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# Statistic Concepts in Research * Dr. A. Asgari

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### Statistic Concepts in Research * Dr. A. Asgari

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