Statistical Analysis with Software Application

• Statistics plays a crucial role in research by providing evidence to support opinions or judgments
• Statistics are needed because all real-world processes exhibit variability due to changes in underlying conditions
• In most applications, it is not possible to study the whole population, leading to an element of uncertainty
• Some applications of statistical analysis include:

  • Visualization of company's performance over time and in real-time
  • Comparing the effects of different fertilizers on crop yield
  • Determining associations between income and educational attainment
  • Comparing the effectiveness of different diet programs
  • Assessing job satisfaction scores
  • Evaluating student performance
• Descriptive statistics are used to summarize and describe data collected from surveys, experiments, historical records, or observations
• Measures of central tendency include mean, median, and mode
• Measures of variability include range, variance, standard deviation, and coefficient of variation
• Inferential statistics are used to draw conclusions about a population based on sample data
• Parametric tests include T-test, Z-test, linear regression, Pearson r, and ANOVA
• Non-parametric tests include Mann-Whitney U, Kruskal-Wallis H, Spearman, Wilcoxon, Friedman, and Chi-Square
• Two classifications of statistics are descriptive statistics and inferential statistics
• Descriptive statistical analysis describes what is shown in the data using graphical and numerical descriptions
• Levels of measurement:

  • Nominal: Numbers or symbols used to classify, distinct categories (e.g., Sex)
  • Ordinal: Accounts for order without distance indication (e.g., Size of Shirt)
  • Interval: Equal intervals, can be added or subtracted, no absolute zero (e.g., Temperature, IQ)
  • Ratio: Has an absolute zero (e.g., Income, Production)
• Sample exercise:

  • Amount of travel expense of employees is quantitative, continuous, and interval
  • Zip code is qualitative and nominal
  • Membership in an organization is qualitative and nominal
  • Length of service is quantitative, discrete, and ratio
  • Satisfaction with the training program is qualitative and ordinal
  • Reproductive Health Bill stance is qualitative and nominal
  • Number of employees given bonuses is quantitative, discrete, and ratio
  • Proportion of employees benefiting from a program is quantitative, continuous, and ratio