1. DATA ATTRIBUTES ; SUMMARY 1.1Introduction to biostatistics 1.2 The Mean 1.3Measures of Variability 1.4The Normal Distribution 1.5 Distribution; Data components

1.1Introduction to biostatistics Statistics is the science of data, involves -collecting, classifying, summarizing, organizing, analyzing, and interpreting numerical information -Biostatistic deals with biological data

definition Inferential statistics utilizes sample data to make estimate, decision, predictions, or other generalizations about a larger set of data

definition A population is a set of units (usually of people, animals, objects, transactions, or events) in a study or a survey

definition A sample is a subset of the units of a population

definition A variable is a characteristic or property of an individual population unit

definition A statistical inference is an estimate or prediction or some other generalization about a population based on information contained in a sample

definition A measure of reliability is a statement (usually quantified) about the degree of uncertainty associated with a statistical inference

definition Quantitative data are measurements that are recorded on a naturally occurring numerical scale

definition Qualitative data are measurements that cannot be measured on a natural numerical scale; they can only be classified into one of a group of categories

Data sources Publication Experiment Survey Observations Tacit knowledge

definition A representative sample exhibits characteristics typical of those possessed by the target population

definition A random sample is one obtained through a sampling procedure which ensures that every subset of fixed size in the population has the same chance of being included in the sample

definition Statistical thinking involves applying rational thought to assess data and the inferences made from them critically - involves need to measure, analyze, evaluate, and infer-from, data sets intelligently

Abuse of statistics UNTRUE; 150, 000 women a year die from anorexia TRUTH; 150, 000 women a year die from problems that were likely caused by anorexia

Abuse of statistics UNTRUE; Only 29% of school girls are happy with themselves TRUTH; Of 3,000 school girls, 29% responded “Always true” to the statement “I am happy the way I am”. Most answered “Sort of true” and “Sometimes true”

opportunities Research environment Teaching profession Consultancy expertise Advisory role Management system Decision support system Information/Knowledge Specialist

1.2The Mean Population means are often denoted by The equivalent mathematical statement is

1.3Measures of Variability

Or mathematically

1.4The Normal Distribution Its any given value of X is

When the population values are not distributed symmetrically about the mean, reporting the mean and standard deviation can give the reader an inaccurate impression of the distribution of the values in the population.

Figure 1a. Panel A shows the true distribution of the height of the 100 Jovians (note that it is skewed toward taller heights).

Figure 1b. Panel B shows normally distributed population with 100 members and the same mean and standard deviation as in panel A (Fig 1a)

1.5 Distribution; Data components Qualitative & Quantitative Data

A dependent variable assumes value from one or more independent variables An independent variable contributes value to the dependent variable - indep var is frequently controlled by the investigator

A class is a category of data classification Class frequency is no. observations in a class Class relative frequency is class frequency divided by total no. of observations in the data set

Dependent variable – hierarchy of components y i = F i + residual or y i = mx + c or y i = bx + residual

1.5.1 Quantitative data Attributes of class, class frequency, and class relative frequency also apply to quantitative data

Both data types can be used to - DESCRIBE sets of data - PREDICT values of other measurements

1.5.2 Forecasting techniques Qualitative techniques - human judgment & rating system - turn qualitative info. into quantitative estimates Quantitative techniques - statistical (stochastic, probabilistic) deterministic (causal)

1.5.3 MODELS – LINEAR & NON- LINEAR Straight lines Y = ß 0 + ß 1 X i + ε i, where ε i is the residual Parabola or quadratic Y = ß 0 + ß 1 X i + ß 2 X i 2 + ε i Cubic Y = ß 0 + ß 1 X i + ß 2 X i 2 + ß 3 X i 3 + ε i

Quartic Y = ß 0 + ß 1 X i + ß 2 X i 2 + ß 3 X i 3 + ß 4 X i 4 + ε i Nth-Degree Y = ß 0 + ß 1 X i + ß 2 X i 2 + … + ε i

Exponential Y = ab X + ε i or Log Y = log a + (log b)X + ε i = a 0 + a 1 X + ε i Geometric Y = aX b + ε i or Log Y = log a + b (log X) + ε i = a 0