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# Statistic Concepts in Research * Dr. A. Asgari

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• 1. STATISTIC CONCEPTS IN RESAERCH
• 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
• CONTINUOUS VARIABLE:
• Variables that do not have a minimum unit value.
• Conceptually, the value may occur till infinity.
• e.g.: Distance measured, score, time, age
• DISCRETE VARIABLE
• 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
• 10. POPULATION SAMPLE DATA FROM POP? DESCRIBE THE POP. INFERENTIAL STAT. DATA FROM SAMPLE? RELATIONSHIPS BETWEEN POPULATION & SAMPLE
• 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.