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LECTURE

LECTURE. Saturday : 0830 – 1020 am Location : A 104. LAB. Tuesday : 1400-1700 Location : Makmal Biometri, Blok D. EVALUATION. Lab and Quiz 20 %. Mid Term Exam (17 Oktober) 40 %. Final Examination 40 %.

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LECTURE

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  1. LECTURE Saturday : 0830 – 1020 am Location : A 104

  2. LAB. Tuesday : 1400-1700 Location : Makmal Biometri, Blok D

  3. EVALUATION Lab and Quiz 20 % Mid Term Exam (17 Oktober) 40 % Final Examination 40 %

  4. TESTS Mid Term Exam Final Exam

  5. PRINCIPLES OF EXPERIMENTAL DESIGN

  6. Population SAMPLE

  7. Parameter Statistic

  8. Difference When describing a population, one may use a parameter or a statistic. However, they differ in the quality of information. A parameter is a numerical value that is equivalent to an entire population while a statistic is a numerical value that represents a sample of an entire population. To distinguish between whether something is a parameter or a statistic, you might ask yourself if the data you are looking at includes the entire population that you are examining or some of the people from the entire population. For instance, 'What percentage of people in your household like sweet potatoes?' is a question that can easily be answered by polling everyone at home, which would be a parameter. But, in order for this question, 'How many people in the world like sweet potatoes?' to be answered as a parameter requires that you ask every single person in the world – not likely. This is where a representative sample becomes important. And, when there is a sample of the population, there is a statistic to be found.

  9. VARIABLES Characteristics of the experimental unit that can be measured

  10. VARIABLES QUANTITATIVE QUALITATIVE

  11. DISCREET CONTINUOUS

  12. DATA Characteristics Count Status Measurement Digital

  13. Examples: Variable Data Weight 75 kg Speed of a lorry 35 km hr -1 Number of female student 54 purple Colour of a flower

  14. STATISTICS Central Tendency Dispersion

  15. Distribution of Data Normal Curve or Bell Curve

  16. A pot experiment was conducted to determine the effect of N rate(0, 45, 90, 135 and 180 kg N ha-1) with four replications on yield of maize cobs

  17. Examples: Complete Randomized Design (CRD) Randomized Complete Block Design (RCBD) Latin Square Design Split Plot Design

  18. Complete Randomized Design It is used when an area or location or experimental materials are homogeneous. For completely randomized design (CRD), each experimental unit has the same chance of receiving a treatment in completely randomized manner.

  19. Randomized Complete Block Design In this design treatments are assigned at random to a group of experimental units called the block. A block consists of uniform experimental units. The main aim of this design is to keep the variability among experimental units within a block as small as possible and to maximize differences among the blocks.

  20. Latin Square Design Latin square design handles two known sources of variation among experimental units simultaneously. It treats the sources as two independent blocking criteria: row-blocking and column-blocking. This is achieved by making sure that every treatment occurs only once in each row-block and once in each column-block. This helps to remove variability from the experimental error associated with both these effects.

  21. ANALYSIS OF VARIANCE (ANOVA) Analysis of variance (ANOVA) is to determine the ratio of between samples to the variance of within samples that is the F distribution. The value of F is used to reject or accept the null hypothesis. It is used to analyze the variances of treatments or events for significant differences between treatment variances, particularly in situations where more than two treatments are involved. ANOVA can on only be used to ascertain if the treatment differences are significant or not.

  22. F =s2, calculated from sample mean s2, calculate from variance between individual sample = sa2 (variance between samples) sd2 (variance within samples)

  23. HYPHOTHESIS TESTING FOR MORE THAN TWO MEANS F Distribution

  24. TESTING OF HYPOTHESIS

  25. HYPOTHESIS Null Alternative

  26. Null Hypothesis Statement indicating that a parameter having certain value Alternative Hypothesis Statement indicating that a parameter having value that differ from null hypothesis

  27. Critical area Probability level Critical value

  28. Critical area • area to reject null hypothesis

  29. Probability level

  30. Critical value

  31. Analysis of Variance (ANOVA) Sum of Squares (SS) Source of Variation Mean Square (MS) F df Between (B) Within (W) Total (T)

