Basics and Beyond: Displaying Your Data Mario Davidson, PhD Vanderbilt University School of Medicine Department of Biostatistics Instructor
Objectives 1.Understand the types of data and levels of measurement 2.Understand how a Table 1 typically looks 3.Be able to interpret all of the basic graphs. 4.Know the type of displays that may be used dependent upon the type of data and level of measurement 5.Be introduced to less familiar displays of the data
Types of Data (Obj1) Qualitative Data Consist of attributes, labels, or non-numerical entries. If you can t perform mathematical operations or order data, it s qualitative. Ex: Colors in a box of crayons; names; county Quantitative Data Consist of numerical measurements or counts. Ordering is a dead give away Ex: BMI; age; numerical grade
Levels of Measurement (Obj1) Nominal Qualitative Categorized using names, qualities, or labels Ex: Top 5 movies, jersey numbers, type of drug Ordinal Quantitative or Qualitative Can order Differences between data are not meaningful. Ex: Letter grade, Likert scale such as very dissatisfied to very satisfied
Levels of Measurement (Obj1) Interval Level of Measurement Quantitative Can order Can calculate meaningful differences No Value that means nothing/none. A zero entry merely represents a position on a scale (i.e. no inherent zero). Ex: Time of day, temperature Ratio Level of Measurement Quantitative Can order Can calculate meaningful differences There s a value that means nothing/none. Ex: Age, weight, test score
Popular Displays
Description of Table 1 (Obj2) Typically summarizes baseline characteristics of the data. Compares statistics between groups May provide means, medians, confidence intervals, percentiles, percentages, p-values, standard deviations, etc. Summaries of all types of data (e.g. continuous, categorical, nominal, ordinal, interval, ratio) may be used. Likert scale: Scale indicating degree of agreement (e.g. Rate the following statement: I have a had a difficult time focusing on my studies this semester: SD D N A SA
Example of a Table 1 (Obj2)
Test Your Knowledge Interpret the following graphs.
Test Your Knowledge Interpret the following graphs. Cherry or Apple Pies sold the most in January. Other pies sold the least Nearly 15 subjects chose Saturday as their favorite day. Sunday was the least chosen.
Pie Charts (Obj3) Features (Obj4) Nominal or Ordinal Compares Levels of One Characteristic Advantages: Easily Interpreted Larger Area; Greater Proportion Easy to Create Disadvantages Difficult to Judge Areas Wastes Ink
Bar Plots (Obj3) Features (Obj4) Nominal and Ordinal Compares Advantages Same as Pie Chart Disadvantages Similar to Pie Chart No such thing as an Analyte 2.5 Ordering can Change Perception
Test Your Knowledge Interpret the following graphs
Test Your Knowledge The most frequent BMI seems to be approximately around 24-26. There were 8 subject weighing approximately 0 grams. There was only one weighing 10 grams.
Histograms (Obj3) Features Shows Distribution Continuous One Characteristic (Obj4) Advantages Easy to Interpret Easy to Produce Disadvantages Size of Bins can Change Perception Cannot Read Exact Values
Dot Plot (Obj3) Features (Obj4) One Characteristic Ordinal Advantages Good for Small and Moderate Data Easily Interpreted Disadvantages May not be Best Option with Large Data Not Produced in all Packages
Stem and Leaf Plot (Obj3) Features (Obj4) One Characteristic Ordinal Advantages The most frequent USMLE1 scores in our data were in the 220's, 230's, and 260's. The highest and lowest scores were 190 and 278 respectively. Useful with Small Data and May be Used with Large Data Can be produce by hand Easily Interpreted Useful with Numeric Disadvantages May be Difficult to Measure Center Not Appealing
Test Your Knowledge Why is this graph difficult to interpret? What is the trend? What is the trend? An outlier is data that is a numerical distance from the rest. Can you find one?
Test Your Knowledge There is no y-label. R is a statistical software. From Jan-Dec, there is an upward trend. Seems to be a slight positive trend: as age increases so does POMS. The arrows suggest 2 possibly outliers.
