Week 4: Analyzing Descriptive Statistics
As a practice scholar, you are searching for evidence to translate into practice. In your review of evidence, you locate a quantitative descriptive research study as possible evidence to support a practice change. You notice the sample of this study includes 200 participants and is not normally distributed. Reflect upon this scenario to address the following.
Please read the question carefully to answer all components. Our interactive discussion addresses the following course outcome:
- Differentiate selected statistical methods for the purpose of translation science (PO 3, 5, 9).
- Evaluate selected statistical methods for the purposes of critical appraisal of evidence (PO 3, 5, 9).
- Synthesize literature relevant to practice problems. (PO 3, 5, 9)
What is Analyzing Descriptive Statics?
- What statistical procedure is needed to determine an effective sample size to make a reasonable conclusion? Explain your rationale.
- Reading through the study, you observe that the researcher used a chi-square analysis to analyze nominal and ordinal data. Is this the appropriate level of statistical analysis to answer the research question? Explain your rationale.
- Reading further, the researcher reports that the p-level led her to conclude that the null hypothesis was rejected. In your critique of the study, you determine that the null hypothesis is true. Do these findings impact your decision about whether to use this evidence to inform practice change? Why or why not?
Reflection on Learning
- Provide one specific example of how you achieved the weekly objectives.
- How has the course information influenced your understanding of descriptive statistics?
- How can you bring this information of statistical analysis to practice?
Analyzing Data
As we learned in the first three weeks, researchers begin with a research question to be answered. The researcher attempts to answer the question by collecting relevant information. This relevant information most often comes from human beings who serve as subjects in a research study. In the context of a research investigation, the information usually is referred to as data. Researchers collect data in a number of different ways—by asking people questions, by observing and recording their behavior, or by taking biophysiologic measurements. Whatever the method, data serve as the foundation for addressing the research question.
The expectation that practice be evidence-based has made it more important that DNP-prepared nurses acquire the knowledge and skills in reading and critically appraising the results of statistical tests. In this week and Week 5, we will dispel anxiety associated with statistics and facilitate your critique of published research studies. The statistical information provided over the next 2 weeks is from the perspective of reading, reviewing, and critically appraising published quantitative research studies, rather than from that of selecting statistical procedures or performing statistical analyses. To critique a quantitative research study, you need to be able to
- identify the statistical procedures used;
- judge whether these procedures were appropriate for the hypotheses, questions, or objectives of the study, and for the level of measurement of the variables;
- comprehend the discussion of data analysis results in the study;
- judge whether the researcher interpretation of the results is appropriate; and
- evaluate the clinical significance of the findings.
Data in a research study can be of two basic types: qualitative or quantitative.
Click on each tab below to view the differences in qualitative and quantitative data.
Qualitative data consists of verbal, narrative pieces of information.
Consider the following question: Have you felt sad or depressed at all lately, or have you generally been in good spirits? Click on the responses below to see how a qualitative response might look.
Research Variables
In a scientific study, the concepts in which a researcher is interested are referred to as variables. A variable is something that varies or takes on different values. Height, weight, gender, blood pressure, and heart rate are all examples of characteristics that vary from one person to the next. If there was no variation, these would be called constants. Researchers are interested in explaining and understanding variation. Why do some people exercise while others do not? Why do some people comply with a medication regimen while others fail to do so? Researchers collect data about variations and examine relationships among them.
View the following activity to investigate research variables.
BLANK_AUDIO] Variables can be characterized in several different ways that have implications for how researchers analyze data. One distinction relates to independent and dependent variables. An independent variable is the variable that’s changed or controlled in a scientific experiment to test the effects on the dependent variable. A dependent variable is the variable being tested and measured in a scientific experiment.
The dependent variable is dependent on the independent variable. As the researchers change the independent variable, the effects on the dependent variable is observed and recorded. In the research question, does a low-cholesterol diet reduce the risk of heart disease. The independent variable is the amount of cholesterol in a person’s diet.
And the dependent variable is heart disease. Cholesterol level is a variable because people consume different amounts of it. And heart disease is a variable because not everyone has this disease. The research question is whether variation in the independent variable causes or influences variation in the dependent variable. Take a closer look at these examples.
