Statistic Concepts in Research * Dr. A. Asgari

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    • Dr. Azadeh Asgari
    Basic Statistic
  • 2. Measurement Scales
    • Measurement is the process of assigning values to whatever variable being measured.
    • Classification of measured variables = measurement scales.
    • There are FOUR scales:
    • nominal,
    • ordinal,
    • interval,
    • Ratio.
  • 3. 1. Nominal Measurement Scale
    • Measured by categories or labels
    • Given codes / categories are in numerical values / alphabet
    • Used to measure qualitative variables
    • e.g.: gender, race, program of study, types of houses, type of cars
    • Lowest level of measurement
  • 4. 2. Ordinal Measurement Scale
    • Measurement also in the form of categories / labels, but are arranged in order.
    • Each given value shows level of rating.
    • Suitable for qualitative & quantitative variables.
  • 5. 3. Interval Measurement Scale
    • Measurement is in quantitative scores / values
    • Given / measured quantities may have +ve / -ve values
    • Suitable for quantitative variables
    • e.g.: Performance in a subject, IQ scores, levels of self-concept, job satisfaction levels
  • 6. 4. Ratio Measurement Scale
    • Measurement is in quantitative values
    • For all variables that have absolute zero value
    • Given/measured quantities may have +ve/ -ve, and ratio values
    • e.g.: Training time, number of mistakes, time taken to run 100m, body weight, distance travelled
  • 7. Type of Variables
    • Variables that do not have a minimum unit value.
    • Conceptually, the value may occur till infinity.
    • e.g.: Distance measured, score, time, age
    • Variables that use finite countable minimum unit value
    • Use whole numbers most of the time
    • Value cannot be subdivided further
    • e.g.: Number of children, number of cars, number of programs
  • 8. Statistics
    • A mathematical technique or process to collect, organize, analyze, and interpret numerical data obtained from an observed group for a researched group.
    • Sometimes used for describing collected numerical data.
  • 9. Data Statistics
    • Describes group behaviour or characteristics obtained through observations on individuals in a group, so that generalizations may be made.
    • e.g.: Mean of monthly income = rm3,000.00
    • Mean age of year 4 students = 10 years
  • 11. Quantitative Research
    • Descriptive
    • Purpose is just to describe a studied group
    • e.g.: To study teacher attitude towards use of corporal punis.hment
    • Inferential
    • Purpose is to describe a population based on collected data from a sample
  • 12. Descriptive Statistics
    • Method of describing observed, processed, and analyzed data.
    • Main purpose is to obtain a picture or description of the observed data.
    • Another purpose is to give meaning and to summarize the data.
  • 13. Descriptive Statistics
    • Quantitatively
    • Describing using numeric values or quantities
    • Contains texts described using quantitative data analysis
    • Qualitatively
    • Describing in the form of pictures, texts, etc.
  • 14. Descriptive Statistics
    • Organizing data so that it would be more meaningful (quantitative)
      • Tables
      • Measures of central tendencies
    • Using pictures (qualitative)
      • Pie / bar charts
      • Histograms
      • Polygon frequencies
  • 15. Technique of Describing Data – Using Pictures
    • Nominal or Ordinal Data
    • Frequency distribution table
    • Bar chart
    • Pie chart
    • Contingency table
    • Interval or Ratio Data
    • Frequency distribution table
    • Histogram
    • Polygon frequency
    • Scatter diagram
    • Regression line
  • 16. Frequency Distribution Table RESULTS M F A B C D E F TOTAL
  • 17. Contingency Table BEd.TESL BEd.(G&C) TOTAL AGREE TO PUNISHMENT 120 18 138 DO NOT AGREE TO PUNISHMENT 20 98 118 TOTAL 140 116 256
  • 18. Technique of Describing Data – Measures of Central Tendencies
    • Mode
      • Nominal data
      • Most frequently occurring score
      • Commonly used measurement
    • Median
      • Ordinal data
      • Middle measurement
      • Suitable for skewed distribution
    • Mean
      • Interval or ratio data
      • Typical measurement
      • Average measurement
      • Suitable for further analysis
  • 19. Measures of Central Tendency
  • 20. Normal Curve
    • mode
    • median
    • mean
  • 21. Skewed to the Right (+ve)
    • mode median mean
  • 22. Skewed to the Left (-ve)
    • mean median mode
  • 23. Variability
    • Spread or dispersion distribution concept:
      • Homogeneous
      • Heterogeneous
  • 24. Measures of Variability
    • Range: highest minus lowest score
    • Interquartile Range: describes range of values for middle 50% of scores
    • Semi- Interquartile Range: describes avg. Spread of scores for 25% above and below the median
    • Standard Deviation: provides index of the average amount by which scores deviate from the mean
    • Variance: similar to standard deviation
  • 25. Inferential Statistics
    • Method of making conclusion on the researched population based on observations made on the sample .
    • e.g.:
      • Mean Difference
      • Analyses of Relationships
      • Process of describing or estimating the population characteristics using the characteristics of samples that are representative of the population.
  • 26. Inferential Strategies
    • Estimation – estimating the parameter value based on sample statistics.
    • Hypothesis Testing – testing the extent the parameter value is similar to the value observed from the sample.
  • 27. Inferential Precision
    • Sample Size
    • Variability of Population Data
    • Representativeness of Observed Sample, Taking into Consideration the Correct Sampling Procedure Used
  • 28. Inferential Technique
    • Parametric Test Making Assumptions on the Population From Which the Sample Was Selected.
    • More Powerful Than Nonparametric Tests & Able to Show Differences or True Relationships.
  • 29. Assumptions of Parametric Tests
    • Requires Data That Are At Least:
      • Interval data
      • Distribution is normal
      • Involves statistical & hypothesis testing
  • 30. Inferential Technique
    • Nonparametric tests make fewer assumptions about the population from which the sample was selected = distribution-free tests.
    • Advantage – safer to use if the assumptions necessary for parametric tests appear to have been violated.
  • 31. Hypothesis Testing
    • Testing null hypothesis using different tests based on type of measurement scale and data.
    • Making conclusion on the null hypothesis.
    • Making decision on the alternative hypothesis.