Starting out in Statistics (eBook)

An Introduction for Students of Human Health, Disease, and Psychology

Patricia De Winter, Peter M. B. Cahusac (Autoren)

eBook Download: EPUB

2014
John Wiley & Sons (Verlag)
9781118920558 (ISBN)

Infos

Starting out in Statistics aims to provide an accessible book on a topic that many students find difficult. It includes modern, up-to-date methodology and is illustrated throughout with current examples, relevant to students taking courses in a range of human-related sciences, from biomedicine to psychology.

It is essential for students to grasp the underlying statistical concepts which give them a stronger grounding in the subject, rather than simply learning to use statistical software, which although useful, does not arm a student with the skills necessary to formulate the experimental design and analysis of a research project in their later years of study or indeed, if working in research. This book gives the necessary background and tools for students to use statistics confidently and creatively in their studies and future career.

Written in an engaging and accessible style this book provides the statistical foundations needed to successfully pursue a degree in the biological and social sciences.

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To form a strong grounding in human-related sciences it is essential for students to grasp the fundamental concepts of statistical analysis, rather than simply learning to use statistical software. Although the software is useful, it does not arm a student with the skills necessary to formulate the experimental design and analysis of a research project in later years of study or indeed, if working in research. This textbook deftly covers a topic that many students find difficult. With an engaging and accessible style it provides the necessary background and tools for students to use statistics confidently and creatively in their studies and future career. Key features: Up-to-date methodology, techniques and current examples relevant to the analysis of large data sets, putting statistics in context Strong emphasis on experimental design Clear illustrations throughout that support and clarify the text A companion website with explanations on how to apply learning to related software packages This is an introductory book written for undergraduate biomedical and social science students with a focus on human health, interactions, and disease. It is also useful for graduate students in these areas, and for practitioners requiring a modern refresher.

Autor

Patricia de Winter, Research Associate, University College London; Sessional Lecturer, Birkbeck College London; Translational Uro-Oncology, Division of Surgury & Interventional Science, University College London. Peter M. B. Cahusac, Lecturer, University of Stirling, Department of Psychology, University of Stirling, Scotland.

Textauszug

Basic Maths for Stats Revision

If your maths is a little rusty, you may find this short revision section helpful. Also explained here are mathematical terms with which you may be less familiar, so it is likely worthwhile perusing this section initially or referring back to it as required when you are reading the book.

Most of the maths in this book requires little more than addition, subtraction, multiplication and division. You will occasionally need to square a number or take a square root, so the first seven rows of Table A are those with which you need to be most familiar. While you may be used to using ÷ to represent division, it is more common to use / in science. Furthermore, multiplication is not usually represented by × to avoid confusion with the letter x, but rather by an asterisk (or sometimes a half high dot ·, but we prefer the asterisk as it's easier to see. The only exception to this is when we have occasionally written numbers in scientific notation, where it is widely accepted to use x as the multiplier symbol. Sometimes the multiplication symbol is implied rather than printed: ab in a formula means multiply the value of a by the value of b. Mathematicians love to use symbols as shorthand because writing things out in words becomes very tedious, although it may be useful for the inexperienced. We have therefore explained in words what we mean when we have used an equation. An equation is a set of mathematical terms separated by an equals sign, meaning that the total number on one side of = must be the same as that on the other.

Table A Basic mathematical or statistical calculations and the commands required to perform them in Microsoft Excel where a and b represent any number, or cells containing those numbers. The Excel commands are not case sensitive

Function

Symbol

Excel command

Comments

Addition

+

= a + b

Alternatively use the Σ function to add up many numbers in one operation

Subtraction

−

= a − b

Multiplication

*

= a * b

Division

/

= a / b

Sum

Σ

= Σ(a:b)

Seea for meaning of (a:b)

Square

a2

= a^2

Alternatively you may use = a * a

Square root

√

= sqrt(a)

Arithmetic mean

= average(a:b)

Seea for meaning of (a:b)

Standard deviation

s

= stdev(a:b)

Standard error of the mean

SEM

= stdev(a:b)/sqrt(n)

Where n = the number of observations and seea for meaning of (a:b)

Geometric mean

= geomean(a:b)

Seea for meaning of (a:b)

Logarithm (base 10)

log10

= log10(a)

Natural logarithm

ln

= ln(a)

The natural log uses base e, which is 2.71828 to 5 decimal places

Logarithm (any base)

loga

= log(a,[base])

Base 2 is commonly used in some genomics applications

Arcsine

asin

= asin(a)

Sometimes used to transform percentage data

Inverse normal cumulative distribution

= invsnorm(probability)

Returns the inverse of the standard normal cumulative distribution. Use to find z-value for a probability (usually 0.975)

aPlace the cursor within the brackets and drag down or across to include the range of cells whose content you wish to include in the calculation.