Discrete and Continuous Variables
Another distinction that has relevance for statistical analysis concerns discrete and continuous variables. A discrete variable is one that has a finite number of values between any two points. For example, if people were asked how many times they had ever been hospitalized, they might answer 0, 1, 2, 3, or more times. The variable for number of times hospitalized is discrete because a number such as 1.5 is not a meaningful value. A continuous variable is one that can assume an infinite number of values between any two points. Weight is an example of a continuous variable. Between 1 and 2 pounds, there is an unlimited number of possible values: 1.01, 1.234. 1.365, and so on.
Levels of Measurement
View the activity below to learn more about levels of measurement. BLANK_AUDIO] There are 4 different levels of measurement commonly used in nursing research: nominal, ordinal, interval, and ratio. Please note the significance of this classification system, because the type of analysis that the researcher can undertake depends on the level of measurement. Nominal measurement, the lowest form of measurement, involves using numbers simply as labels to classify attributes into different categories.
Researchers sometimes refer to these variables as categorical variables. A wide variety of characteristics can be measured on a nominal scale, for example, gender, marital status, and blood type. Here are some examples of nominal level variables and their codes. Ordinal measurement involves the use of numbers to designate ordering on an attribute.
Ordinal measurement allows the researchers to classify subjects and to indicate their relative standing on some dimension of interest. While the numbers are no longer arbitrary, ordinal measurement does not tell us anything about the distance between categories. As an example, the distance between having a graduate degree and a college degree is not equivalent to the distance between having a college degree and some college education.
But the ordinal codes provide no clue about the relative magnitude of the differences. Let’s look at some examples, interval measurement involves assigning numbers that indicate both the ordering on an attribute and the distance between different amounts of the attribute. Temperature on the Fahrenheit scale is an example of interval level measurement.
Equal distances on the Fahrenheit scale represent equal differences in temperature. That is, the difference between 101 degrees and 102 degrees Fahrenheit is equivalent to the difference between 103 degrees and 104 degrees Fahrenheit. Interval level measures provide information about not only rank ordering, but also about the magnitude of difference between different values on the scale.
Ratio measurement combines the features of interval level measurements with one additional characteristic, the presence of a natural, meaningful zero point. Because of this feature, variables measured on the ratio scale provide information about the absolute amount of the property being measured. If the researchers are measuring the amount of pain medication administered to a patient, 0 milligrams would be a perfectly legitimate value indicating the total absence of pain medication.
Interval measures, by contrast, do not have a rational 0 point. A temperature of 0 degrees Fahrenheit does not indicate the total absence of heat. While it is possible to add, subtract, multiply, and divide the values on a ratio scale, it is not meaningful to say that 80 degrees Fahrenheit is twice as hot as 40 degrees Fahrenheit.
Researchers strive to have variables measured on the highest level of measurement possible. There are three advantages to using higher levels of measurement, greater analytic flexibility, availability of more powerful statistical techniques and a greater amount of information than at lower levels.
Reasoning Behind Statistics
Data Analysis Techniques
Many of us were taught mathematical procedures of calculating statistical equations with little or no explanation of the logic behind these procedures or the meaning of the results. Computation today is a mechanical process performed by a computer. Let’s take a look at data analysis through the lens of enhancing understanding of the statistical analysis process. You can then use this understanding to critique data analysis techniques in the published research studies you are considering as support for your practice problem. Click on each section below to learn more.
Probability Theory
Probability, which is deductive, is used to explain the extent of a relationship, the probability that an event will occur in a given situation, or the probability that an event can be accurately predicted. A researcher may want to know the probability that a practice outcome results from a nursing action. A researcher may want to know the probability that subjects in the experimental group are members of the same larger population from which the control group subjects were taken.
Probability is expressed as a lowercase letter p, with values expressed as percentages or as a decimal value ranging from 0 to 1. A research study may find that the probability that the experimental groups subjects were members of the same larger population as the control subjects was less than or equal to 5% (p<0.05). In other words, it is NOT very likely that the control group and the experimental group are from the same population. Put another way, you might say that there is a 5% chance that the two groups are from the same population and 95% chance that they are not from the same population. Probability values often are stated with the results of statistical analysis.