Line Graph (Obj3) Features (Obj4) One Characteristic Used with Ordinal and Continuous Displays Associations, Trends, and Range Advantages Produced in Most Packages
Line Graph with Rugplot
Scatterplot (Obj3) Features (Obj4) Continuous and Ordinal Shows Associations Shows Trend Advantages Shows all of Data Produced in Most Packages not the Line Exact values shown Easily Interpreted Disadvantage May not be Best Way for Large Data
Less Familiar Graphs
Boxplot (Obj3 and Obj5) Features Advantages Continuous by Nominal or Ordinal (Obj4) May Compare Groups Good Summary: Min, 1Q, 2Q(median), 3Q, Max Disadvantages Does not Display All the Data Not as Appealing Cannot be Created in All Packages May not be as Recognized by Some
Boxplot The median tooth length for orange juice at 1dose of Vitamin C was roughly 25 units. The first quartile length for 1 dose of ascorbic acid was approx. 15. As Vitamin C doses increase tooth length increases. Overall, it appears that those using orange juice had greater length given the same dose and excluding possibly a Vitamin C dose of two. There was an outlier for the ascorbic acid at dose 1.
Boxplot Overlayed with Stripchart (Obj5) Features Same as Boxplot Advantages Same as Boxplot Can See All of the Data Disadvantage Many Programs Cannot Create
Dot Chart (Obj5) Features Nominal, Ordinal Characteristics with a Continuous Outcome (Obj4) Can Compare Levels and Groups Advantages Easily Interpreted Size of Data Irrelevant Disadvantage Not as Recognized as Bar Graphs and Pie Charts
Kaplan Meier Curve (Obj5) Demonstrates the probability of survival The plot suggests that males have a more favorable rate of survival over the years. Can be created in most programs Number at Risk
Probably Even Less Familiar Graphs
Spaghetti Plot (Obj5) Alzheimer's Disease Verbal IQ Words that could not be sounded out (e.g. Depot)
Spaghetti Plot Features (Obj4) The overall trend suggest that as age increases so do earnings. Continuous, Longitudinal Two Characteristics Shows Trend Advantages Shows all of the Data Disadvantages Not Available in All Packages May be Difficult to Interpret odf o ds ht ( s gni nr a E Age(yrs)
Dendogram: Cluster (Obj5) Useful for Determining Clustering May Help to Remove Variables (Data Reduction) PGY clustered Clinical Year
Scatter Plot with Marginal Histograms (Obj5) Continuous Virtually appealing Shows trends, associations, and the distributions of the data Cannot be created in many programs
Large Data Sets
Sunflower Plot (Obj5) Large data sets The more ink used, the more dense the data Ordinal More fresh embryos to the uterine were transferred on day 3.
Heat Map (Obj5) Encephalitis Red Proportion of Presence Green Proportion of Absence White Missing Light/Dark Intensity of Presence of Attribute
Heat Map Similar to the Hexagon Plot Lightness or Darkness Indicates Intensity May not be Created in Some Programs
Nomogram (Obj5) May Provide Risk, Probability, etc. Useful in Providing Predictive Scores Sum the Points for each category, find the Total Points, then look at the corresponding Risk of Death. 40 yo, Male, 200 Cholesterol, and 170 BP has Approximately a 48% Risk of Death
Multidimensional Plot (Obj5) http://data.vanderbilt.edu/rapache/bbplot/
Multidimensional Plot (Obj5)
Conclusion Always try to think of the best way to display your story (data). Consider your target audience. When publishing, color may cost.
References Hamid, et al. BMC Infectious Diseases 2010, 10:364. http://www.biomedcentral.com/1471-2334/10/364 Grober, E, Hall, CB, Lipton, RB, Zonderman, AB, Resnick, SM, and Kawas, C (2009). Memory impairment, executive dysfunction, and intellectual decline in preclinical Alzheimer's disease. Journal of the International Neuropsychological Society, 14(2), 266-278. http://data.vanderbilt.edu/rapache/bbplot/