Analysis of Variance (ANOVA)One-way ANOVA for

Completely Randomized Design (CRD)

Group 5

• Mohd. Saddam Bin Zainuddin UK28366

• Tengku Muriana Binti Tengku AzmanUK28331

• Nor Atiqah Binti Lokman UK28376

• Siti Nur Adila Binti Hamzah UK28361

• Asmiza Binti Abdullah UK28373

• Nurfatanazirah Binti Saad UK28377

• Farah Nabila Binti Ali UK28380

• Siti Norhajar Binti Zakaria UK28316

Outline of CRD Presentation

1. The Group Number and its Members

2. The research Problem

3. Treatments and Explanations

4. Field Layout of Experimental Designs

5. Step-by-step Procedures of Experimental Designs

6. Test of Homogeneity

7. ANOVA Table

8. Hypothesis Testing (Null Hypothesis)

9. Conclusions of Hypothesis Testing

10. Post Hoc Test (i.e. Tukey Test)

11. Result & Discussion (Give some logical Reasons)

12. Summary

The Research Problem

Diets Replications1 2 3 4 5 6

D1 25 50 24 36 41 33D2 81 54 45 62 80 30D3 67 87 62 45 59 70D4 65 61 46 48 60 69

Twenty-four rats were selected to study the effects of four extra different types of diets: (D1: 0.1 % vitamin and 10 % protein, D2: 0.1 % vitamin and 25 % protein, D3: 0.5 % vitamin and 20 % protein and D4: 0.2 % vitamin and 20 % protein). The diets were given for a two-week period. The experiment was using 6 times of replications. After CRD experiment period, the gains in weights were recorded. Using P=0.01 and P=0.05 as the level of significance, the null hypothesis is stating that the diets have no different effects on weights. The observations are follows:

Table 5: Weight gains of rats due to the effects of four different types of diets

Treatments and Explanations

D1: 0.1 % vitamin and 10 % protein

D2: 0.1 % vitamin and 25 % protein

D3: 0.5 % vitamin and 20 % protein

D4: 0.2 % vitamin and 20 % protein

Treatments and Explanations

The treatments were already used for different diets to know the weight gains of rats with the same environments and different rats.

This research would compare the above treatment also with the same environments and the different rats with purpose to find out which diet (0.1 % vitamin and 10 % protein, 0.1 % vitamin and 25 % protein, D3: 0.5 % vitamin and 20 % protein, D4: 0.2 % vitamin and 20 % protein) is the highly optimal diet to gain the weight of rats.

We hope with this research results, we are able to know the appropriate diet to produce more healthy rats for many reasons such as biomedical research and laboratory purposes.

Background of Treatments

Varloud M. et al., (2009)

Animals used in biomedical research are maintained in strictly controlled conditions. The diet is one parameter that must be managed in order to limit random variations of the phenotypic expression, ensure the reliability of the animal models. Therefore, the diet served must not only comply with palatability, stability and safety requirements, but above all it must meet the animal nutritional needs which may vary and depend upon it’s physiological status. Currently there is a huge concern in providing diets to rodents which are free of any source of raw material which may contain animal product and by-product of animal origin.

Knapka et al., 1974

A fixed-formula diet may contain multiple sources of protein, fat, and carbohydrate, thereby reducing the importance of variation in the composition of any particular ingredient from batch to batch.

Background of TreatmentsWostmann (1975)

Adjustments in nutrient concentrations, the kinds of ingredients, and methods of preparation must be considered when formulating diets for laboratory animals reared in germ-free environments or environments free of specific pathogens.

Karmas (1975)

Target nutrient concentrations must take into account estimated nutrient requirements, possible nutrient losses during manufacturing and storage, bioavailability of nutrients in the ingredients, and potential nutrient interactions.

National Research Council (1995)

A laboratory animal's nutritional status influences its ability to reach its genetic potential for growth, reproduction, and longevity and to respond to pathogens and other environmental stresses. A nutritionally balanced diet is important both for the welfare of laboratory animals and to ensure that experimental results are not biased by unintended nutritional factors.

Field Layout of Experimental DesignsLayout of Rats Research by using CRD Experiment (before randomized)

Treatments (as Diets, D)

Rats+D1 Rats+D2 Rats+D3Rats+D4

Replication (6 Times)

Experimental units will be randomly assigned to treatments by using lottery or other methods.

