The document provides an overview of a Design of Experiments (DOE) training consisting of 5 sessions covering basic statistics, factorial designs, central composite designs, and mixture designs. The first session introduces key concepts in basic statistics including population versus sample, variables, descriptive statistics such as mean and standard deviation, and the normal distribution. Variables can be quantitative or qualitative, and dependent or independent. Descriptive statistics summarize data, while inferential statistics make inferences about populations based on samples using techniques like point estimation, interval estimation, and hypothesis testing. The normal distribution is an important theoretical distribution defined by its mean and standard deviation.

1. 1
Design of Experiments

2. DOE Training Overview
• Basic StatisticsSession 1
• Basic StatisticsSession 2
• Factorial DesignSession 3
• Central Composite DesignSession 4
• Mixture DesignSession 5

3. Basic Statistics – Session 1
Part I
 Population Vs Sample
 Variables
 Descriptive statistics
 Normal Distribution
“I always find that statistics are hard to swallow
and impossible to digest”
 [Mrs Robert A Taft]

4. Population Vs Sample
Sample Ỹ
s
Population μ ,
sigma σ
Population: Complete set of Data, Observation or individuals of interest
Sample: A sample is a collection of n objects representing only a portion of
population
Y bar is used to estimate the population mean
Sample standard deviation (s) is used to estimate population standard deviation

5. Variables
Variables
Quantitative
(Numerical)
Continuous
e.g. Hardness, DT,
pH etc.
Discrete
e.g. Dice, coin
Qualitative
(Categorical)
Nominal
e.g. Grade of
excipient, Different
vendor
Ordinal
e.g. severity of
illness - mild,
moderate or severe
Variables are attributes that we want to study in the sample

6. Variables
 Variables can be further classified as:
 Dependent/Response. Variable of primary interest
(e.g. Dissolution, Hardness ). Not controlled by the experimenter.
 Independent/Factor
 called a Factor when controlled by experimenter.
(e.g. Disintegrant level, Binder level, Kneading time, Chopper
Speed etc. )

7. Descriptive and Inferential Statistics
 Descriptive - The branch of statistics devoted
to the summarization and description of data is called descriptive statistics.
 Inferential - The branch of statistics devoted concerned with using sample
data to make an inference about a population of data is called inferential statistics.
 Descriptive statistics includes
 Listing (charts and tables)
 Summary Statistics (Mean, SD, Variance etc.)
 Graphics
 Inferential statistics includes (Based on probability theory)
 point estimation,
 interval estimation and
 hypothesis testing

8.  Characteristics:
 Smooth Bell Shape Curved
 Symmetric: Mean = Median = Mode
 Defined by two parameters: Mean and standard deviation
(About 68% of values are within ± 1 s from the mean; about 95% of the values lie within ±
2 s; and about 99.7% are within ± 3 s. This fact is known as the 68-95-99.7 (empirical)
rule, or the 3-sigma rule)
Normal Distribution

9. NORMAL DISTRIBUTION
AREA BEYOND TWO STANDARD
DEVIATIONS ABOVE THE MEAN
MEAN=MEDIAN=MODE
CASES DISTRIBUTED
SYMMETRICALLY ABOUT THE
MEAN
THE EXTENT OF THE ‘SPREAD’
OF DATA AROUND THE MEAN
– MEASURED BY THE
STANDARD DEVIATION
99.7%± 3s

10. Computation of Descriptive Statistics
 We can use Design Expert software or Excel to compute
basic statistics

11. Thank you !!!!!