A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes (“heads” and “tails”) are both equally probable; the probability of “heads” equals the probability of “tails”; and since no other outcomes are possible, the probability of either “heads” or “tails” is 1/2 (which could also be written as 0.5 or 50%).
Decision Theory, Hypothesis Testing, and Level of Significance
Decision Theory, which is inductive, assumes that all of the groups in a research study (experimental and control groups) used to test a particular hypothesis are components of the same population relative to the variable under study. This expectation is frequently expressed as a null hypothesis which states that there is no difference between (or among) the groups in a study, in terms of the variables included in the hypothesis. It is up to the researcher to provide evidence for a genuine difference between the groups.
An example… a researcher may hypothesize that the frequency of urinary tract infections that occurred after discharge from the hospital in patients who were catheterized during hospitalization is not different from the frequency of such of such infections in those who were not catheterized. To test the assumption, the researcher selects a cutoff point before data collection. The cutoff point, referred to as alpha (Need the symbol for alpha), or the level of statistical significance, is the probability level at which the results of statistical analysis are judged to indicate a statistically significant difference betweenthe groups. The level of significance selected for most nursing research studies is 0.05. This means that if the level of significance found in the statistical analysis is 0.05 or less, the experimental and the control groups are considered to be significantly different. (members of different populations). In some studies, the more rigorous level of significance of 0.01 may be chosen.
As you critically review each quantitative research study, be sure to include the following: 1. Identify the level of significance and determine whether the findings show statistically significant differences. 2. Judge the risk of a Type II error.
An inference is a conclusion or judgment based on evidence. Statistical inferences are made by researchers cautiously and with great care. The decision theory rules used to interpret the results of statistical procedures increase the probability that inferences are accurate.
Type I and Type II Errors
According to decision theory, two types of error can occur when a researcher is deciding what the result of a statistical test means: Type I and Type II.
A Type I error occurs when the null hypothesis is rejected when it is true (e.g. when the results indicated that there is a significant difference, when, in reality, there is not). The risk of a Type I error is indicated by the level of significance. There is a greater risk of a Type I error with a 0.05 level of significance than with a 0.01 level of significance. As the level of significance becomes more extreme, the risk of a Type I error decreases.
A Type II error occurs when the null hypothesis is regarded as true but it is in fact false. For example, a statistical analysis may indicate no significant differences between groups, but, in reality, the groups are different. There is a greater risk of a Type II error when the level of significance is 0.01 than when it is 0.05. However, Type II errors often are caused by flaws in the research methods. Nurse researchers tend to have small sample sizes and tend to use instruments that do not precisely measure the variables under study. In many nurse-led research studies, multiple variables interact to cause differences within populations. When only a few of the interacting variables are examined, small differences may be overlooked, which can lead to a false conclusion that there are no differences. Thus, the risk of a Type II error is high in many nursing research studies.
Descriptive Statistics: Using Statistics to Describe
View the activity below to explore descriptive statistics.
Descriptive Statistics (Links to an external site.)
In any research study in which the data are numerical, data analysis begins with descriptive statistics also called summary statistics. Let’s take a look at common descriptive statistics employed by researchers to describe the study data to the reader.
Frequency Distribution
Frequency Distribution is usually the first method used to organize study data. There are two types of frequency distributions: ungrouped and grouped.
Ungrouped Frequency Distributions
Most studies have some categorical data presented in the form of an ungrouped frequency distribution in which a table is developed to display all numerical values obtained for a particular variable. This approach is generally used on discrete data such as gender, marital status, and diagnosis rather than continuous data.
Grouped Frequency Distributions
Continuous variables such as age lend themselves to grouped frequency distributions. Other data collected during the research study such as body temperature, vital lung capacity, weight are appropriate for display in a grouped frequency distribution.
Measures of Central Tendency
A measure of central tendency is frequently referred to as an ‘average’ which is a lay term not commonly used in statistics because it is vague. The three most commonly used in statistics are the mode, median, and mean.
Mode is the numerical value of score that occurs with greatest frequency. It is does not necessarily represent the center of the data set. The mode is the appropriate measure of central tendency for nominal data.
