# BIO120H1 Chapter Notes - Chapter B: Significant Figures, Scale Factor, Scientific Notation

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BIO120: Adaptation and Biodiversity Lab Manual (Appendix B –

Introduction to Statistics)

In association with Test 2

- After reading this, you should be able to:

o Appreciate why and how biologists use statistics

o Understand the use of scientific notation and significant figure

o Distinguish between the kinds of measurement data

o Understand how descriptive statistics – mean, median, mode, range, variance, standard

deviation, and standard error – are used

o Describe the relationship between hypothesis testing and statistics

o Choose which test of significance is appropriate for what kind of data

o Perform and interpret a t – test and x2 – test

Introduction

- Statistics give special meaning to significance, error, hypothesis, and variance → can lead to

confusion for many students unless special attention is paid to distinct meaning of statistical

words

Part A: Collecting Data

- Data are information obtained by measurements and from which conclusions can be drawn

- Measurement plays major role in scientific method

- Measurement Error

o If a single object is measured repeatedly, values obtained aren’t all identical; some

variation exists in repeated measurements

o Measurement error reflects discrepancy between our repeated measurements and true

value of object being measured

o Potential sources of air must be eliminated when designing and conducting experiments,

or to compensate for them in data analysis

- Precision and Accuracy

o Measurements have associated with them both precision and accuracy

o Precision is repeatability of the measurement; if single measurement when repeated

shows little variation, it has high precision; if it shows great variation, it has low

precision

o Measurement can be precise but not be close to true value of object being measured →

precise but source of error exists that caused measurements to differ consistently from

true value

o Accuracy is tendency for measured value to be close to, or approximate, the true accepted

value

Significant Figures

- Single measurement consists of three parts:

o Unit measured

o Scale factor showing relative magnitude of value

o Significant figures

- Number of significant figures depends upon accuracy of measuring instrument

- As a general rule, number of significant figures should reflect numbers known to be correct, and

no figures which are known to be correct should be omitted

- To avoid confusion between scale factors and significant figures, measurements can be expressed

using scientific notation

- When performing arithmetic operations, assume following when estimating significance of

results:

o When multiplying and dividing numbers, results should have no more reliability than

initial value which has least number of significant figures

o When adding and subtracting numbers, result should contain only as many decimal

places as did the initial value which as least number of decimal places

Rounding Numbers

- Do not change digit to be rounded if it is followed by a digit less than five

- If the digit to be rounded is followed by a digit greater than five, followed by digits greater than

zero, increase it by one

- If digit to be rounded is followed by a five followed by zeros, then

o If digit is even, leave it unchanged

o If digit is odd, increase it by one

o This is done so that one – half of the time the figure will be rounded higher and the other

half will be rounded lower, avoiding error in the procedure

Sample Size

- A sample is a subset of a population and consists of only a small proportion of all the individuals

in the population

- To adequately describe population, randomly selected sampling units are examined and hope that

units represent range and frequency of values present in population

- Information about population is statistically inferred from information in our sample

- In general, larger samples give more reliable information about population

- Size of sample must always be reported → allows scientist to judge importance of reported

findings for themselves

- Sample size is typically abbreviated with a small “n”; size of population is denoted as “N”

- You can’t increase sample size by endlessly repeating measurements on same sampling unit →

must measure more units to increase sample size

Part B: Organizing Data

- All data have certain characteristics or attributes; before data can be analyzed, they’re grouped

according to qualitative or quantitative nature

- Qualitative attributes (i.e. sex, hair colour, presence of a particular disease) are easy to group as

only a definite number of possibilities exist

- Quantitative data may be of two types:

o Discrete

▪ Those in which only whole units can be counted or measured

o Continuous

▪ Those in which measurement can be a fractional part depending on the fineness

of measurement

- There are two common methods of presenting quantitative data