Statistics

Page $1$

• Statistics: science of collecting, organizing, presenting, analyzing, interpreting numerical data for efficient decision-making.

• Key applications: marketing, accounting, quality control, sports, education, politics, medicine.

• Branches:

  • Descriptive Statistics – summarizes data via numbers, charts, graphs, tables.

  • Inferential Statistics – draws conclusions about a population from a sample and measures reliability.

• Population vs. Sample: population = complete set; sample = subset used when full census impractical.

• Variables:

  • Qualitative – categorical (e.g., name, gender, address).

  • Quantitative – numeric; classified as
    • Discrete: countable values (e.g., number of children).
    • Continuous: any value in an interval (e.g., height).

• Levels of Measurement (intro): Nominal described here — labels only; only counting applicable.

Page $2$

• Levels of Measurement (cont.):

  • Ordinal – ranking; indicates order, not magnitude.

  • Interval – equal intervals; arbitrary zero (e.g., temperature $^\circ C$).

  • Ratio – all interval properties plus absolute zero (e.g., weight); all stats applicable.

• Data Collection: systematic gathering to answer questions/test hypotheses.

  • Sources: Primary vs. Secondary data.

  • Primary data methods:
    $1$. Direct Personal Interview – face-to-face; rich data, but time-consuming/expensive/bias risk.
    $2$. Questionnaire (Indirect) – suited for large samples.
    • Design principles: keep short, choose type, clear wording/order, intro letter, instructions, translation, pretest.

Page $3$

• Questionnaire Types:

  • Open-ended – free text; detailed but hard to analyze, lower response.

  • Closed-ended – fixed options; easy to analyze, high response but may bias/frustrate.

• Other Primary Methods:
  $3$. Focus Group – $6$–$12$ similar participants; faster/cheaper than interviews; response bias possible.
  $4$. Experiment – researcher controls conditions to study cause–effect; objective but costly, prone to recording error.
  $5$. Observation – record phenomena as they occur; objective, but limited info and costly.

Page $4$

• Secondary Data: previously collected; cheaper & quicker.
  Advantages: economical, time-saving, comparative base, new insights.
  Disadvantages: questionable accuracy, possible irrelevance, limited availability/cost.

• Key Secondary Sources:
  $1$. Published reports (newspapers/periodicals).
  $2$. Financial data in annual reports.
  $3$. Institutional records.
  $4$. Government department reports (e.g., census).

• Consequences of Poor Data Collection:
  • Inaccurate answers • Irreproducible studies • Wasted resources • Misleading future research • Faulty public policy • Potential harm to subjects.