Median is the score at the exact center of the ungrouped frequency distribution – the 50th percentile. The median is the most appropriate measure of central tendency for ordinal data.
Mean is the most commonly used measure of central tendency. The mean is the sum of the scores divided by number of scores being summed. Like the median, the mean may not be a number of the data set. The mean is the appropriate measure of central tendency for interval and ratio-level data.
Measures of Dispersion
Measures of dispersion, or variability, are measures of individual differences of the members of the study sample. They provide some indication of how scores in a sample are dispersed around the mean. These measures provide information about the data that is not available from measures of central tendency. They indicate how different scores are, or the extent to which individual scores deviate from one another. If the individual scores are similar, measures of variability are small, and the sample is homogeneous, or similar, in terms of those scores. A heterogeneous sample has a wide variation in scores. The measures of dispersion most commonly used are range, variance, and standard deviation.
- Range is obtained by subtracting the lowest score from the highest score.
- Variance is calculated with a mathematical equation.
- Standard Deviation is the square root of the variance.
Understanding Descriptive Statistical Results
Researchers frequently report these study findings in the “Results” section of the published article.
Descriptive statistics are used in published research studies to describe differences between groups or variables. One additional statistical procedure that is available to describe differences is use of the chi-square test.
Chi-Square Test of Independence
This test determines whether two variables are independent or related; the test can be used with nominal or ordinal data. The procedure is not very powerful and is not designed to test for causality. Most researchers who use a chi-square place little importance on results in which no differences are found. Researchers frequently perform multiple chi-square tests in a sample. Results are generally presented only when a chi-square analysis show a significant difference.
Practice Problem Exemplar Using Descriptive Statistics
A rural clinic has a large population of patients with diabetes whose HbA1c levels are greater than 7% and body mass index (BMI) is over 30. The practice scholar implements a 9-month quality improvement project to improve these values.
A wellness education program is implanted that addresses exercise, healthy eating, and understanding the importance of regular blood glucose monitoring. Before implementing the program, the practice scholar collected aggregate data 3, 6, and 9 months before the intervention. Data included HbA1c levels, BMIs, and numbers of patients with uncontrolled HbA1c. Demographic data also were collected. The practice scholar collected the same data 3, 6, and 9 months after implementation of the program.
Preintervention and postintervention data includes the following.
| Patient | Column A HbA1c Preintervention | Column B HbA1c < 7 | Column C HbA1c Postintervention | Column D HbA1c < 7 |
| 1 | 7.4 | Y | 6.9 | N |
| 2 | 7.8 | Y | 7.1 | Y |
| 3 | 7.1 | Y | 6.7 | N |
| 4 | 6.8 | N | 6.4 | N |
| 5 | 7.4 | Y | 6.8 | N |
| 6 | 7.8 | Y | 7.7 | Y |
| 7 | 7.8 | Y | 7.4 | Y |
| 8 | 8.2 | Y | 8 | Y |
| 9 | 7.5 | Y | 6.7 | N |
| 10 | 11.8 | Y | 11.3 | Y |
Adapted from “Use these tools to analyze data vital to practice-improvement projects,” by B. Conner and E. Johnson, (2017), American Nurse Today, (12), 11.
The practice scholar analyzes descriptive statistics, such as measures of central tendency and variability, to describe outcomes of this quality improvement initiative.
_____________________________________________________________________________________ Question:
Based on the above data set, calculate the average percentage of patients with uncontrolled diabetes (HbA1c>7) both preintervention and post intervention.
Answer:
Preintervention mean = 9/10 (90%)
Postintervention mean = 5/10 (50%)
Calculation:
Nine of 10 patients have HbA1c levels greater than 7% preintervention. Five of 10 patients have HbA1c levels greater than 7% postintervention. Columns B and D present the number of patients with HbA1c levels greater than 7%.
__________________________________________________________________________________
Question:
Next, calculate the mean preintervention and postintervention HbA1c values for patients involved in this quality improvement project.
Answer:
Mean HbA1c levels preintervention = 7.96
Mean HbA1c levels postintervention = 7.5
Calculation:
Mean HbA1c preintervention is the sum of all HbA1c levels in column A/10 (number of patients).
