPTIVE STATISTICS INFERENTIAL STATISTICS Used to analyze & describe Is concerned with data & relationships between population and the use of 2 variables. sample data to predict Refers to statistics intended to future occurrences. organize and summarize numerical data from the population and sample.  USES OF DESCRIPTIVE STATISTICS A. Measures & condenses data in: Frequency Distribution – arrangement of values from lowest to highest & a count or percentage of how many times each value occurred. Frequency Polygon Graphic Presentation – data are presented in graphic form to make frequency distribution data readily apparent. B. Measures of central tendency – used to describe the the 3 indexes: Mean, Median and Mode.  USES OF DESCRIPTIVE STATISTICS 3 INDEXES OF CENTRAL TENDENCY Mode: the number that occurs most Mean Formula frequently in a distribution. In the following distribution, the mode is 53: X = ∑ (wm) N 50 51 51 52 53 53 53 53 54 55 56 Where: ∑ (w m) = sum of the weighted means per item within a Median: the point in a distribution that given criterion divides scores in half. N = number of items Mean: is equal to the sum of all values divided by the number of participants— what people refer to as the average.  VARIABILITY OR MEASURE OF DISPERSION Describes how far apart data points lie from each other and from the center of a distribution, w/ 2 common indexes: Range & Standard Deviation. RAN GE STANDARD DEVIATION (SD) Simplest measure of dispersion. Represents the average of deviations from the mean. Obtain by subtracting the lowest score from the highest score. Mean tell us the best value for summarizing an entire Range is a difference score, w/c distribution. uses only 2 extreme scores for SD tells us how much the score the comparison. deviate from the mean & can be interpreted as degree of error.  VARIABILITY OR MEASURE OF DISPERSION STANDARD DEVIATION (SD) - C ONT’D Determines the homogeneity Most widely used. or sameness of degree or Calculated based on every dimension of given variables value in the distribution. or the heterogeneity or Summarizes the average degree of dispersal of variance of variables. amount of deviation of values Formula: S ∑ (X-X)2 from the mean. n-1 Interpreted as degree of error Where: ∑ (X-X)2 = sum of squares of the differences between scores/ratings and when mean is used to the mean. describe an entire sample.  BIVARIATE DESCRIPTIVE STATISTICS CROSS TABUL ATIONS C ORREL ATION Crosstabs Table - frequency Correlation Methods - described relationships between 2 variables by distribution in which the calculating the correlation frequencies of two variables coefficient w/c describes the are cross-tabulated. intensity & direction of a relationship Correlation Coefficient - indicates how “perfect” a relationship is w/ possible values ranging from -1.00 thru.00 to +1.00 Pearson’s r - most widely used correlation statistic.  CORRELATION COEFFICIENT VALUES 1. A correlation coefficient of 1.00: 3. A correlation coefficient of 0.00: represents a perfect positive linear suggests no linear relationship between relationship. It means that when one the two variables. They are statistically variable increases, the other variable independent of each other. increases in a perfectly linear fashion. 4. A correlation coefficient between All data points fall along a straight line with a positive slope. -1.00 and 0.00: represents a negative linear relationship. As the correlation 2. A correlation coefficient between coefficient gets closer to -1.00, the 0.00 and 1.00: indicates a positive negative relationship becomes stronger. linear relationship. As the correlation A value of -1.00 means a perfect coefficient gets closer to 1.00, the negative linear relationship, where one relationship becomes stronger. A v a r i a b l e i n c re a s e s a s t h e o t h e r value of 0.00 means no linear relationship. decreases in a perfectly linear fashion.  PEARSON’S R 1. A d e s c r i p t i v e s t a t i s t i c , summarizes the characteristics of a d a t a s e t. S p e c i f i c a l l y, i t describes the strength & direction of the linear relationship between two quantitative variables. 2. Also an inferential statistic, meaning that it can be used to test statistical hypotheses. Specifically, we can test whether there is a significant relationship between two variables.  DECIDING RISK Absolute Risk (AR) -the proportion of people who experienced an undesirable outcome in each group. Absolute Risk Reduction (ARR) -comparison of 2 risks, computed by subtracting the absolute risk for the exposed group from the absolute risk for the unexposed group. Odds Ratio (OR) - the proportion of subjects with the adverse outcome relative to those without it. NUMBER NEEDED TO TREAT (NNT) = 1/.30 = 3.33 Number Needed to Treat (NNT) - estimates how many people would need to receive an intervention to prevent one undesirable outcome.  