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Analysis of Data from Designed Experiments

Tests of Significance Based on T - Distribution 

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                                                                                                                                                                                      Analysis Using SAS

Analysis Using SPSS

Analysis  Using  MS-EXCEL

 

 

To test whether the mean of the population of Seed yield/plant (g) is 200 or not one can use the following steps in MS-EXCEL:

 First compute sample mean and sample variance and then compute the test statistic

                                         t =

where n denotes the sample size.

Sample mean and sample standard deviation can be obtained using functions “AVERAGE” and “STDEV” of MS-EXCEL as follows

 and the sample standard deviation comes from the function “STDEV”.

Null hypothesis for this example is H0: mean=200, therefore the test value is 200.

We now compute the value of test statistics as here n=20, sample mean =180.80, testvalue=200 and sample standard deviation = 37.31.

Computed t-value= -2.30; Modulus value of the computed t-value is 2.30.

To find the p-value, use “TDIST” function by giving = TDIST(X, degrees of freedom, tail).

1. X is the modulus value of the computed t-value i.e.,  2.30

2. Type in the df = n – 1=20-1=19
3. If tails = 1, TDIST returns the one-tailed distribution. If tails = 2, TDIST returns the two-tailed distribution. In our case it is the 
     two-tailed distribution i.e., 2.

 

Therefore the p-value= 0.03

To answer the question number 2 follow the following steps:

·       Once the data entry is complete, Choose Tools from the Menu Bar. Now select Tools → Data Analysis…

 ·       In the Data Analysis  dialog box select t-Test: Two-Sample Assuming Equal Variance. This selection displays the following screen.

   ·       Click OK. This displays the dialog box for the analysis of  t-Test: Two-Sample Assuming Equal Variance.

  ·       For the two groups select the variable  number of fruit Set (45days)  and select the range for Variable 1 Range:  and Variable 2 Range:  in the Input box. Now select Output Range: to get the output. This displays the following screen.

 

 ·       Click OK to get the output at the selected output range.

   ·       Similarly one can perform the analysis for the other variables also.

·        For the analysis of t-Test: Two-Sample Assuming Unequal Variances, in the Data Analysis  dialog box select t-Test: Two-Sample Assuming Equal Variance.

 

  • This selection displays the following screen.

·       For the two groups select the variable  No. of fruit Set (45days)  and select the range for Variable 1 Range:  and Variable 2 Range:  in the Input box. Now select Output Range: to get the output. This displays the following screen

·       Click OK to get the output at the selected output range.

·       Similarly one can perform the analysis for the other variables also.

Data File

Result File

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Analysis Using SAS                       Analysis Using SPSS                     Analysis Using MS-EXCEL                      

 

 

 

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Descriptive Statistics
Tests of Significance
Correlation and Regression
Completely Randomised Design
RCB Design
Incomplete Block Design
Resolvable Block Design
Augmented Design
Latin Square Design
Factorial RCB Design
Partially Confounded Design
Factorial Experiment with Extra Treatments
Split Plot Design
Strip Plot Design
Response Surface Design
Cross Over Design
Analysis of Covariance
Diagnostics and Remedial Measures
Principal Component Analysis
Cluster Analysis
Groups of Experiments
Non-Linear Models
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Other Designed Experiments
   
(Under Development)

For exposure on SAS, SPSS, 
MINITAB, SYSTAT and
 
MS-EXCEL for analysis of data from designed experiments:

 Please see Module I of Electronic Book II: Advances in Data Analytical Techniques

available at Design Resource Server (www.iasri.res.in/design)