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# Statistics

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### Statistics

1. 1. STATISTICS <ul><li>DESCRIPTIVE STATISTIC </li></ul><ul><li>describe & organize data in a meaningful way </li></ul><ul><li>Summarize data </li></ul><ul><li>Investigate relationships between variables </li></ul><ul><li>A preliminary analysis before using inferential techniques </li></ul>
2. 2. INFERENTIAL STATISTICS <ul><li>To draw conclusions </li></ul><ul><li>To make generalization about population </li></ul>
3. 3. TYPES OF DATA <ul><li>NOMINAL DATA </li></ul><ul><li>a. Categories of names with no implied in order </li></ul><ul><li>b. Represent different characteristics of given variable. </li></ul><ul><li>c. e.g. Gender 1. male 2 Female </li></ul><ul><li>Name of town </li></ul><ul><li>Exam subjects </li></ul>
4. 4. ORDINAL DATA <ul><li>Ordered data with spaces or interval between data values –not necessarily equal. </li></ul><ul><li>The numbers assigned to the items-numerical significance indicate –ranking of those items </li></ul><ul><li>e.g. strongly agree =1, agree = 2 no opinion = 3, disagree = 4 strongly disagree = 5 </li></ul><ul><li>Birth position in family, exam grades </li></ul>
5. 5. Interval Data <ul><li>Ordered data with spaces or intervals between data values that are equal. </li></ul><ul><li>The number assigned to the items within a variable have numerical significance, indicate the ranking of those items </li></ul><ul><li>Indicate the interval between those item </li></ul>
6. 6. e.g. Interval Data <ul><li>IQ Scale </li></ul><ul><li>The interval between 100 and 101 is the same as those between 101 and 102 and between 102 and 103 </li></ul><ul><li>Exam scores </li></ul>
7. 7. RATIO DATA <ul><li>The ordered data with space intervals between data values that are equal. </li></ul><ul><li>Contain a true or rational zero point </li></ul><ul><li>Ratio data have meaningful ratios. </li></ul>
8. 8. ratio <ul><li>e.g. (1) interval between 5 and 6 (correct) is the same as those 6 and 7 and between 7 and 8. (2) there is a true zero point (0 correct) (3) a score 10 is twice as much as score of 5 and half as much as a score of 20 </li></ul><ul><li>Family size, number of exam passes </li></ul>
9. 9. COMPARING TWO MEANS <ul><li>Test the statistical significance of the differences between two means – consideration: </li></ul><ul><li>a. the nature of data </li></ul><ul><li>b. the nature of samples </li></ul>
10. 10. Parametric Test (t-test) <ul><li>Interval or ratio data </li></ul><ul><li>Data normally distributed </li></ul><ul><li>Homogeneity of variance </li></ul>
11. 11. Samples paired-dependent or correlated <ul><li>Use a t-test for paired sample </li></ul>
12. 12. Sample unpaired – independent or uncorrelated <ul><li>Use a t-test for unpaired sample </li></ul>
13. 13. Non- Parametric Test <ul><li>Nominal or ordinal data </li></ul><ul><li>If the samples are paired – a Wilcoxon sign-ranked test would be use </li></ul><ul><li>If the sample are unpaired- a Mann- Whitney U test </li></ul>
14. 14. Comparing Three or More Means <ul><li>Considerations </li></ul><ul><li>a. Nature of the data </li></ul><ul><li>b. Interval or Ratio Data </li></ul><ul><li>c. Data are normally distributed </li></ul><ul><li>Use analysis of Variance (ANOVA) </li></ul>
15. 15. Use Kruskal – Wallis one – way analysis of variance if <ul><li>Any variable is ordinal data and there is only one factor. </li></ul><ul><li>Non-parametric </li></ul>
16. 16. ANOVA <ul><li>Common inferential statistical technique </li></ul>