statistics full

Statistics Overview

  • What is Statistics?

    • The science of collecting, organizing, analyzing, interpreting, and presenting data.

    • Focus on Descriptive Statistics for this course.

Key Definitions

  • Population:

    • All active-duty enlisted personnel in the AETDC.

  • Sample:

    • 100 randomly selected active-duty enlisted personnel from the AETDC.

  • Variable:

    • Number of completed professional military education (PME) courses.

Data Types

  • Data Example:

    • Values indicating the number of PME courses: 0, 1, 2, 1, 3...

  • Parameter:

    • The average characteristic of a population (e.g., average age of all PAF Colonels).

  • Statistic:

    • Average age of a sample (e.g., sample of 50 PAF Colonels).

Sampling Design

  • Sampling Concepts:

    • Target Population:

      • The group from which representative information is desired.

    • Sampling Population:

      • The population from which a sample will be taken.

    • Sample:

      • A part or subset of the population from which information is collected.

Criteria of Sampling

  • Must be representative of the population.

  • Adequate sample size, practical, feasible, economical, and efficient.

Advantages of Sampling

  1. Cheaper

  2. Faster

  3. Higher quality of information

  4. More comprehensive data

  5. Only method for destructive procedures.

Types of Sampling Design

  • Probability Sampling:

    • Members of the population have a known chance of being selected.

    • Types include Simple Random, Stratified, Systematic, Cluster, Multi-stage.

  • Non-Probability Sampling:

    • Difficult to determine the probability of selection.

    • Types include Convenience, Judgmental, Quota, Accidental, Snowball.

Probability Sampling Methods

  • Simple Random Sampling:

    • Each member has an equal chance of selection, can use replacement or not.

  • Stratified Random Sampling:

    • Population divided into strata; a random sample is drawn from each.

  • Systematic Sampling:

    • Selecting every kth unit from an ordered population.

  • Cluster Sampling:

    • Selecting separate groups (clusters) and collecting data from each member of the selected clusters.

Non-Probability Sampling Methods

  1. Consecutive Sampling

    • Collecting data from a set period.

  2. Judgment (Purposive) Sampling

    • Selection based on expert judgment.

  3. Convenience Sampling

    • Using readily accessible subjects.

  4. Accidental Sampling

    • Collecting data from whoever is available.

  5. Quota Sampling

    • Fixed size samples from predetermined population segments.

  6. Snowball Sampling

    • Each participant refers additional participants.

Data Collection Methods

  1. Surveys/Questionnaires:

    • Asking questions to assess various factors (e.g., morale, job satisfaction).

  2. Interviews:

    • Direct conversation for detailed information (e.g., insights from experienced personnel).

  3. Observations:

    • Systematic recording of behaviors (e.g., evaluating training sessions).

  4. Document Review:

    • Analyzing existing records (e.g., flight logs).

  5. Data from Sensors:

    • Electronic data collection (e.g., radar, aircraft sensor data).

Measurements of Central Tendency

  • Mean:

    • The average calculated by summing values and dividing by number of values.

  • Median:

    • The middle value in an ordered data set.

  • Mode:

    • The most frequently occurring value in a data set.

Measures of Variance

  • Range:

    • The difference between the largest and smallest values.

    • Indicates how spread out the values are.

  • Variance:

    • Measures how much data points differ from the mean.

    • Types: Population Variance, Sample Variance.

  • Standard Deviation:

    • Square root of variance; indicates data dispersion around the mean.

Coefficient of Variation (CV)

  • CV Definition:

    • A measure of relative variability; expressed as a percentage.

  • Formula:

    • For population: CV = (standard deviation / mean) * 100%

    • For sample: CV = (sample standard deviation / sample mean) * 100%

Conclusion

  • Understanding sampling design and data collection methods is crucial for effective statistics in research.

  • Properly measuring central tendency and variation helps in data analysis and understanding underlying patterns.