1. Pharmaceutical Statistics
Chapter 1
Basic Concepts

2. Definitions Statistics is the field of study concerned with:
the collection, organization, summarization and analysis of data, and
the drawing of inferences about a body of data when only apart of the data is observed.
Statistics has its own vocabulary:
Data
Variables (quantitative, qualitative, random, discrete random, continuous random).
Population
Sample

3. Definitions
Data are the raw material of statistics. We may define data as numbers.
There are two kinds of numbers that we use in statistics:
Numbers resulting from taking a measurement (Cmax, tablet hardness, patient temperature etc.)
Numbers that result from a process of counting (patients discharged from a hospital in aday, tablets produced by a certain process per shift etc)

4. Definitions
The performance of a statistical activity is motivated by the need to answer a question (reproducibility of manufacturing procedure, compliance with product specifications, relative merits of competing treatment procedures).
Data may be obtained from one or more of the following sources:
Routinely kept records
Surveys
Experiments
External resources

5. Definitions
Variable: a characteristic monitored, capable of taking different values in different persons, places or things (diastolic blood pressure, heights of students, hardness of tablets).
A quantitative variable is one that can be measured in the usual sense (heights, weights, drug content, plasma concentration at some time point).
Measurements made on quantitative variables convey information regarding amount.

6. Definitions
Whenever the values obtained from a measurement arise as a result of chance factors, so that they can not be exactly predicted in advance, the variable is called a random variable.
Continuous random variables indicate numerical observations that contain intervals with infinite (uncountable) possible values - e.g., weight, height, time, speed, etc.
Discrete random variables Discrete variables are also numerical measurements, but they are sparse in space and any characterized by gaps or interruptions in the values that it can assume. (number of students in a school, age??).

7. Definitions
Qualitative variables are characteristics that are not capable of being measured in the sense that height, weight, age and blood pressure are.
A person may be designated as belonging to an ethnic group or a place, an object may be said to possess or not possess some characteristic of interest.
In such cases measuring consists of categorizing (categorical variables).
Measurements made on qualitative variables convey information regarding attribute.

8. Definitions
Although in the case of qualitative variables, measurement in the usual sense is not achieved, we can count the number of persons, places or things (units) with a certain attribute.
These counts are referred to as frequencies.
Frequencies are numbers that we can manipulate when our analysis involves qualitative variables.

9. Definitions
Population: A population is an entire group, collection or space of objects which we want to characterize.
Sample: A sample is a collection of observations on which we measure one or more characteristics. Frequently, we use (small) samples of (large) populations to characterize the properties and affinities within the space of objects in the population of interest. For example, if we want to characterize the US population, we can take a sample (poll or survey) and the summaries that we obtain on the sample (e.g., mean age, race, income, body-weight, etc.) may be used to study the properties of the population, in general.

10. Definitions
A statistical inference is the procedure by which we reach a conclusion about a population on the basis of information contained in a sample that has been drawn from that population.
there are many kinds of samples that may be drawn from a population. The simplest type of scientific samples that may be used to draw inferences is the simple random sample.

11. Definitions
If you use the letter N to designate the size of a finite population and the letter n to designate the size of sample then:
If a sample of size n is drawn from a population of size N in such a way that every possible sample of size n has the same chance of being selected, the sample is called a simple random sample.

12. Measurement and Measurement Scale
A measurement may be defined as the assignment of numbers to objects or events according to a set of rules.
The various measurement scales result from the fact that measurements may be carried out under different set of rules:
The nominal scale
The ordinal scale
The interval scale
The ratio scale

13. Measurement and Measurement Scale
A nominal scale consists of “naming” observation or classifying them into various mutually exclusive and collectively exhaustive categories.
Male:female, well:sick, under 65 years of age: 65 and over, child:adult.

14. Measurement and Measurement Scale
An ordinal scale deals with observations that are not only different from category to category but can be ranked according to some criterion.
Rank in college (freshman, sophomore, junior, senior), size of soda (small, medium, large), the intelligence of children (above average, average, below average).
In each of the previous examples, the members of any one category are considered equal but the members of one category are considered lower, better or smaller than those in another category.
The function of numbers assigned to ordinal data is to order or rank the observations from lowest to highest.

15. Measurement and Measurement Scale
The interval scale is a more sophisticated scale than the nominal or ordinal scales.
In the interval scale, it is not only possible to order measurements but also the distance between any two measurements in known.
e.g. we know that the difference between a measurement of 20 and a measurement of 30 is equal to the difference between measurements of 30 and 40.
The ability to do this implies the use of a unit distance and a zero point.

16. Measurement and Measurement Scale
The selected zero point is not necessarily a true zero in that it does not have to indicate a total absence of the quantity being measured.
Temperature (degrees fahrinhite or Celsius)
"If it's twice as cold today as it was yesterday," runs a popular joke, "and it was zero degrees yesterday, how cold is it today?" This illustrates the limitation of interval measurements such as Celsius and Fahrenheit temperature: by setting zero at an arbitrary point, they make it impossible to multiply and divide meaningfully.

17. Measurement and Measurement Scale
The ratio scale is the highest level of measurement.
This scale is characterized by the fact that equality of ratios as well as equality of intervals may be determined.
The numbers assigned to objects have all the features of interval measurement and also have meaningful ratios between arbitrary pairs of numbers. Operations such as multiplication and division are therefore meaningful.
Variables measured at the ratio level are called ratio variables.