  32. Below are yield (t/ha) for 5 varieties of corn Variety V1 V2 V3 V4 V5 3.8 5.2 8.8 10.9 7.3 4.6 5.0 6.3 9.4 8.6 4.6 6.7 7.4 11.3 7.2 4.8 6.1 8.3 12.4 7.8 Test at α = 0.05 whether there a significant difference among the means

  33. HYPOTHESIS TESTING State your hypothesis Choose your probability level Choose your statistics Calculation Result Conclusion

  34. Analisis Varian (ANOVA) Jumlah kuasa dua (JKD) Min kuasa dua (MKD) Sumber variasi F dk Antara (A) Dalam (D) Jumlah (J)

  35. ANALYSIS VARIANCE FOR ONE FACTOR EXPERIMENT ARRANGED IN DIFFERENT EXPERIMENTAL DESIGNS CRD RCBD LATIN SQUARE

  36. COMPARISON OF MEANS Comparison of means is conducted when HO is being rejected during the process of ANOVA. When HO is rejected, there is at least one significant difference between the treatment means. There are various methods of to compare for significant difference between the treatments means. The means of more than two means are often compared for significant difference using Least Significant Difference (LSD) test, Duncan New Multiple Range (DMRT) test, Tukey’s test, Scheffe’s test, Student –Newman-Keul’s test (SNK), Dunnett’s test and Contrast. However, more often than not, such tests are misused. One of the main reasons for this is the lack of clear understanding of what pair and group comparisons as well as what the structure of treatments under investigation are. There are two types of pair comparison namely planned and unplanned pair.

  37. MEANS SEPARATION LSD Tukey CONTRAST

  38. = tα/2 LSD 2 MS (within) r

  39. TUKEY (HSD)

  40. CONTRAST 1. Calculate the total 2. Assign the coefficient for the means selected to see the difference 3. Determine Σci2, Q and r 4. Calculate MSQ 5. Calculate F

  41. CONTRAST T1 T2 T3 T4 T5 ci2 Q r MSQ F

  42. DATA TRANSFORMATION Data that are not conformed to normal distribution need to be transformed to normalize the data. Usually discrete data are required to be transformed so as various statistical analyses can be carried out.

  43. LOG TRANSFORMATION conducted when the variance or standard deviation increase proportionally with the mean Examples • number of insects per plot • number of eggs of insect per plant • number of leaves per plant If there is zero, convert all the data to log(x+1)

  44. SQUARE ROOT TRANSFORMATION • conducted for low value data or occurrence of unique/weird situation Examples • number of plants with disease • number of weeds per plot If there is zero, use x + 0.5 • can also be used for percentage data 0 – 30 or 70 - 100

  45. ARC SINE TRANSFORMATION • conducted for ratio, number and percentages Criteria 1: If percentages fall between 30-70, no transformation Criteria 2: If percentages fall between 0-30 atau 70-100, use square root transformation Criteria 3: If di not qualifies for criteria 1 and 2 use 1 or 2, use arc sine When there is 0 (1/4n) When there is 100 (100 - 1/4n)

  46. NON-PARAMETRIC TEST • Sign test – one sample • Sign test – two samples • Wilcoxon-Mann-Whitney

  47. NON-PARAMETRIC TEST A non parametric test is a hypothesis that does not require specific conditions concerning the shape of the populations or the value of any populations parameters. Non parametric tests are sometime called distribution free statistics because they do not require the data fit a normal distribution.

  48. Percentage octane content in petrol A are as the following: 97.0, 94.7, 96.8, 99.8, 96.3, 98.6, 95.4, 92.7, 97.7, 97.1, 96.9, 94.4 Test = 98.0 compare to < 98.0 at = 0.05

  49. Sign test – two samples (paired) Two types of paper was judged by 10 judges to determine which which paper is softer based on the scale 1 to10. Higher value indicate is more soft. 1 2 3 4 5 6 7 8 9 10 Judge Paper A 6 8 4 9 4 7 6 5 6 8 Paper B 4 5 5 8 1 9 2 3 7 2

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