The Square Root Transformation in Analysis of Variance

We evaluated the nut harvesting date (NHD), nut weight (NW), pericarp splitting (PS), and infestation by insects (II) in eight cultivars/selections of Japanese chestnut, including a Japanese–Chinese hybrid, over 6 years. Data were analyzed by analysis of variance (without transformation for NHD, after log-transformation for NW and PS, and after square root transformation for II). The among-tree variance accounted for only 1.1% to 8.5% of the total variance. The variance component resulting from residual factors for the tree × year interaction and sampling errors was the largest component for NW, PS, and II, accounting for 46% to 54% of the total environmental variance. Because tree replication is costly and time-consuming in chestnut breeding, increasing the number of yearly repetitions is more efficient than increasing the number of tree replicates. Broad-sense heritability was 0.84 for NHD, 0.27 for NW, 0.48 for PS, and 0.17 for II in evaluations with one tree without yearly repetition. It increased to 0.91 for NHD, 0.40 for NW, 0.62 for PS, and 0.29 for II in evaluations with one tree in 2 years. For NHD, the heritabilities are sufficiently high to distinguish genetic differences among cultivars/selection. In contrast, the low heritability of II suggests that this trait should not be evaluated with an emphasis on the initial selection stage but rather with an emphasis on the secondary selection stage based on testing at several locations with a large number of yearly and tree replications.

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The Use of the Square Root Transformation and Analysis of Variance with Contagious Distributions1

Journal of Economic Entomology ◽

10.1093/jee/35.4.536 ◽

1942 ◽

Vol 35 (4) ◽

pp. 536-543 ◽

Cited By ~ 3

Author(s):

Wm. M. Upholt

Keyword(s):

Analysis Of Variance ◽

Square Root ◽

Root Transformation

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Analysis of proportional data in reproductive and developmental toxicity studies: Comparison of sensitivities of logit transformation, arcsine square root transformation, and nonparametric analysis

Birth Defects Research ◽

10.1002/bdr2.1755 ◽

2020 ◽

Vol 112 (16) ◽

pp. 1260-1272

Author(s):

Paul I. Feder ◽

Laura L. Aume ◽

Cheryl A. Triplett ◽

Jane Ellen Simmons ◽

Michael G. Narotsky

Keyword(s):

Developmental Toxicity ◽

Nonparametric Analysis ◽

Square Root ◽

Toxicity Studies ◽

Logit Transformation ◽

Root Transformation ◽

Proportional Data

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Control of Citrus Thrips on Lemons, 1996

Arthropod Management Tests ◽

10.1093/amt/22.1.64 ◽

1997 ◽

Vol 22 (1) ◽

pp. 64-65

Author(s):

D. L. Kerns ◽

T. Tellez

Keyword(s):

Square Root ◽

Air Blast ◽

Root Transformation ◽

Fruit Damage

Abstract Eight year old lemon trees in Yuma, AZ were treated with insecticides for control of citrus thrips. The treatments were arranged in a RCB design, consisting of four replicates. Each plot (30 by 90 ft) consisted of three trees 30 ft apart in a row. Applications were made using a backpack air-blast sprayer calibrated to deliver 100 gpa. Treatments were initiated approximately 14 days after petal fall and were applied on Apr 3, Apr 30 and May 15. Evaluations were made on 5 Apr, 9 Apr, 15 Apr, 23 Apr, 29 Apr, 2 May, 6 May, 13 May, 17 May, 20 May and 29 May. Percent infested fruit were estimated by sampling by sampling ten fruit per tree for the presence or absence of immature CT. Fruit damage was assessed on Aug 16 by rating the degree of rind scarring: 1 = no scarring, 2 = slight scarring around the calyx, 3 = significant scarring around the calyx, 4 = slight scarring on the side of the fruit and 5 = major scarring on the side of the fruit. Percentage fruit infested with immature CT were transformed using a square-root transformation for analysis, percentage values are presented in the tables. Differences among treatments were separated using ANOVA and an F protected LSD.

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Efficacy of Experimental Insecticides to Citrus Thrips on Lemons, 1996

Arthropod Management Tests ◽

10.1093/amt/22.1.62a ◽

1997 ◽

Vol 22 (1) ◽

pp. 62-63

Author(s):

D. L. Kerns ◽

T. Tellez

Keyword(s):

Square Root ◽

Air Blast ◽

Root Transformation ◽

Fruit Damage

Abstract Eight year old lemon trees in Yuma, AZ, were treated with experimental insecticides for control of citrus thrips. The treatments were arranged in a RCB design, consisting of four replicates. Each plot (30 by 90 ft) consisted of three trees, spaced 30 ft apart, in a row. Applications were made using a backpack air-blast sprayer calibrated to deliver 100 gpa. Treatments were applied approximately seven days after petal fall on Apr 2, Apr 23 and May 08. Evaluations were made on 4 Apr, 9 Apr, 15 Apr, 23 Apr, 25 Apr, 29 Apr, 6 May, 10 May, 13 May, 20 May and 29 May. Percent infested fruit were estimated by sampling ten fruit per tree for the presence or absence of immature CT. Fruit damage was assessed on Aug 19 by rating the degree of rind scarring: 1 = no scarring, 2 = slight scarring around the calyx, 3 = significant scarring around the calyx, 4 = slight scarring on the side of the fruit and 5 = major scarring on the side of the fruit. Percentages fruit infested with immature CT were statistically analysed using a square-root transformation, but the data presented in the tables is untransformed. Differences among treatments were separated using ANOVA and an F protected LSD.

