Statistics & Evidence-Based Practice The Pennsylvania State university College of nursing Nursing 200w

Objectives Identify the purposes of statistical analyses. Describe the process of data analysis. Describe probability theory and decision theory that guide statistical data analysis. Describe the process of inferring from a sample to a population. Discuss the distribution of the normal curve.

Objectives Identify descriptive analyses. Describe the results obtained from inferential statistical analyses. Describe the five types of results obtained from quasi- experimental and experimental study designs. Compare and contrast statistical significance and clinical importance of results. Critically appraise statistical results, findings, limitations, conclusions, and generalization of findings.

A Statistical Primer

Statistics in Nursing Practice Reading or critiquing published research Examining outcomes of nursing practice by analyzing data collected in a clinical site Developing administrative reports with support data Analyzing research done by nursing staff and other health professionals at a clinical site Demonstrating a problem or need and conducting a study

Critically Appraising Statistics Identify statistical procedures used Determine whether statistics used were appropriate or not Evaluate researchers interpretation of statistics

Stages in Data Analysis Prepare data for analysis. Describe the sample. Test reliability of measurement methods. Conduct exploratory analysis. Conduct confirmatory analysis guided by hypotheses, questions, or objectives. Conduct posthoc analyses.

Major Statistics in Nursing Studies Descriptive Inferential

Descriptive Statistics Describe and summarize the sample and variables Also referred to as summary statistics

Inferential Statistics Infer or address the objectives, questions, and hypotheses

Descriptive Statistics If a research study collects numerical data, data analysis begins with descriptive statistics Not limited to quantitative research! May be the only statistical analysis conducted in a descriptive study

Types of Descriptive Statistics Frequency distributions Measures of central tendency Measures of dispersion

Two-Tailedness

Ungrouped Frequency Distribution Data in raw form: 1: ☺ 2: ☺ ☺ ☺ ☺ ☺ ☺ ☺ 3: ☺ ☺ 4: ☺ ☺ ☺ ☺ 5: ☺

Grouped Frequency Distribution Data are grouped into categories: Ages 15 to 20: 12 Ages 20 to 25: 14 Ages 25 to 30: 19….

Example of a Percentage Distribution Housing: 41.7% Textbooks: 8.3% Clothing: 16.7% Food: 8.3% Additional Supplies: 25%

How Frequency Distributions are Presented in Research Articles

Measures of Central Tendency Mean Median Mode

Normal Curve

Normal Curve A theoretical frequency distribution of all possible values in a population Levels of significance and probability are based on the logic of the normal curve

Mean Is the sum of values divided by the number of values being summed

Median Is the value in exact center of ungrouped frequency distribution Is obtained by rank ordering the values

Mode Is the numerical value or score that occurs with greatest frequency Is expressed graphically

Bimodal Distribution

Measures of Dispersion Range Variance Standard deviation Standardized scores Scatterplots

Range Is obtained by subtracting lowest score from highest score

Difference Scores Are obtained by subtracting the mean from each score Sometimes referred to as a deviation score because it indicates the extent to which a score deviates from the mean

Standard Deviation Is the square root of the variance Just as the mean is the “average” value, the standard deviation is the “average” difference score

Standardized Scores Raw scores that cannot be compared and are transformed into standardized scores Common standardized score is a Z-score Provides a way to compare scores in a similar process

Scatterplots

Probability Theory

Probability Theory Used to explain: Extent of a relationship Probability of an event occurring Probability that an event can be accurately predicted

Probability If probability is 0.23, then p = 0.23 There is a 23% probability that a particular event will occur

Inferences A conclusion or judgment based on evidence Judgments are made based on statistical results

Decision Theory

Decision Theory Assumes that all the groups in a study used to test a hypothesis are components of the same population relative to the variables under study It is up to the researcher to provide evidence that there really is a difference To test the assumption of no difference, a cutoff point is selected before analysis

Statistics Judging the appropriateness of the statistical tests used

Critical Appraisal Factors that must be considered include: Study purpose Hypotheses, questions, or objectives Design Level of measurement

Critical Appraisal You must judge whether the procedure was performed appropriately and the results were interpreted correctly.

Information Needed Decide whether the research question focuses on differences or associations/relationships.

Information Needed Decide whether the research question focuses on differences or associations/relationships. Determine level of measurement.

Data Types Nominal Ordinal Interval/Ratio

Information Needed Decide whether the research question focuses on differences or associations/relationships. Determine level of measurement. Select the study design that most closely fits the one you are looking at.

