Introduction to Statistics

• Mai Waheed (name).

Topic: Statistics

• Definition: The science that deals with collecting, organizing, tabulating, presenting, analyzing data to reach results that help in making rational decisions.
• It's a branch of science that deals with quantitative data of different phenomena, describing, tabulating, analyzing, testing, and inferring from them.
• The word statistics refers to the statistical method used in a specific research or study.
• Quantitative data related to a specific phenomenon in contrast to qualitative data about the same phenomenon or another phenomenon.

Importance and Benefits of Studying Statistics:

• Importance:Helps in describing the studied phenomenon with precise quantitative description.
• Explaining phenomenon and guiding the researcher to be specific in the steps of thinking in solving problems.
• Helps in summarizing the results of research in an easy and useful way.
• Helps in predicting different phenomena, based on objective indicators.
• Summary:Helps in describing the phenomenon in a precise quantitative description, explaining the phenomenon and knowing its relationship with other phenomena and variables, even knowing the impact of other changes on the phenomenon under study and the impact of some intervention programs on it, even predicting it through a set of objective indicators.
• Benefits: Enables the researcher to formulate the research problem, highlight it, and describe the phenomenon under study.
• Enables the researcher to verify the psychometric efficacy of the measurement tools used, which supports the accuracy of the results.
• Helps the researcher in answering the research questions and verifying the validity of scientific hypotheses based on ideal methods.
• Helps the researcher in summarizing the results in a suitable and understandable form, even generalizing the results of the study to the original population.
• Helps the researcher in predicting some phenomena.
• Helps the researcher in identifying the impact of one variable on another.

Types of Statistics

According to their functions in science:

• Descriptive Statistics: Refers to methods of organizing, summarizing, and describing data quantitatively. It specializes in collecting quantitative data related to a phenomenon, then drawing graphs.
• The most famous forms of classification: Measures of central tendency, dispersion, and correlation relationships.
• Inferential/Analytical Statistics: Deals with methods of inferring characteristics of a large group of individuals using observations made on a relatively small subgroup.
• It is concerned with setting sufficient objective conditions for the results extracted from a small sample to be valid for generalization to larger groups.

According to the nature of the data and the measurement level:

• Parametric Statistics: It involves treatments, equations, and statistical coefficients that are used when the distribution of values or scores in samples or populations they represent is generally a normal distribution, and the samples studied are relatively large.
• In the opposite case, non-parametric statistics should be used.
• Non-parametric Statistics: Refers to treatments, equations, and statistical coefficients.
• Differences between parametric and non-parametric statistics:-
  • Sample size: If the sample size is small, less than 30 individuals, non-parametric statistics are used, and vice versa.
  • Measurement level: If the extracted data follows the nominal or ordinal level, non-parametric statistics are used, while parametric statistics are used with variables from the interval or ratio level.
  • Availability of certain assumptions: The use of non-parametric statistics does not require certain assumptions such as the normality of data distribution.

Statistics and Measurement

• Measurement: The process of defining or estimating the size, dimensions, capacity, or quantity of something.
• It uses the language of quantity.
• Measurement Levels:
  • Nominal Scales:
    • Characteristics: The numbers do not indicate quantity or amount (separate numbers).
    • Function: Numbers are used to classify things into categories.
    • Mathematical Operations: Counting.
    • Examples: Gender, types of cars, numbers of soccer players.
  • Ordinal Scales:
    • Characteristics: Quantity is not indicated by a number (separate values).
    • Function: Numbers are used to classify things in descending or ascending order.
    • Mathematical Operations: Ranking.
    • Examples: Economic, social level, student estimates in exams.
  • Interval Scales:
    • Characteristics: Number indicates quantity or amount (separate values).
    • Function: Numbers are used to compare individuals' scores and place them on a continuum with equal intervals with an arbitrary zero.
    • Mathematical Operations: Addition and subtraction.
    • Examples: Student scores on psychological and achievement tests, Celsius thermometer readings for temperature.
  • Ratio Scales: Characteristics: Number indicates quantity or amount (continuous values). Function: Numbers are used to determine precise relationships between things and place them on a continuum with equal units and an absolute zero. Mathematical Operations: Addition, subtraction, multiplication, and division. Examples: Weight, height, time, temperature in Kelvin

Statistics and Scientific Research Steps:

• Scientific Research Steps:
  • Identifying and selecting the research problem.
  • Collecting data and determining the study sample.
  • Sources of the research problem Observation, contradictions in previous studies, theory.
  • Hypotheses and their formulation.
  • Types of hypotheses: Null hypothesis, non-directional alternative hypothesis.
  • Directional alternative hypothesis.
  • Data Sources: International sources, secondary sources, field sources.
• Types of Data: Self-data, objective data, quantitative data, and qualitative data.
• Data Collection Tools: Note its types, structured observation, non structured observation
• Interview Types: Structured interview and Non-structured Interview
• Questionnaire.
• Methods of Data Collection: Comprehensive inventory or census or Sample survey
• Data Tabulation: Descriptive Data Analysis & Inferential Data Analysis
• Interpretation.
• Preparing the final report of the study.

Statistics and Computer Science

• A computer can be used with efficiency when the data volume is large and when we need to repeat a type of work several times.
• Statistical Programs: A set of steps that guide the work of the computer and give it the ability to perform the required work steps to solve a statistical problem.