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Use of various functions to analyse the fertiliser responses of maize ( Zea mays L.) hybrids in long-term experiments

Acta Agronomica Hungarica ◽

10.1556/aagr.54.2006.1.1 ◽

2006 ◽

Vol 54 (1) ◽

pp. 1-14 ◽

Cited By ~ 5

Author(s):

Z. Berzsenyi ◽

Q. L. Dang

Keyword(s):

Analysis Of Variance ◽

Response Pattern ◽

Root Function ◽

Quadratic Function ◽

Maize Yield ◽

Maximum Point ◽

Square Root ◽

Maize Hybrids ◽

Year Effect

The effect of various fertiliser treatments on the yield of maize hybrids was studied on the basis of 26 years of data obtained in a long-term bifactorial split-plot experiment set up in 1967. The seven treatments (NPK ratio 2:1:1) applied were as follows (rates per hectare): 1. Control (no fertiliser), 2. 100 kg NPK, 3. 200 kg NPK, 4. 300 kg NPK, 5. 400 kg NPK, 6. 600 kg NPK, 7. 800 kg NPK. The maize was grown with the conventional cultivation techniques in continuous cropping. The results of analyses carried out with three different methods (analysis of variance, cumulative yield analysis and regression analysis) all indicated that under the given conditions the yield of maize hybrids was highest at an NPK fertiliser rate of 200-400 kg ha -1 . The effect of fertilisation on the maize yield was significant in 21 of the 26 years. Combined analysis of variance for the years showed that the year effect (quantity of rainfall) had the greatest effect on the maize yield, but although the year effect had a fundamental effect on the yield level it did not influence the fertiliser response pattern. The fertiliser responses of the maize hybrids were described by fitting four types of functions (quadratic, square root, inverse exponential, linear-plateau) to the yield data. It was found that when selecting the best function a consideration of the regression deviations (measured yield - calculated yield) was just as important as the coefficient of determination (R 2 ). In 12 of the 26 years the fitting of the quadratic function was not significant and overestimated the fertilisation optimum. The fertiliser response curve generally has a broad maximum which is far better described by the square root function than by the quadratic. If the fertiliser response pattern includes a depressive phase, a square root function should definitely be used in place of the quadratic function. If the maximum of the response surface forms a plateau (as opposed to a maximum point) a linear-plateau function or an inverse exponential function can be recommended. In the present work the linear-plateau function gave the best results.

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Preliminary research for testing Baptisia tinctoria 30c effectiveness against salmonellosis in first and second quality broiler chickens

British Homeopathic Journal ◽

10.1054/homp.1999.0228 ◽

1998 ◽

Vol 87 (03) ◽

pp. 131-134 ◽

Cited By ~ 5

Author(s):

CH Sandoval ◽

LL Morfin ◽

BB Lopez

Keyword(s):

Diagnostic Tests ◽

Death Rate ◽

Broiler Chickens ◽

Statistical Difference ◽

Live Weight ◽

Square Root ◽

Significant Statistical Difference ◽

Root Transformation ◽

Poultry Birds ◽

Preliminary Research

AbstractThe aim of this research was to compare the effectiveness of Baptisia tinctoria 30c and Ciprofloxacin against salmonellosis in fowl. Eight hundred (400 first quality and 400 second quality) poultry birds were used. All were the same commercial brand. There were two treatments, both with four repetitions. Treatment began when chickens were eight days old; two drops/kg live weight/d Baptisia tinctoria or 15 mg/kg live weight/d of Ciprofloxacin. Both treatments lasted ten days and were given in the drinking water. Salmonella diagnostic tests were made on day 0, day 8 and day 49 of age and death rate was when treatments had finished. Death rate values were applied a square root transformation and a 2×2 factorial analysis was made.The mortality for first and second quality fowl in the Baptisia tinctoria group were 0.7125 and 2.037, respectively, and in the Ciprofloxacin group, 0.7245 and 2.1848, respectively. No significant statistical difference was observed (P>0.1) regarding treatments, only regarding different quality fowl (P<0.01). After comparing, Baptisia tinctoria 30c and Ciprofloxacin treatments against salmonellosis, it was concluded that there were no meaningful differences between outcomes.

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