Introduction to Statistics

• The lecture introduces statistics, covering its definition, types, historical context, and key concepts such as population and sample.
• The lecture also touches on measures of central tendency and dispersion, skewness, kurtosis, moments, normal distribution, sampling, Estimation Theory, and hypothesis testing.

Introduction to Statistics

• Business executives, managers, hospitals, universities, and other organizations rely on statistics for decision-making.
• Much of the information used in decision-making is in the form of numbers called "statistics".
• The word "statistics," derived from "world state," entered the English vocabulary in the 18th century.
• Statistics used to refer to sets of numerical data on population, taxes, wealth, exports, imports, and crop production for state officials.
• Now, statistics are a crucial branch of mathematics and tool for scientific research across all sciences.

Definition of Statistics

• Statistics is demonstrated through examples such as antibiotics reducing throat infection duration by 1-2 days.
• Examples also include the diagnosis of 50 angina patients at Ibn Al-Haythem hospital last year.
• Statistics is the science of assembling and interpreting numerical data (Blad, 2000).
• Statistics is a discipline for treating numerical data derived from groups of individuals (Armitage et al., 2001).

Types of Statistics

• Statistics is of two types: descriptive and inferential.

Descriptive Statistics

• Descriptive statistics involves the collection, organization, presentation, and summarization of data using tables or graphs.
• Examples include statistics on vital events like births, deaths, marriages, divorces, and disease incidence.

Inferential Statistics

• Inferential statistics uses a logical basis to draw conclusions about populations from sample results.
• Examples of inferential statistics include testing a new drug or medical procedure, then drawing conclusion regarding the drug's performance when it is used in a sample of patients with a disease, then the conclusion is drawn as to how it would perform among a target population
• The Iraqi National Health Survey is another example, that collects data on illness and disability to infer characteristics in the total population.

History of Statistics

• Descriptive statistics were used in early civilizations like Babylonia, Assyria, and Greece to count soldiers, agriculture production, and estimate taxes.
• Inferential statistics are mainly based on probability theory and developed mostly in 16th-century Europe.

Famous Scientists in Statistics

• Key mathematicians included Pascal and Bernoulli.
• De Moivre discovered the Normal distribution in 1833.
• Karl Pearson and Francis Galton discovered correlation and regression in 1822-1911.
• R.A. Fisher developed and applied statistics in biology, economics, and agriculture.

Population and Sample

• In everyday language, a population refers to all people in a specific area, like the population of Baghdad.
• In statistics, population has a broader meaning, referring to all houses in a town where each house is considered an element.
• Information about a population is needed to make decisions.
• It is often too costly or time-consuming to obtain information about all elements in a population.
• A sample is a subset of elements from a population.
• Target and study populations should be distinguished.
• The target population is the group an investigator wants to draw conclusions about.
• The study population is the actual population from which the sample is drawn.
• Target population are patients with hypertension
• Study Population are patients admitted to Al-Sadder hospital
• The sample are records of the above patients
• If the target population and study population are identical, there are no interpretation difficulties.
• Conclusions are valid for the study population if the target differs from the study population.
• Selective examples can indicate an issue with the approach.
• Samples can be selective depending on the proportion of patients who have not been hospitalized, potentially impacting results.
• A population is a complete set of people or subjects to be studied.
• A sample is a smaller part of that population.
• "All the smokers in Iraq" can be taken as an example of a population. In the study of smoking, it would be almost impossible to study every single smoker.
• Sample size is chosen because of time and money constraints.
• Say 1000 smokers are to be sample. This constitutes the sample.
• A sample of units selected from a population provides data.

Population types

• Population can be finite or infinite.
• Finite population allows collection of data on everyone.
• Measuring student height at the university of Kufa constitues a finite population.
• Infinite populations do not allow the collection of data on everyone.
• Number of bacteria in a study field counts as an infinite study.