Analysis of Series of Experiments in Randomized Block Designs
Generally, a single factor experiment is conducted over a number of locations/seasons/years for crop improvement programmes. The objective is to study the performance of treatment effects over different locations/time, aiming to identify treatments suitable for particular environments. The performance of crops generally depends on treatment, environment, and treatment × environment interactions.
Pooled ANOVA
Pooled ANOVA is used to check the existence of treatment × environment interactions. Highly significant interactions indicate that the treatments interacted considerably with environmental changes. In cases where experiments are repeated over time, combined analysis of data is conducted with the following objectives:
- To draw conclusions regarding the suitability of treatments
- To recommend a new variety or fertilizer dose after conducting series of experiments
- To identify technologies whose average effects over years are stable and high
- To reveal the differential response of genotypes to environmental changes
- To study genetic diversity among the genotypes used in an experiment
- To check whether yield trends throughout the experimental period are significantly different from zero
Series of Experiments
Series of experiments are generally conducted in two ways:
- Over seasons/environments
- Over years
Experiments over seasons/environments
For a given crop at a specific site, planting is usually not spread uniformly over a year but bunched to determine whether a separate technology recommendation is needed for each planting season. In such experiments, the objective of pooled analysis over seasons is to examine the interaction between season and treatment.
Experiments over years
The variability of the environment over years is usually unpredictable. Thus, the objective of pooled analysis over years is to identify technologies whose average effect over years is stable and high.
Procedure for Pooled Analysis
The procedure for pooled analysis is as follows:
- Conduct individual analysis for each season, year, or location.
- Compute the error mean square (MSE) values for each season/year/location.
- Test the homogeneity of error variances using Hartley’s test or Bartlett’s chi-square test.
- If error variances are homogeneous, proceed with pooled analysis.
- If error variances are heterogeneous, perform weighted analysis.
Interpretation of Results
1. Homogeneity of Error Variances is Established
a) Check the significance of season, treatment, and interaction. If both treatment and its interaction with season/year are significant, it can be concluded that there is a significant response to treatment, but the response differed between seasons.
b) If season × treatment interaction is significant, partition the interaction sum of squares (SS) into orthogonal contrasts to understand the nature of the interaction.
2. Homogeneity of Error Variances is Not Established
When error variances differ significantly, transform the data by dividing each observation by the square root of the MSE of the environment before performing the combined analysis.
Output of the Program
The output of this module includes:
- Means of treatments for different seasons/years in tabular form
- Separate ANOVA for each season/year
- Bartlett’s test statistics with significance
- Combined ANOVA for pooled data
- Broad interpretation of results
Procedure for Data Entry
A data entry page is provided where users can input data as well as year/season names. Data for all replications of the first treatment for the first year/season must be entered in the first row, with each value separated by at least one space. After entering data for the first treatment, enter data for subsequent treatments and seasons in a similar manner. Data can be copied from Excel and pasted into the interface.
Example: The dataset for a varietal trial conducted to study the performance of nine new mustard strains versus three checks, using an RCB design with three replications at each environment, is provided. The seed yield in kg/ha recorded have been taken from the table 8.2 of the book “Statistical Analysis of Agricultural Experiments Part I: Single Factor Experiments” by Gupta et al. 2016) ICAR-IASRI, Library Avenue, Pusa, New Delhi.
Data of Grain yield of rice tested with five rates of nitrogen over two seasons.
____________________________________________________________________________________________
Environ Treat Replication Environ Treat Replication
___________________ ____________________
1 2 3 1 2 3
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Bathinda 1 1794 2014 2581 Hisar 1 3286 2459 3286
2 1134 1736 1898 2 2518 2364 2364
3 718 764 880 3 757 993 875
4 1852 1551 1887 4 2553 2388 2884
5 2245 2361 2407 5 2908 2482 2884
6 1111 1065 1111 6 1797 1560 2033
7 1181 880 1528 7 1749 1537 1537
8 1644 1991 2060 8 1501 2317 2577
9 1551 1435 1991 9 1513 1608 2104
10 1968 1551 2569 10 2447 2459 2813
11 2662 2338 3056 11 2600 2884 2648
12 1065 1227 1343 12 1631 1466 1844
IARI New Delhi 1 2600 2444 2711 Ludhiana 1 1370 1209 1320
2 3289 2667 2889 2 904 729 1007
3 2756 2511 2400 3 858 942 839
4 2600 2444 2222 4 904 959 1155
5 2689 2422 2444 5 1438 1456 1695
6 2578 2400 2222 6 873 959 946
7 3178 3044 2889 7 848 639 643
8 3244 2911 3111 8 1668 1770 1607
9 2444 2222 2667 9 910 907 1081
10 3156 2978 2756 10 1558 1606 1705
11 2667 2267 2111 11 1508 1389 1447
12 2689 2444 2289 12 1280 1207 1256
Navgaon 1 2233 2222 2222 TERI,New Delhi 1 1666 1333 2222
2 2222 2444 2722 2 1611 1389 1944
3 2000 1778 1778 3 1389 1244 2056
4 2667 3289 3333 4 1511 1778 1889
5 2444 2000 2000 5 1644 1622 1711
6 1778 1889 1556 6 1833 1822 2111
7 1778 1722 1722 7 1788 2333 1711
8 3000 2889 3222 8 1644 2220 2220
9 1778 1611 1333 9 1889 1822 2444
10 3778 3667 3556 10 2000 1556 1356
11 3111 3111 3222 11 944 388 722
12 2222 2000 2222 12 1488 1400 1356
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Using the above Example you have arrange the data in text area as give under :
1794 2014 2581 1134 1736 1898 718 764 880 1852 1551 1887 2245 2361 2407 1111 1065 1111 1181 880 1528 1644 1991 2060 1551 1435 1991 1968 1551 2569 2662 2338 3056 1065 1227 1343 2600 2444 2711 3289 2667 2889 2756 2511 2400 2600 2444 2222 2689 2422 2444 2578 2400 2222 3178 3044 2889 3244 2911 3111 2444 2222 2667 3156 2978 2756 2667 2267 2111 2689 2444 2289 2233 2222 2222 2222 2444 2722 2000 1778 1778 2667 3289 3333 2444 2000 2000 1778 1889 1556 1778 1722 1722 3000 2889 3222 1778 1611 1333 3778 3667 3556 3111 3111 3222 2222 2000 2222 3286 2459 3286 2518 2364 2364 757 993 875 2553 2388 2884 2908 2482 2884 1797 1560 2033 1749 1537 1537 1501 2317 2577 1513 1608 2104 2447 2459 2813 2600 2884 2648 1631 1466 1844 1370 1209 1320 904 729 1007 858 942 839 904 959 1155 1438 1456 1695 873 959 946 848 639 643 1668 1770 1607 910 907 1081 1558 1606 1705 1508 1389 1447 1280 1207 1256 1666 1333 2222 1611 1389 1944 1389 1244 2056 1511 1778 1889 1644 1622 1711 1833 1822 2111 1788 2333 1711 1644 2220 2220 1889 1822 2444 2000 1556 1356 944 388 722 1488 1400 1356
Step 1:The entered data in the data entry web page looks as under:-
Step 1:After entering the data and locations/years/seasons name press “Submit” button. Another web page will be displayed as given below:-
Step 2: Enter the number of treatments, number of replications and number of years/seasons in the text boxes provided. Also select seasons or year from the option buttons as per your requirements. After filling all the required information press “Analyse” button. The results will be displayed on separate web page.