Data Analysis

As you start making observations and collecting data for an investigation, you will probably notice patterns. These patterns may or may not be real, or valid. Quantitative data analysis is one of the first steps toward determining whether an observed pattern has validity. This analysis includes descriptive statistics, tabular and graphical data display

Descriptive Data serves to summarize the data. It helps show the variation in the data, standard errors, best-fit functions, and confidence that sufficient data have been collected.

Inferential Data involves making conclusions beyond the data analyzed using your experimental sample data to infer parameters in the natural population.

Most of the data you will collect will fit into two categories: Measurements: are recordings of quantitative data, such as absorbance, size, time, height, and weight. Most measurements are continuous, meaning there is an infinite number of potential measurements over a given range. Count data: are recordings of qualitative, or categorical, data, such as the number of hairs, number of organisms in one habitat versus another, and the number of a particular phenotype.

Descriptive Statistics Mean, median, mode, sample standard deviation, and sample standard error of the sample mean Descriptive statistics is used to estimate important parameters of the sample data set. The parameters can also describe the entire or true population that you are studying, but collecting the data to compute these statistics is most often not possible. That’s where inferential statistics comes in.

Inferential Statistics includes tools and methods (statistical tests) that rely on probability theory and an understanding of distributions to determine precise estimates of the true population parameters from the sample data. This is a key part of data analysis and allows you to support and draw conclusions from your data about the true population.

Variables for statistical Test: Mean Average value from data Median Middle value in a set of data Mode Value that appears most frequently Range Dispersion of data points Variables for statistical Test: __ x = sample mean n = sample size s = standard deviation o = observed results e = expected results

Standard Deviation (s): a tool for measuring the spread (variance) in the sample population, which in turn provides an estimate of the variation in the entire sample set. A large sample standard deviation indicates that the data have a lot of variability. A small sample standard deviation indicates that the data are clustered close to the sample mean.

Standard mean error (SE): a statistic that allows you to make an inference about how well the sample mean matches up to the true population mean. A sample mean of ±1 SE describes the range of values about which an investigator can have approximately 67% confidence that the range includes the true population mean. Even better, a sample with a ±2 SE defines a range of values with approximately a 95% certainty.