7.4 + 7.8 + 7.1 + 6.8 + 7.4 +7.8 + 7.8 + 8.2 +7.5 + 11.8 = 79.6
79.6 /10 = 7.96
Mean HbA1c postintervention is the sum of all HbA1c levels in column C/10 (number of patients)
6.9 + 7.1 + 6.7 + 6.4 + 6.8 + 7.7 + 7.4 + 8 + 6.7 + 11.3 = 75
75/10 = 7.5
_____________________________________________________________________________________
Question:
Now calculate the preintervention and postintervention median score of HbA1c levels.
Answer:
Median HbA1c levels preintervention = 7.65
Median HbA1c levels postintervention = 7.0
Calculation:
Median HbA1c levels preintervention is the score at the exact center of all HbA1c values in column A.
Median HbA1c levels postintervention is the score at the exact center of all HbA1c values in column C.
_____________________________________________________________________________________
Question:
Next, calculate the preintervention and postintervention standard deviation of HbA1c levels of patients involved in the quality improvement project. The standard deviation will determine the spread of increase or decrease in HbA1c levels.
Answer:
Standard deviation for HbA1c levels preintervention = 1.4
Standard deviation for HbA1c levels postintervention = 1.4
Calculation:
The standard deviation is the square root of the sum of all numbers minus the mean (squared) divided by one less than the number of values.
The standard deviation for the preintervention is
√(((7.4-7.96)2 + (7.8-7.96)2 + (7.1-7.96)2 + (6.8-7.96)2 + (7.4-7.96)2)+ (7.8-7.96)2 + (7.8-7.96)2 +
(8.2-7.96)2 + (7.5-7.96)2 + (11.8-7.96)2) /(10-1)) = 1.4
The standard deviation for the postintervention is
√(((6.9-7.5)2 + (7.1-7.5)2 + (6.7-7.5)2 + (6.4-7.5)2 + (6.8-7.5)2)+ (7.7-7.5)2 + (7.4-7.5)2 +
(8-7.5)2 + (6.7-7.5)2 + (11.3-7.5)2) /(10-1)) = 1.4
_____________________________________________________________________________________
Question:
Finally, calculate the preintervention and postintervention range of HbA1c levels. If no outliers exist, the range will determine how close together HbA1c levels are in the patients involved.
Answer:
The range is obtained by subtracting the lowest score from the highest score.
Range of HbA1c levels preintervention = 5
Range of HbA1c levels postintervention = 4.9
Calculation:
Range of HbA1c levels preintervention is obtained by subtracting the lowest score from the highest score in column A.
Range of HbA1c levels postintervention is obtained by subtracting the lowest score from the highest score in column C.
_____________________________________________________________________________________
The practice scholar analyzes the descriptive statistics and determines that the mean HbA1c levels decreased from 7.96 to 7.5 following the intervention. The scholar reflects upon HbA1c levels and determines that patient 10 HbA1c levels are an outlier, which may have skewed the mean. The scholar also notes that the median HbA1c is lower in postintervention data, while the standard deviation and range are similar in pre- and postintervention data. This suggests that the HbA1c levels don’t vary much from the mean pre- and postintervention. The practice scholar concludes that a larger patient sample may be helpful to determine the effectiveness of the intervention.
Conner, B., & Johnson, E. (2017). Use these tools to analyze data vital to practice-improvement projects. American Nurse Today, (12), 11.
References
Dang, D., & Dearholt, S. (2018). Johns Hopkins nursing evidence-based practice model and guidelines (3rd ed.). Sigma Theta Tau International.
Polit, D. F., & Beck, C. T. (Eds.). (2017). Nursing research: Generating and assessing evidence for nursing practice (10th ed.). Wolters Kluwer.
White, K. M., Dudley-Brown, S., & Terhaar, M. F. (2016). Translation of evidence into nursing and health care (2nd ed.). Springer Publishing Company.
Polit, D. F., & Beck, C. T. (Eds.). (2017). Nursing research: Generating and
assessing evidence for nursing practice (10th ed.). Wolters Kluwer.