INTRODUCTION TO INFERENTIAL STATISTICS Inferential Statistics -a Uses of Inferential Statistics: branch of statistics that A. To estimate population parameter involves drawing Sampling error w/c is the difference b/n data conclusions, making obtained from a random sampled population & predictions, and data that would be obtained if an entire generalizing findings from population is measured. a sample to a larger Sampling distribution is a theoretical frequency population. distribution based on an infinite number of Concerned with samples. population and the use Sampling bias occurs when samples are not of sample data to predict carefully selected as in non-probability sampling. future occurrences. B. Testing the Null Hypothesis  INTRODUCTION TO INFERENTIAL STATISTICS SAMPLIN G DISTRIBUTION Are used in statistics to understand how sample statistics, such as means, variances, or proportions, vary when re p e a t e d l y d r a w i n g r a n d o m samples from a population. To c o m p u t e t h i s , s t a t i s t i c a l software or programming languages like R, Python, or specialized statistical tools may be used.  INTRODUCTION TO INFERENTIAL STATISTICS PARAMETER ESTIMATION STEPS IN TESTIN G HYPOTHESIS Consists of 2 Techniques: 1. S e l e c t i n g a n a p p r o p r i a t e statistical test. 1. Parameter Estimation is used to estimate a parameter. 2. S p e c i f y i n g t h e l e v e l o f Takes 2 forms: Point Estimation significance. & Interval Estimation. 3. Compute a test statistic. 2. Hypothesis Testing - provides 4. Determining degrees of freedom. objective criteria for deciding whether research hypotheses 5. Comparing the test statistic to a should be accepted as true or theoretical value. rejected as false.  INTRODUCTION TO INFERENTIAL STATISTICS T YPE I & T YPE II ERRORS LEVEL OF SIGNIFIC ANCE (LOF) Ty p e I E r r o r - f a l s e - p o s i t i v e Frequently used LOF are.05 conclusion &.01. Occurs when the null hypothesis Often denoted by the is rejected when in reality it is not. symbol α (alpha). Type II Error - false-negative conclusion Use to determine whether Occurs when the null hypothesis the results of a statistical is regarded as true but it is in fact test are statistically false. significant or not.  BIVARIATE STATISTICAL TESTS Analysis of Variance (ANOVA) t-TESTs Used to test mean group differences of three or more groups. One-Way Analysis of Variance or ANOVA - for testing mean differences among three or more groups by comparing variability between groups to variability within groups. Two -way analysis of variance - used to test the relationship between one independent variable & multiple dependent variables, commonly used in factorial design. Repeated Measures ANOVA (RM-ANOVA) - used when the means being compared are means at different points in time.  BIVARIATE STATISTICAL TESTS Chi-Squared Test Used to test hypotheses about differences in proportions. Computed by summing differences between the observed frequencies in each cell (such as those in Table 15.10) and the expected frequencies—the frequencies that would be expected if there were no relationship between the two variables. Correlation Coefficients Pearson’s r - already discussed in slide #14.  MULTIVARIATE STATISTICAL ANALYSIS Multiple Regression Analysis of Covariance (ANCOVA) Used to collate more than two Combines features of ANOVA & variables. muliple regression, used to control confounding variables statistically Microstat software in which the —that is to “equalize’ groups being formulas are embedded is used. compared. Logistic Regression Printouts contain the computed values of R1 R2 and the critical Analyzes the relationships between values, R at 0.05 or 0.01 multiple independent variables & a significance level. nominal-level dependent variable e.g., compliant versus noncompliant Does not have negative values.  MEASUREMENT STATISTIC Reliability Assessment Validity Assessment Content Validity - relevant for composite Test-retest Reliability measures such as multi-item scales. Usually relies on expert ratings of each item & ratings Interrater Reliability are used to compare an index called CVI. Criterion Validity - concerns the extent to w/c Internal Consistency scores on a measure are consistent w/ a “gold Reliability standard” criterion. Construct Validity - concerns the extent to w/c a measure is truly measuring the target construct & often assessed using hypothesis testing.  ASSESSING QUALITY DATA 1. Credibility 2. Dependability A. Prolonged engagement 3. Confirmability B. Persistent observations 4. Transferability C. Triangulation 5. Authenticity D. Peer debriefing & member checks E. Search for disconfir ming evidence