The California Lettuce Research Board was originally formed...

The California Lettuce Research Board was originally formed as the Iceberg Lettuce Advisory Board in 1973. The primary function of the board is to fund research on iceberg and leaf lettuce. The California Lettuce Research Board published research (M. Cahn and H. Ajwa. "Salinity Effects on Quality and Yield of Drip Irrigated Lettuce") concerning the effect of varying levels of sodium absorption ratios (SAR) on the yield of head lettuce. The trials followed a randomized complete block design where variety of lettuce (Salinas and Sniper) was the main factor and salinity levels were the blocks. The measurements (the number of lettuce heads from each plot) of the kind observed were a. Determine if blocking was effective for this design. b. Using a significance level of 0.05 , produce the relevant ANOVA and determine if the average number of lettuce heads among the SARs are equal to each other. c. If you discovered that there were differences among the average number of lettuce heads among the SARs, use the LSD approach to determine which populations have different means.

The California Lettuce Research Board was originally formed as the Iceberg Lettuce Advisory Board in 1973. The primary function of the board is to fund research on iceberg and leaf lettuce. The California Lettuce Research Board published research (M. Cahn and H. Ajwa. "Salinity Effects on Quality and Yield of Drip Irrigated Lettuce") concerning the effect of varying levels of sodium absorption ratios (SAR) on the yield of head lettuce. The trials followed a randomized complete block design where variety of lettuce (Salinas and Sniper) was the main factor and salinity levels were the blocks. The measurements (the number of lettuce heads from each plot) of the kind observed were

a. Determine if blocking was effective for this design.
b. Using a significance level of 0.05 , produce the relevant ANOVA and determine if the average number of lettuce heads among the SARs are equal to each other.
c. If you discovered that there were differences among the average number of lettuce heads among the SARs, use the LSD approach to determine which populations have different means.

Key Concepts

Randomized Complete Block Design (RCBD)

An RCBD is an experimental design that aims to control for potential confounding variables by grouping experimental units into blocks that are similar, and then randomly assigning treatments within each block. This design helps to reduce the variability from extraneous factors, thereby increasing the accuracy of the treatment effect estimates.

Blocking

Blocking is a technique used in experimental designs to control the effects of variables that are not of primary interest but might influence the outcome. By grouping subjects or experimental units with similar characteristics into blocks, the design can reduce error variability and allow for a more precise comparison among the treatment groups.

Analysis of Variance (ANOVA)

ANOVA is a statistical method used to compare the means of three or more groups simultaneously to determine if there are any statistically significant differences among them. In the context of blocked experiments, ANOVA partitions the total variability into components due to the treatment effects, block effects, and random error.

Least Significant Difference (LSD) Approach

The LSD approach is a post-hoc comparison method used after obtaining a significant overall F-test in ANOVA. It allows for pairwise comparisons between the treatment means, determining which specific groups differ from one another. This method helps in identifying the specific levels or populations that contribute to the overall significant differences observed in the experiment.

Transcript

00:02 Okay, this question says scientists in the department of plant pathology at virginia tech devised an experiment in which five different treatments were applied to six different locations in an apple orchard to determine if there were significant differences in growth among the treatments.

00:22 Treatments one through four represents different herbicides and treatment five represents a control.

00:29 The growth period was from may to november in 1980, to in the new growth measured in centimeters for samples selected from the sixth location in the orchard were recorded as follows so you can see the recording for the six then the question says perform an analysis of variance variance separating out the treatment location and error sum of squares determine if there are significant differences among the treatment means, right, caught a pfad, right? okay, so this is the presentation that i've done here.

01:15 So i'm saying our hypothesis are the null hypothesis is alpha 1 to alpha 5 are equal to 0 and treatment effects are zero there.

01:27 And then the now hypothesis, the alternative hypothesis says at least one of the alphasis is not equal to zero there.

01:41 So, and the computation, our significance level is roma zero one.

01:45 Then the computations, right, with the round, random mind.

01:50 So our cf, the first thing that we need to find out is the connection factor.

01:55 The connection factor is the cf.

02:00 Our cf, that means the summation of all the data sets there and you divide by n there.

02:12 Right.

02:13 So if we sum up all data and divide by n, what do we get? we get 4 .65.

02:25 4265.

02:27 All right.

02:28 I'm just trying to get it from a calculator.

02:30 40 65 66 4 comma right comma 5 3 3 all right so that's the figure that we are getting there 533 3 day i raise my port there okay so our n we have how many data sets there right six by five we have 30 datasets there okay so our n is 30 divide by 30 there let me just check this thing yes there 30 data sets there so now um let's uh let's continue and then our we need to find the assess totals there which is the right my sest totals you sum up all you square up all the data sets right and you square them up then you sum them up so this is how you do it you it's a summation of all the squares then you separate cf there when you separate cf what you get i got 140 3071.

04:11 0 .4666 which is 677 there.

04:14 Right...

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