Statistics Overview

Statistical Summary

• Course Objectives: Analytical statistics in scientific research aims for accurate and trustworthy results; it saves researchers time and effort in analysis, organizes and combines various phenomena and arguments; it gathers data and information following clear steps; it seeks precise results about the phenomenon.

Origins of Statistics

• Early Stages: Statistics began in the middle ages with state population counts, used to assess available manpower (military potential) and to levy taxes.

Definition of Statistics

• Comprehensive Definition: Statistics is the science of designing, collecting, organizing, summarizing, presenting, and analyzing data.

Types of Statistics

Descriptive Statistics

• Focus: Gathering, organizing, and summarizing data to understand information.
• Methodology: Primarily relies on descriptive methods.

Analytical Statistics

• Alternative Name: Inferential statistics.
• Focus: Aims to analyze and interpret numerical data using samples to reach logical conclusions and confirm the validity of hypotheses.

Data Handling Steps

• Data Organization and Management: Includes organizing, classifying, presenting, and analyzing data to extract meaningful information, and make informed choices.

Stages of Statistical Methodology

• Data Collection: Defining the research scope with specified time and geographic parameters, and defining concepts; selecting suitable samples based on specific guidelines and principles.
• Sampling Methods:
  • Random Sampling: Choosing samples randomly.
  • Stratified Sampling: Choosing samples based on specific strata (e.g., rich/poor).
  • Systematic Sampling: Choosing samples in a systematic manner.

Statistical Population and Sample

• Population: The entire group of individuals or items that are the subject of study. The goal is to draw conclusions about the population characteristics.
• Sample: A subset of the population that is selected for analysis to represent the population.

Types of Data

Quantitative Data

• Numerical Data: Represents quantities and is used in various contexts like student counts, classroom numbers, or individuals' counts.
  • Discrete: Numerical data represented by whole numbers (e.g., 1, 2, 3).
  • Continuous: Numerical data represented by numbers with decimal points (e.g., 4.6). This is applicable to measurements like temperature, height, or age.

Qualitative Data

• Descriptive Data: Represents characteristics.
  • Nominal: Categorical or descriptive data without a particular order (e.g., majors, gender (male/female), occupations).
  • Ordinal: Categorical data represented by order (e.g., student level (freshman, sophomore, junior, senior)).

Significance of Data Types

• Importance: Suitable analysis methods depend on data type.

SPSS Analysis Steps

• Data Entry: Naming variables, inputting data into rows and columns.
• Analysis Selection: Choosing the appropriate statistical analysis method.
• Output Review and Adjustment: Assessing and modifying analysis results.

SPSS Features

• Ease of Data Input: Provides separate input windows for variables and data.
• Easy Result Extraction: Results appear in separate windows for easier printout.
• Visual Presentation: Offers diverse graphical representations.
• External Data Compatibility: Allows integration with other programs like Excel and Access.

SPSS File Types and Functions

• File: Used for tasks like opening files, creating files, editing files, and displaying file information.
• Edit: Used for editing operations, copy-paste, text search, and variable selection.
• View: Used for showing and hiding toolbars, grids, and adjustments to the display format.
• Data: For variable and data value definition.
• Utilities: Used to select specific variable subsets.
• Transform: Used to generate new variables by recoding variables or creating random values.
• Analyze: The primary tool for conducting statistical analyses.
• Graphs: For creating various graphical representations.
• Windows: For managing and switching between windows.
• Help: Information and guidance within the software.

Preparing Data Files

• New File: Entering data in a new file.
• Existing File: Importing data from other programs. (e.g., SPSS or other applications).

Variable View and Data View

• Variable View: Defines columns (variables).
• Data View: Shows inputted data.

Variable Content

• Variable Name: Variable names, limited to 8 characters without spaces or special characters.
• Variable Type: Specifies variable types (numerical, dates, strings).
• Numeric Type: Integer, comma-separated, decimal separator, scientific notation, dollar, currency.
• Data Types: Numeric, comma, dot, scientific, dollar, currency, date, string.
• Missing Values: Handling missing values.
• Alignment: Variables’ data arrangement.
• Values: Variable values, providing categories for categorical variables.
• Column Width: Setting column widths in the Data View.
• Measurement Types: Scale, ordinal, nominal.

SPSS Data Input

• Excel File Import: Importing data from Excel.

Descriptive Statistics Analysis

• Frequency Analysis: Analyzing qualitative data (categorical data or frequencies).
• Descriptive Statistics: Analyzing numerical data. Calculating central tendency (mean, median, mode), and dispersion (standard deviation, variance, minimum, maximum).

Assessing Data Distribution

• Graphical Methods: Histograms, box plots, normal probability plots.
• Statistical Summaries: Skewness, kurtosis.

Hypothesis Testing

• Hypothesis: A logical assumption/inference based on data not on exact calculations, and thus, unable to perform a detailed study of the whole population. This is the core of hypothesis testing.
• Hypothesis Tests: Used to solve scientific problems regarding acceptance/rejection of a specific hypothesis.
• Types:
  • Parametric: Concerned with the unknown parameters of a population (e.g., means, proportions, variances, and correlation coefficients).
  • Non-parametric: More focused on qualitative aspects related to the population.
• Methods:
• Determine Hypothesis: Define the null hypothesis (no change or equality) and the alternative hypothesis (change or inequality).
• Significance Level: Establish a significance level (e.g., 5% representing 95% confidence indicating the possible error rate that one may accept).
• Test: Select an appropriate statistical test based on the null and alternative hypotheses.
• Decision: Compare computed results with critical values from a suitable statistical table.
• Error Rate: The decision to accept/reject the null hypothesis depends on whether the p-value is less than or equal to/greater than the significance level (alpha). Alpha (α) is the significance level, usually set to 0.05 (or 5%).

T-Tests

• Application: Comparing means of single samples or two independent/paired experimental groups.
• Types:
  • One Sample t-test: Testing whether a sample mean is statistically different from a known population mean.
  • Independent Samples t-test: Comparing the means of two independent groups (e.g., males vs. females).
  • Paired Samples t-test: Comparing means of two dependent groups/paired observations (e.g., data collected before and after an intervention).

One-Way ANOVA

• Application: Analyzing the differences between three or more groups.
• Conditions: Random samples, normal distributions, equal variances across groups.
• Understanding the ANOVA test results (interpretation of significance): Understanding variance (variation) in the data, and homogeneity.

Correlation

• Definition: Assessing the strength and direction of a relationship between two variables (i.e., their dependency.)
• Types:
  • Positive correlation: Variables tend to change in the same direction.
  • Negative correlation: Variables tend to change in opposite directions.
• Correlation coefficients: Numerical values that quantify the strength and direction of the correlation. (values range from -1 to +1). A coefficient of 1 or -1 indicates perfect positive or negative correlation, respectively, while a coefficient of zero signifies no linear correlation.

تتناول هذه الاختبار أساسيات علم الإحصاء، بدءًا من تعريفه إلى أنواعه المختلفة. يتضمن ذلك الإحصاءات الوصفية والإحصاءات التحليلية، مع التركيز على كيفية جمع البيانات وتحليلها. يعتبر هذا الاختبار مفيدًا للباحثين في فهم الأدوات الأساسية للإحصاء.