Measurement & Experimental Design

Types of Variables Dependent variables – those variables we expect to change as the result of an experimental manipulation Independent variables – those variables we control – we determine the values for these variables and then manipulate them during the experiment Treatment – the actual experimental manipulation

Measurement The assignment of symbols to events according to a set of rules. Four scales of measurement for measuring dependent variables. 1. Nominal scale - the simplest; categories with names (e.g., for drinking vessels: mugs, goblets, cups, juice glasses, etc.) 2. Ordinal scale - when the terms in question can be rank ordered (intervals between ranks may not be ordered) (e.g., 1st, 2nd, 3rd place at a track meet - no information about how far apart the winners were) 3.Interval scale - when the terms in question can be rank ordered and equal intervals separate them, but there is no zero point (e.g., temperatures in °C, when at 0 °C temperature doesn't cease to exist but interval of 1°C is constant) 4. Ratio scale - goes one step further; it assumes the presence of a zero point (e.g., measurement of sound in decibels, zero means no sound and intervals are strict)

Nominal and ordinal scales are for discrete data – data in which each item is a separate, whole unit – number of individuals or species, members of particular groups (species, type of car, round or square, heavy or light, etc.) Interval and ratio scales are for continuous data – data for points along a scale that, at least theoretically, could be subdivided – temperature, weight, lengths, units of time, etc.

Classify each of the following variables as nominal, ordinal, interval or ratio and as discrete or continuous: a) birth order b) number of teeth c) tail length d) area of inhibited growth e) species f) sucrose concentration g) major (i.e. biology, sociology etc.) h) military rank

Precision and Accuracy in Measurement Precision concerns repeatability. This is connected to how well the instrument is calibrated. Accuracy concerns the closeness of the measurement to the “true” value -- the ability to home in on a target. Greater precision does not always mean greater accuracy, and accuracy does not guarantee precision. Digital watches can be precise to the hundredth of a second, but not necessarily accurate.

Actual Observed Actual Observed (dashed line is “reality”)

Actual Observed Actual Observed More preciseMore accurate

Assessing Accuracy & Precision Necessary in Your Measurements A general rule of thumb: Aim to have between 30 and 300 categories for ranking sizes. For example, going from 30 to 39°C by 1.0° increments provides 10 categories. Going by 0.01° increments provides 1000 categories.

You want to compare the circumference of some trees that vary between 2.54 cm and cm. How accurate should you be in making your measurements? Assessing Accuracy & Precision Necessary in Your Measurements

You want to compare the circumference of some trees that vary between 2.54 cm and cm. How accurate should you be in making your measurements? Measuring to the nearest centimeter provides 119 possible steps, which is sufficient accuracy to make meaningful comparisons. Assessing Accuracy & Precision Necessary in Your Measurements

Frequency Days Until Geese Fly South Frequency Days Until Geese Fly South OY OY -> significant difference -> no significant difference Poor Measurement = Poor Control, Geese counted weekly Good Measurement = Good Control, Geese counted daily

Replication Because nature is inherently variable and it is almost impossible to find identical individuals of a species, identical field locations, etc. it is vital that all studies have adequate replication – the more individuals measured, the more confident we are that we have accurately measured the average response

Control A scientific control is an experiment or observation designed to minimize the effects of variables other than the single independent variable.. This increases the reliability of the results, often through a comparison between control measurements and the other measurements.experimentobservationindependent variable Controls help eliminate alternate explanations of experimental results, especially experimental errors and experimenter bias. Many controls are specific to the type of experiment being performed

Control Figure 1. Treated leaves with BABA and GTE showed smaller necrotic lesions than control and other treatments. Leaves were infected by injection with 1 × 10 7 cfu ml -1 Xanthomonas citri subsp. Citri. Leaves were photographed at the indicated time with post chemical application. A, BABA; B, GTE; C, copper oxychloride; D, control. Lime leaves infected with citrus canker

Sample Size Deciding on the number of data points for a given sample (sample size) is a bit of a conundrum. You need to have a sufficient number of samples so that variance between individuals or replicates is statistically minimal, yet you don’t necessarily know the degree of variance among your samples until you start taking measurements.... But you can’t take an infinite number of samples Another rule of thumb: If you have a 2-group experiment (1 control and 1 experimental sample), you should aim for 12 replicates within each sample group. This must eventually be reconciled with the difficulty of obtaining a sample. This can be better weighed (and then refined) once sampling gives you an idea of the range of variance.