Basics of Statistical Methodology, Data Types, Variable Classes, and Variable Types: Foundational Support

An educational column by Statistics can be appreciated by gaining a firm foundation in a few important pillars of understanding. First, there are two chief types of methods and second, it is important to note how variables are classed. Let us first start out with data. Data are plural and datum is singular. As an example, data (e.g., catheters per patient hospital admissions, dwell times, or cost savings) are distributed in different ways. One would look at the data to examine the issue being explored. For example, plotting catheters per patient admission on the horizontal axis (x-axis or abscissa) and the number of times it occurred (or frequency), you would have the shape (or distribution) of the data.The shape of distributions is the main way statisticians make decisions of what statistical procedure they choose. There are essentially two types of statistical methods, parametric and nonparametric. Parametric statistical standards are the most common statistical tests. Parametric methods are based on the normal distribution. The normal distribution is also known as a bell-shaped curve. One example of normally distributed data is pulse. Nonparametric statistical methods test data not adhering to the normal distribution. One example of nonparametric data would be length of stay in hours, days, or weeks.Parametric methodology leverages knowledge we have about the distribution of data resulting in a more statistically powerful test (more about that later in another column). If we choose a parametric test, there are more strict assumptions we make about the data. Mainly we assume we know the distribution of the data (e.g., normal, Poisson, or uniform; see Breakout Box 1). There may be other assumptions like the data are not associated [i.e., measurements are not taken on the same patients or patients that may have a factor or characteristic that might influence the outcome (e.g., the same vascular access specialist placing a peripheral venous catheter)]. Nonparametric methodology does not rely on the assumptions that are that strict; however, statistical power is lower. It has been demonstrated a nonparametric test will never have less than 85% of the ­statistical power of a parametric statistical test.1 Data can be tested to see if it fits the normal distribution (there are several tests like the Anderson-Darling test, D'Agostino test, Shapiro-Francia test, and Shapiro-Wilk test with their own advantages and disadvantages) and plotted using what is called a normal probability plot or a Q-Q plot to see if data are normally distributed.2–6 Examples of nonparametric methodology include the: Wilcoxon-Mann-­Whitney test, Wilcoxon signed-rank test, the chi-square test, and Fisher's exact test (see Breakout Box 2).A handy statistical tidbit to know is that if a statistical method cannot be identified, any parametric method can be applied to non-normally distributed data by ranking the data.7 If this is done, remember to interpret the results in terms of the ranks and not the original data.Results can be divided into two main areas: descriptive statistics and inferential statistics; often they are both reported in the same study. Descriptive statistics illustrate, portray, or characterize the data and consist of counts (frequencies), relative frequencies (frequencies divided by the total number in the category), percentages (relative frequency multiplied by 100%), measures of central tendency [mode, median, mean (arithmetic average)], measures of dispersion or measures of how the data are spread (e.g., interquartile range, standard deviation, variance), and graphs, figures, or plots. These measures describe what the data look like, where it congregates, and how spread out it is or depict it graphically.Inferential statistics on the other hand focuses on drawing conclusions from the sample to the population at large. This primarily involves hypothesis testing, which is accomplished using the various statistical tests. The vascular access specialist might postulate that a new device (Device B) might lead to fewer hospital-acquired infections or compared to a current device (Device A). From this idea the null hypothesis is formed (signified by H0). The null hypothesis is a statement of no difference or involves equality at some level. In this case, H0: Device A has the same or more infections as Device B. The thinking is that if there is statistical evidence to reject the null hypothesis we must conclude the alternative hypothesis (signified by HA or H1). In the above example the alternative hypotheses would be H1 (or HA): Device A has less infections than Device B. From either conclusion, we reject the null hypothesis or we fail to reject (we do not "accept") the null hypothesis in our sample; we would infer the results to the population from which we sampled.Data generally falls into two types: independent or dependent. This can be a little confusing. Independent and dependent variables will be discussed later. Independent data are not related. For example, you may record whether a patients had one or more catheter-related bloodstream infections (yes or no). This is an example of independent data. One patient is not related to another patient. Now compare this to counting the number of catheter-related bloodstream infections on a unit. If you included multiple infections in the same patient one would have to take this into consideration because one patient might be more prone to getting catheter-related bloodstream infections. Another example is if you measured knowledge of peripheral vascular catheter insertion before and after an educational intervention. The scores on the test for each learner would be ­related—someone who scored well pre-intervention will probably do well post-intervention. Those scores are going to be more related than the scores of two different learners. These types of data are called dependent data. Data that are not related are called independent. As pointed out before, the outcomes of patients with peripheral vascular catheters placed in different patients by the same specialist would be considered dependent data (Think of comparing a vascular access specialist working a 40-hour work week vs. a per diem floor nurse holding everything else equal such as schooling, time as a nurse, etc. Who has a greater probability of vascular access success?)Data that are completely unrelated are termed independent. For example, if you were examining one or more infections at two different hospitals with two different types of peripheral access devices with the caveat that a vascular access specialist could only place one device. In this case everything is independent: the patients are unrelated, the specialists placing the peripheral access devices are unrelated, and the devices themselves are unrelated.Independence or dependence of data means we have to shift our statistical methodology. For example, if we have continuous data (see below) we might use a paired t test or a ­Wilcoxon signed-rank test (see Breakout Box 