Introduction to statistics

By Dr. Amira Talic

What is “Statistics”?• •Statistics is the science of data that involves:• •Collecting• •Classifying• •Summarizing• •Organizing and• •Interpretation

• Of numerical information.• •Examples:• •Cricket batting averages• •Stock price• •Climatology data such as rainfall amounts, average temperatures• •Marketing information• •Gambling?

Key Terms

• What is Data? facts or information that is relevant or

appropriate to a decision maker• Population? •the totality of objects under

consideration• Sample? •a portion of the population that is

selected for analysis

Key Terms

• Parameter? a summary measure (e.g., mean) that

is computed to describe a characteristic of the population

• Statistic? a summary measure (e.g., mean) that

is computed to describe a characteristic of the sample

Variables

• Traits or characteristics that can change values from case to case.

• A variable is what is measured or manipulated in an experiment

•Examples:•Age•Gender•Income•Social class

Types Of Variables

• In causal relationships:• CAUSE =>EFFECTindependent variable & dependent variable•Independent variable: is a variable that can be

controlled or manipulated.An independent variable is the variable you have

control over (dose of drug)•Dependent variable: is a variable that cannot

be controlled or manipulated. Its values are predicted from the independent variable ( effect on the condition)

Types Of Variables

•Discrete variables are measured in units that cannot be subdivided. Example: Number of children

•Continuous variables are measured in a unit that can be subdivided infinitely. Example: Height

Statistical analysis

• Descriptive Statistics

• Inferential statistics

• Predictive modeling

Descriptive Statistics

•Gives us the overall picture about data•Presents data in the form of tables, charts and

graphs•Includes summary data•Avoids inferencesExamples:•Measures of central locationMean, median, mode and midrange•Measures of Variation•Variance, Standard Deviation, z-scores

Inferential Statistics

•Take decision on overall population using a sample

• “Sampled” data are incomplete but can still be representative of the population

•Permits the making of generalizations (inferences) about the data

• Probability theory is a major tool used to analyze sampled data

Predictive Modeling

• The science of predicting future outcomes based on historical events.

• Model Building: “Developing set of equations or mathematical formulation to forecast future behaviors based on current or historical data.”

• Regression, logistic Regression, time series analysis etc.,

Calculation of the probability

• Based on the characteristics of the population for the observed parameter

• (e.g. . Duration of the pregnancy, duration of the first labor stage, height, et cetera)

• To describe the population, “distribution”

will be used

Distribution

• A statistical distribution describes the numbers of times each possible outcome occurs in a sample

• Distributions for continuous variables are called continuous distributions ( e.g. height)

• They also carry the fancier name probability density

Distribution

• Some probability densities have particular importance in statistics. A very important one is shaped like a bell, and called the normal ( Gaussian) distribution.

• Many naturally-occurring phenomena can be approximated surprisingly well by this distribution. It will serve to illustrate some features of all continuous distributions.

Gaussian distribution

What are the Components of A Distribution?

• Measures of central tendency• Suppose we have a sample with 4

observations: 4, 1, 4, 3• Mean = the sum of a set of numbers

divided by the number of observations (4+1+4+3=12:4=3) Median - the middle point of a set of

numbers(3.5)

Components of distribution

• Mode - the most frequently occurring number. Mode=4

• Median - the middle point of a set of numbers(3.5)

Components of distribution

Measures of variationRange - the maximum value minus

the minimum value in a set of numbers. Range = 4-1 = 3

Standard Deviation - the average distance a data point is away from the mean.

[ (4 3)+( 1 3)+ (4 3)+ (3 3)]: 4=1standard deviation= 1

Standard deviation

Why to know about it ?

• Mean, Median, Mode, Range, and Standard Deviations are measurements in a sample (statistics) and can

also be used to make inferences on a population.

What do we expect from the statistical analysis?

• To find out whether there is a statistically significant difference between our sample

(e.g. pregnancy loss in Al Ain Hospital Patient) and general population

How to perform the statistical analysis?

• Statistics can take us to a beautiful journey of understanding ,but

Festina lente! make haste slowly

Let us take it easy!

With the love,

Dr. Amira