Arithmetic

When sequence matters

The sequence of addition or multiplication does not alter a result, 2 + 3 is the same as 3 + 2 and 2 * 3 is the same as 3 * 2.

The sequence of subtraction or division does alter the result, 5 − 1 = 4 but 1 − 5 = −4, or 4 / 2 = 2 but 2 / 4 = 0.5.

Decimal fractions, proportions and negative numbers

A decimal fraction is a number that is not a whole number and has a value greater than zero, for example, 0.001 or 1.256.

Where numbers are expressed on a scale between 0 and 1 they are called proportions. For example, to convert 2, 8 and 10 to proportions, add them together and divide each by the total to give 0.1, 0.4 and 0.5 respectively:

Proportions can be converted to percentages by multiplying them by 100:

A negative number is a number lower than zero (compare with decimal fractions, which must be greater than zero)

Multiplying or dividing two negative numbers together makes them positive, that is,

Squares and square roots

Squaring a number is the same as multiplying it by itself, for example, 32 is the same as 3 * 3. Squaring comes from the theory of finding the area of a square: a square with sides of 3 units in length has an area 3 * 3 units, which is 9 square units:

Squaring values between 1 and 2 will give answers greater than 1 and lower than 4. Squaring values between 2 and 3 will give answers greater than 4 and lower than 9, etc.

The square sign can also be expressed as ‘raised to the power of 2’.

Taking the square root is the opposite of squaring. The square root of a number is the value that must be raised to the power of 2 or squared to give that number, for example, 3 raised to the power of 2 is 9, so 3 is the square root of 9. It is like asking, ‘what is the length of the sides of a square that has an area of 9 square units’? The length of each side (i.e. square root) is 3 units:

Algebra

Rules of algebra

There is a hierarchy for performing calculations within an equation – certain things must always be done before others. For example, terms within brackets confer precedence and so should be worked out first:

Multiplication or division takes precedence over addition or subtraction irrespective of the order in which the expression is written, so for 3 + 5 * 2, five and two are multiplied together first and then added to 3, to give 12. If you intend that 3 + 5 must be added together before multiplying by 2, then the addition must be enclosed in brackets to give it precedence. This would give the answer 16.

Terms in involving both addition and subtraction are performed in the order in which they are written, that is, working from left to right, as neither operation has precedence over the other. Examples are 4 + 2 − 3 = 3 or 7 − 4 + 2 = 5. Precedence may be conferred to any part of such a calculation by enclosing it within brackets.

Terms involving both multiplication and division are also performed in the order in which they are written, that is, working from left to right, as they have equal precedence. Examples are 3 * 4 / 6 = 2 or 3 / 4 * 6 = 4.5. Precedence may be conferred to any part of such a calculation by enclosing it within brackets.

Squaring takes precedence over addition, subtraction, multiplication or division so in the expression 3 * 52, five must first be squared and then multiplied by three to give the answer 75. If you want the square of 3 * 5, that is, the square of 15 then the multiplication term is given precedence by enclosing it in brackets: (3 * 5)2, which gives the answer 225.

Similarly, taking a square root of something has precedence over addition, subtraction, multiplication or division, so the expression √2 + 7 means take the square root of 2 then add it to 7. If you want the square root of 2 + 7, that is, the square root of 9, then the addition term is given precedence by enclosing it in brackets: √(2 + 7).

When an expression is applicable generally and is not restricted to a specific value, a numerical value may be represented by a letter. For example, √a2 = a is always true whichever number is substituted for a, that is, √32 = 3 or √1052 = 105.

Simplifying numbers

Scientific notation

Scientific notation can be regarded as a mathematical ‘shorthand’ for writing numbers and is particularly convenient for very large or very small numbers. Here are some numbers written in both in full and in scientific notation:

In full

In scientific notation

0.01

1 × 10−2

0.1

1 × 10−1

1

1 × 100

10

1 × 101

100

1 × 102

1000

1 × 103

0.021

2.1 ×...

Produkt-Details

• Erscheint lt. Verlag: 2.9.2014
• Sprache: englisch
• Themenwelt: Geisteswissenschaften ► Psychologie
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Medizin / Pharmazie ► Allgemeines / Lexika
• Themenwelt: Naturwissenschaften ► Biologie ► Allgemeines / Lexika
• Themenwelt: Technik
• Schlagworte: Biostatistics • Biostatistik • Biowissenschaften • Concepts • difficult • Essential • Experimental Design • fundamental • Grounding • humanrelated • learning • Life Sciences • Necessary • Psychological Methods, Research & Statistics • Psychologie • Psychologische Methoden, Forschung u. Statistik • Psychology • Research • Sciences • Simply • Skills • Software • Statistical • Statistics • Statistik • strong • Student • students • topic • useful
• ISBN-13: 9781118920558 / 9781118920558