1. THE BASICS

2. Most Public Health journal articles, reports and abstracts use data to examine public health issues of interest – be it social behavior, policy, biomedical, environmental or epidemiologic. Since data will play a role in your studies and work life, you should use this opportunity to brush up on your math!

3. DATA Suppose we are interested in studying why young people start smoking – this study would have policy and social behavioral implications. Before you implement an intervention program or create a public health policy, you need to have some idea as to why teenagers begin to smoke. You select a simple random sample of teenagers who smoke and ask them to answer a series of questions.

4. EXAMPLE DATA Some of the questions asked are: age: date of birth: mm/dd/yyyy date of first cigarette: mm/dd/yyyy how close to parents: very distant, distant, neither distant nor close, close, very close smoke to lose weight: yes/no number of cigarettes per day do either of your parents smoke: father only, mother only, both, neither

5. TYPES OF DATA Some data are numbers (age, weight, sbp, etc) – This type of data are called quantitative (quantity) Some data are not numbers (sex, disease, etc) – This type of data are called qualitative (quality)

6. TYPES OF DATA Nominal data: – Qualitative – ‘Named’ – Categories Two categories – Dichotomous data More than two categories – Multichotomous data – No specific order

7. TYPES OF DATA Examples of Nominal data sex - dichotomous disease diagnosis - multichotomous ethnic identity - multichotomous disease status (yes/no) – dichotomous consumed alcohol (yes/no) – dichotomous What variables in our dataset are nominal?

8. TYPES OF DATA Ordinal data – Qualitative – Ordered – Ordered groups or categories – Can be counted and ordered but not measured – Can be ranked

9. TYPES OF DATA Examples of ordinal data ratings – poor, fair, good, excellent – strongly dislike, dislike, neutral, like, strongly like categorized age – 21-34, 35-48, 49 plus categorized body mass index – underweight, normal weight, overweight, obese What variables in our dataset are ordinal?

10. TYPES OF DATA Discrete data – Quantitative – Have both order and magnitude (natural number) – Can only take on specific integer values – Sometimes referred to as ‘count’ data

11. TYPES OF DATA Examples of discrete data number of children in a family number of alcohol drinks per day number of tick bites per season What variables in our dataset are discrete?

12. TYPES OF DATA Continuous – Have both order and magnitude (natural number) – Can take on any value including fractions – Often the result of taking a measurement Accuracy depends on precision of measurement

13. TYPES OF DATA Examples of continuous data weight of a subject in pounds or grams height of subject in inches, feet or meters blood lead levels body mass index in kg/m 2 What variables in our dataset are continuous?

14. TYPES OF DATA The study of statistics, epidemiology, risk assessment, etc. require numeric manipulations on all types of data, ergo we need to understand numbers.

15. REAL NUMBERS

16. PROPERTIES OF REAL NUMBER OPERATIONS PropertyAdditionMultiplication Commutativea + b = b + aab = ba 2 + 3 = 3 + 22*3 = 3*2 Associativea+(b+c)=(a+b)+ca(b*c) = (a*b)*c 2+(3+4) = (2+3)+4 Try:4+(2+8)5(3*2) (6+3)+1(7*2)*2

17. PROPERTIES OF REAL NUMBER OPERATIONS PropertyAdditionMultiplication Distributivea(b + c) = ab + ac 2(3 + 6) = 2*3 + 2*6 = 6 + 12 = 18 Try: 5(4 + 2) 2(3 + 7)

18. PROPERTIES OF REAL NUMBER OPERATIONS

19. RULES AND EXAMPLES FOR NEGATIVE NUMBERS -(-a) = a-(-5) = 5 (-a)b = a(-b) = -(ab) (-6)2 = 6(-2) = -(6*2) = -12 (-a)(-b) = ab(-7)(-2) = 14 = 7*2 (-1)a = -a(-1)*2 = -2 Try: (-2)(-4) (2)(-4)

20. PROPERTIES OF FRACTIONS

27. ABSOLUTE VALUES

28. % TO DECIMALS % (percent) means ‘per 100’ percent to a decimal: divide the percent by 100 and remove the ‘%’ sign – (move the decimal point 2 places to the left) 17% = 0.17 26.9% = 0.269 0.05% = 0.0005 Try: 2.3% 0.2%

29. DECIMALS TO % decimal to percentage: multiply the decimal by 100 and add the ‘%’ sign – (move decimal point 2 places to the right) 0.893 = 89.3% 1.359 = 135.9% 0.002 = 0.2% Try: 0.0006 0.3751

30. ROUNDING Know your digits: 1000.0000 thousandsthousands hundredshundreds tenstens onesones tenthtenth hundredthhundredth thousandththousandth ten thousandthten thousandth

31. ROUNDING Common method: 1.target how many ‘places’ to round to 2.find the ‘target’ on the number to be rounded 3.look at the value of the digit one place to the right of the ‘target’ 4.follow these rules: 1.if the digit to the right is between 0 and 4, leave the ‘target’ as is 2.if the digit to the right is 5 or greater, increase the ‘target’ by adding 1

32. EXAMPLES OF ROUNDING Using 13.693 Round to the ones digit: – ‘target’ is 3 (integer), since 6 is 5 or greater, round up to 14.0 Round to nearest tenth digit: – ‘target’ is 6, since 9 if 5 or greater, round up to 13.7 Round to nearest hundredths – ‘target is 9, since 3 is between 0 and 4, keep target as is: 13.69

33. ROUNDING Try: 855.237 round to tens round to tenths round to ones round to hundreds round to hundredth