Information Needed Decide whether the research question focuses on differences or associations/relationships. Determine level of measurement. Select the study design that most closely fits the one you are looking at. Determine whether the study samples are independent, dependent, or mixed.

Statistical Tests Some common statistical tests in research

Chi-Square Nominal or ordinal data Tests for differences between expected frequencies if groups are alike and frequencies actually observed in the data

Chi-Square Regular No Regular Exercise Exercise Total Male 35 15 50 Female 10 40 50 Total 45 55 100

Chi-Square Indicate that there is a significant difference between some of the cells in the table The difference may be between only two of the cells, or there may be differences among all of the cells. Chi-square results will not tell you which cells are different.

Example

Pearson Product-Moment Correlation Tests for the presence of a relationship between two variables Works with all types of data

Correlation Performed on data collected from a single sample Measures of the two variables to be examined must be available for each subject in the data set.

Correlation Results Nature of the relationship (positive or negative) Magnitude of the relationship (–1 to +1) Testing the significance of a correlation coefficient

Response Question Which are the following are significant? A. r = 0.56 (p = 0.03) B. r = –0.13 (p = 0.2) C. r = 0.65 (p < 0.002)

Example

Factor Analysis Examines relationships among large numbers of variables Disentangles those relationships to identify clusters of variables most closely linked Sorts variables according to how closely related they are to the other variables Closely related variables grouped into a factor

Factor Analysis Several factors may be identified within a data set The researcher must explain why the analysis grouped the variables in a specific way Statistical results indicate the amount of variance in the data set that can be explained by each factor and the amount of variance in each factor that can be explained by a particular variable

Regression Analysis Used when one wishes to predict the value of one variable based on the value of one or more other variables

Regression Analysis The outcome of analysis is the regression coefficient R When R is squared, it indicates the amount of variance in the data that is explained by the equation R2 = 0.63

Example

T-test Requires interval level measures Tests for significant differences between two samples Most commonly used test of differences

Example

Analysis of Variance ANOVA Tests for differences between means Allows for comparison of groups

Example

Results A summary of the types of results you will find in experimental and quasi-experimental research studies

Types of Results Significant and predicted Nonsignificant Significant and not predicted Mixed Unexpected

Significant and Predicted Support logical associations between variables As expected by the researcher

Nonsignificant Negative or inconclusive results No significant differences or relationships

Significant and Unpredicted Opposite of what was expected Indicate potential flawed logic of researcher

Mixed Most common outcome of studies One variable may uphold predicted characteristics, whereas another does not Or two dependent measures of the same variable may show opposite results.

Unexpected Relationships between variables that were not hypothesized and not predicted from the framework being used

Findings, Conclusions, & Implications

Findings Results of a research study that have been translated and interpreted

Statistically Significant Findings Significant p-values

Clinically Significant Findings Practical application of findings Somewhat based on opinion

Conclusions A synthesis of findings Researchers should not go beyond what the findings state or interpret too much!

Implications The meaning for nursing practice, research, and/or education Specific suggestions for implementing the findings

Critical Appraisal Questions to ask

Critical Appraisal What statistics were used to described the characteristics of the sample? Are the data analysis procedures clearly described? Did statistics address the purpose of the study? Did the statistics address the objectives, questions or hypotheses of the study? Were the statistics appropriate for the level of measurement of each variable?

Critical Appraisal What statistics were used to described the characteristics of the sample? Are the data analysis procedures clearly described? Did statistics address the purpose of the study? Did the statistics address the objectives, questions or hypotheses of the study? Were the statistics appropriate for the level of measurement of each variable?

Critical Appraisal What statistics were used to described the characteristics of the sample? Are the data analysis procedures clearly described? Did statistics address the purpose of the study? Did the statistics address the objectives, questions or hypotheses of the study? Were the statistics appropriate for the level of measurement of each variable?

Critical Appraisal What statistics were used to described the characteristics of the sample? Are the data analysis procedures clearly described? Did statistics address the purpose of the study? Did the statistics address the objectives, questions or hypotheses of the study? Were the statistics appropriate for the level of measurement of each variable?

Critical Appraisal What statistics were used to described the characteristics of the sample? Are the data analysis procedures clearly described? Did statistics address the purpose of the study? Did the statistics address the objectives, questions or hypotheses of the study? Were the statistics appropriate for the level of measurement of each variable?

Critical Appraisal What statistics were used to described the characteristics of the sample? Are the data analysis procedures clearly described? Did statistics address the purpose of the study? Did the statistics address the objectives, questions or hypotheses of the study? Were the statistics appropriate for the level of measurement of each variable?

The End! Question? Comments?