2). If we had dependent categorical data (see below) we might use McNemar's test. Finally, if we had repeated observations on the same individual or data that were nested (e.g., observations made on the same patient where one specialist did the peripheral vascular access or patients were on several different wards with different levels of care), we would use a linear mixed model or generalized linear mixed model.The significance is not that the vascular care specialist, nurse, or researcher knows these techniques, but that there is an understanding of what is meant when proposing a test, or discussing a test.For lack of a better term and to avoid confusion between independent and dependent data let's identify two classes of variables: independent and dependent variables. Independent variables are variables that are manipulated. Independent variables can also be thought of as predictor variables. Independent variables are under the control of the scholar, evidence-based practitioner, quality improvement investigator, or human-subject researcher. Dependent variables are the ­outcome. They are ­dependent on the independent variable. We are interested on the affect the independent variable has on the dependent variable. For example, if investigating two different types of vascular access devices (independent variable: Device A and Device B) we would like to know the effect on dwell time (dependent variable).No doubt there are many ways to categorize variables; however, the classic and probably most cited method of categorizing data is the method suggested by S. S. Stevens in 1946 when he proposed all data can be classified into nominal, ordinal, interval, and ratio classes.8 The importance of these classes is that they are used to determine the statistical methodology used.Nominal variables are the lowest level of data. Nominal variables are categorical—names. For example, an infection or no infection (i.e., infection: yes/no) or an intervention (i.e., existing device vs. new device). Very few descriptive statistics can be applied to nominal data. About the only descriptive statistics that can be used with nominal data are the mode (the most frequently occurring category), frequencies (also called counts), and relative frequencies (also called percentages when multiplied by 100%). The typical test used with two nominal variables is the chi-square test (or Fisher's exact test or ­McNemar's test).Ordinal is the next level of variables. In addition to the characteristics of nominal variables, ordinal variables can be ordered. Examples of ordinal variables include grades (an A is better than a B, a B is better than a C, a C is better than a D, and a D is better than an F; but we don't know how much better) and Olympic medals (a gold is better than a silver, a silver is better than a bronze; again, we don't know how much better each medal is). One characteristic of ordinal variables is the differences between the data points are meaningless. Although an "A" is better than a "B" we don't know how much better it is. Ordinal data can be reported using frequencies, relative frequencies, as well as percentiles, the median (the point at which the data can be divided in half), and interquartile range (the 75th percentile minus the 25th percentile). Statistical tests used with ordinal data include the Wilcoxon-Mann-Whitney test, the Wilcoxon signed-rank test, and the Sign test.The interval level of data is the first level of data where the differences between data points are meaningful. Although ordinal data can be continuous, the differences aren't meaningful, and the values can only be used to rank the data. Interval data includes all the characteristics of nominal and ordinal data. In addition to these characteristics, more descriptive statistics can be calculated including mean (or arithmetic average) and variance. (The standard deviation can be calculated as it is the positive square root of the variance. We will talk about descriptive statistics in another article.) Zero on the interval scale does not mean absence of what is being measured. The classic example of an interval variable is temperature (with the exception of degrees Kelvin). Zero degrees Celsius does not mean a lack of heat; nor does zero degrees Fahrenheit mean a lack of heat. This property is the reason the interval variables cannot be doubled or halved. For example, if you bake chocolate chip cookies at 375°F for 10 minutes, because temperature is an interval variable, you can't bake the cookies at 750°F for 5 minutes and expect them to be edible. One assumption that can be applicable to interval data is the normality assumption. Statistical tests used with interval data might include regression. If the independent variable is nominal, a t test, Wilcoxon-Mann-Whitney test, or analysis of variance might be used.Ratio data is the highest level of data and as such has all the characteristics of nominal, ordinal, and interval data. Ratio data includes the characteristic that zero indicates the absence of what is being measured. Like interval data, a mean, variance, median, interquartile range, and mode can be calculated for ratio data. For example, pulse is a ratio variable, height is a ratio variable, weight is a ratio variable, and systolic and diastolic blood pressure are ratio variables. The same type of statistical tests can be used for ratio data as interval data. Similar to interval data, before statistical tests are applied to ratio data the data must be tested for normality; if data are not distributed normally nonparametric methods must be used for the analysis.In this installment of Foundational Support fundamental concepts to statistics were discussed. The types of statistics, statistical methodology, data types, variable classes, and variable types (Table 1) all can be understood with a few guidelines. The importance of these fundamental concepts to statistics is that they influence how analyses proceed. The healthcare professional/vascular access specialist who is interested in research must have a basic understanding of the statistical measurements as it guides the conversation with the statistician and develops a better understanding of the research analysis.When proposing a test you should always look at the literature and see how other studies have dealt with similar data. Did they use parametric or nonparametric methods? Then, after data collection, before doing a hypothesis test, test your data to see if it fits the distribution you have proposed.Questions and comments are encouraged regarding this article. Should you have questions or comments please contact AVA Foundation Director at Large Dr. Gregory E. Gilbert at SigmaStatsConsulting@gmail.com. Please put the title of the article in the Subject line.Gregory E. Gilbert and Desiree A. Díaz have no conflicts of interest to declare.GEG conceived of the topic and wrote the first draft. DAD made critical revisions and contributed substantial content to this article. Both authors contributed to subsequent revisions of the manuscript. GEG serves as corresponding author. Both authors approved the final manuscript.