Field Layout of Experimental DesignsLayout of Rats Research by using CRD Experiment (after

randomized) Layout of Experimental Unit

Replication (6 Times)

Note: T : Diets (4 Treatments, T1, T2, T3, T4) R : Rats (6 Replications, R1-R6)

T1R4T2R2T4R5T4R6T1R1T3R5

T4R4T2R4T1R5T3R1T4R3T2R1

T3R3T4R2T3R6T1R6

T2R3T3R2

T2R6T1R2

T4R1T2R5T3R4T1R3

SPSS OUTPUT

Step-by-step Procedures of Experimental DesignsEntering Data into SPSS

Step-by-step Procedures of Experimental DesignsSteps to analyze data

1. Determine the data above is normally distributed and homogeneous.

2. Analyze using one-way ANOVA.

3. Make hypothesis to get a decision.

4. Continue with Post Hoc Test.

5. Result & Discussion.

6. Conclusion

Homogeneous because 0.234 > 0.05

Test of Homogeneity

Significance correction α = 0.05

If the significance obtained > α, so the variance of each sample is homogeneous.

If the significance obtained < α, so the variance of each sample is not homogeneous.

Analysis of Variance (ANOVA)

Note: Between Group = Treatments Within Groups = Error

Hypothesis

H0: µ1 = µ2 = µ3 = ... = µt

All Population Means are Equal

No Treatment Effect

H1 : Not All µi Are Equal

At Least 1 Pop. Mean is Different

Treatment Effect

NOT µ1 ≠ µ2 ≠ ... ≠ µt

Hypothesis Testing

H0: μ1 = μ2 = μ3

H1: μi not all equal. (i=1,2,3)

Significance correction

If the significance obtained > 0.05 , H0 is received

If the significance obtained < 0.05, H0 is rejected, H1 is received

Conclusion: because of the sig is 0.007, that means sig < 0.05. Therefore, H0 is rejected, H1 is reeived. So at least there is a diet (treatment) which effects on weights. Which Diet? To answer the question, we continue to proceed the Post Hoc Test in order to find out which diet that effects the weights.

Post Hoc TestSignificance level: 0.01

Output of Post Hoc Test

Post Hoc TestSignificance level:

0.05

Output of Post Hoc Test

Determining the Best Treatment for Research Recommendations

The selected treatment is accepted based on the statistically and reasonable measurements of genetic, health aspects and environmental condition.

The selected treatment does not give out neither excessive nor deficiency effect but it provides optimum effect.

Its effect is significantly different of those of lower treatments level, but for the treatment effects at same or higher levels, it differs not significantly different with.

Effects of different diets on the weight gains of the rats (day)

Treatment Mean

Tr.1 (D1: 0.1 % vitamin and 10 % protein) 34.83 ± 9.87a

Tr.2 (D2: 0.1 % vitamin and 25 % protein) 58.67 ± 19.98ab

Tr.3 (D3: 0.5 % vitamin and 20 % protein) 65.00 ± 13.84b

Tr.4 (D4: 0.2 % vitamin and 20 % protein) 58.17 ± 9.24ab

Weight gains

Means with the same superscript within the each column are very significantly different at

1% level (p<0.01)

Effects of different diets on the weight gains of the rats (day)

Treatment Mean

Tr.1 (D1: 0.1 % vitamin and 10 % protein) 34.83 ± 9.87a

Tr.2 (D2: 0.1 % vitamin and 25 % protein) 58.67 ± 19.98b

Tr.3 (D3: 0.5 % vitamin and 20 % protein) 65.00 ± 13.84b

Tr.4 (D4: 0.2 % vitamin and 20 % protein) 58.17 ± 9.24b

Weight gains

Means with the same superscript within the each column are significantly different at 5% level

(p<0.05)

Result and Discussion

From the Post Hoc Test, for sig value is 0.006, 0.035 and 0.040 (sig < 0.01) and (sig < 0.05), it means three diets have the different impacts. T1-T2, T1-T3 and T1-T4 are significantly different.

Diets T2, T3 and T4 are less effective than T1. Their causes are that T1 has better vitamin and protein proportion in the diet for weight gain of the rats (34.83 g).

There are sig value of 0.829, 0.859 and 1.000 (sig < 0.01) and (sig >0.05). It means the three diets are statistically not different (T2: 58.67 g, T3: 65.00 g and T4: 58.17 g). These diets have the same ability level in gaining the weight of rats.

Summary The best treatment is T1 (0.1 % vitamin and 10 % protein). It contains

appropriate vitamin and protein proportion for optimum weight gain of the rats. This is may be because of the better amount of protein consumed by the rats. Protein should not be consumed in a large amount but only optimum amount.

This is may be due to the each diet has its own effect. T2 (0.1 % vitamin and 25 % protein) which is may be unsuitable proportion of two type of essential components.

T3 (0.5 % vitamin and 20 % protein) is a combination of excessive proportion of vitamin and protein needed for the rats. This will lead to many health problems.

T4 (0.2 % vitamin and 20 % protein) is a combination of unsuitable proportion that will not lead to optimum weight gain.

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