Data, Tables & Graphs “…the kind of question you ask determines the kind of data you collect” Handbook, p11

Data varies in… Types of data Manner of collection How much collected - population - sampling “Understanding what kind of data you need to answer a particular question, and being able to know statistically that your results were not merely the result of chance, involve advance planning” p13

Statistics Descriptive Inferential

Descriptive Data trends or relationships central tendencies (e.g distribution) descriptive statistics (e.g. avg) representations in form of graphs, photos, drawings, diagrams, maps, etc.

Types of Numerical Data Discrete Categorical (Nominal) Ranking (Ordinal) Continuous Interval Ratio

Handbook: Descriptive Data Central Tendency visualize w/ frequency distribution considers only one variable Which of the following forests would represent a uniform distribution? Dispersion values describe spread of data

Handbook: Descriptive Data Central Tendency visualize w/ frequency distribution considers only one variable Which of the following forests would represent a uniform distribution? Dispersion values describe spread of data A B C - neither

Frequency Distribution Central tendency Measure of the "typical" value in a data set. The mean & the median are two measures of central tendency. Types of distributions: or Poisson or Uniform http://www-micro.msb.le.ac.uk/1010/1011-18.html

Descriptive Statistics Central Tendency: Reporting what usually happens: Mean Median Mode Describing the dispersion: Range Std dev & variance

Normal Distribution 99.6% 95.4% 68.2% What is standard deviation? (Calculator or know formula) 95.4% 68.2%

Means, Variability, Skew http://www-micro.msb.le.ac.uk/1010/1011-18.html

Descriptive Data Provides a summary: so that you can derive some meaning; necessary for interpretation of data often first step required by stat test to represent the original data to others requires balance: derive meaning w/o “hiding” data

What happens to the data in a research notebook? How do you choose what data to include in an article/poster?

Precision & Accuracy

Presenting Scientific Data in graphs & tables “A good illustration can help the scientist to be heard when speaking, to be read when writing. It can help in the sharing of information with other scientists. It can help to convince granting agencies to fund the research. It can help in the teaching of students. It can help to inform the public of the value of the work.” Bullets, added for clarity Mary Helen Briscoe From How to Write… by Day

Tables, Graphs, or Neither

Tables, Graphs, or Neither repetitive data exact numerical values Graph Neither

Tables, Graphs, or Neither repetitive data exact numerical values Graph interested in trend shape reveals relationship Neither

Tables, Graphs, or Neither repetitive data exact numerical values Graph interested in trend shape reveals relationship Neither few determinations, many zeroes or 100%’s std conditions or methods negative data: graphs/table do not make data more important! if able to be put into words in text When data can be represented by one significant value (e.g. max or min)

General considerations Illustrations should be intuitive All symbols should have logical meaning Summarize but represent data Follow conventions of field or journal Titles Oral/poster vs. written

Titles: Oral vs. Written Formats

Arranging Tables Clear concise title Like elements read down, not across Horizontal, but no vertical lines Explanatory footnotes; no excessive experimental detail Avoid exponents (problems w/ conventions)

Arranging Graphs Keep simple & clear Repetition can improve understanding Do not include excessive info per graph Avoid empty space Legible font size Think about the relationship you are trying to convey

What’s wrong with this graph/table? What features are good? Look at the data summarized on the next two slides and make suggestions as to how the table or graph could be improved

Nitrate Introduced at 0 Hours Control 50 mg/L 200 mg/L 100 mg/L Not good: 2 titles? title not informative gray background, but then yellow hard to see if white background Axes labels: Percent what? Time what units? Points floating w/in blocks vs ticks Good: redundancy w/ Color 29 hrs 48 hrs 72 hrs

Regressions & Correlations (Continued) Correlation computes the value of the Pearson correlation coefficient, r. Its value ranges from -1 to +1. Linear regression quantifies “goodness of fit” with r2, sometimes also shown in uppercase as R2.  

Exponential Growth curve https://cig.uw.edu/datasets/washington-state-water-temperature-projections/

Logistics Growth Curves (population ecology)

“Standard Error” of Sample Means (SEM) Undisturbed

P Values in Statistics