PLANT-GROWTH EXPERIMENT

1 PLANT-GROWTH EXPERIMENT15. Brief Version of the Case Problem EXPERIMENT data Displaying Two-Way Problem FormulationIn the following study, you will be involved in the EXPERIMENT of growing a plant of yourchoice. The EXPERIMENT is designed such that the data can be collected with reasonablyinexpensive measuring equipment. The data will be analyzed using spss . Theexperiment can be carried out in a task is to examine and estimate the effects of seed type and amount of water on thegrowth of a particular type of plant. You will have to design the EXPERIMENT , collect thedata, enter the data into spss , carry out the statistical analysis , and formulate PLANT-GROWTH EXPERIMENT will be performed in several versions, and you will see thatthe statistical model used depends heavily on how the EXPERIMENT was carried out.

2 Inparticular, we will consider the EXPERIMENT when data for some of the factor-levelcombinations are not available (the plants did not shoot up). Moreover, various outcomesof the EXPERIMENT will be will need 20 small flowerpots with identification tags, potting soil, seeds for threevarieties of the same vegetable, meter stick, planting trowel, 1/4-cup measure, and abucket of the data are collected, you will answer the following questions:1. What is the effect of seed variety on the plant growth ? Does it appear that plantsobtained from one seed variety tend to grow faster than the other plants regardlessof the watering system used?2. Which watering system contributes the most to the growth of the plants ?3. Is there any interaction between seed variety and watering system in their effecton the plant growth ?

3 How strong is the interaction? EXPERIMENT DesignPlant growth is affected by several factors such as seed variety, amount of water, soiltype, amount of light, temperature, humidity, and other. The factors are displayed in thediagram will use two variables in the EXPERIMENT : seed variety and amount of water. Thesevariables are the factors in the seed factor will be three varieties of the same type of plant, and its levels will bedenoted by 1, 2, and 3. Write the names of these three varieties in the table HeightOtherHumidityTemperatureAmount of LightSoil TypeAmount of WaterSeed VarietyPlant HeightAmount of WaterSeed VarietyNow you should decide on four reasonable watering plans. An example of possiblewater-factor levels is:Level 1 of water is 1/3 cup once a 2 of water is 1/2 cup once a 3 of water is 1/3 cup twice a 4 of water is 1/2 cup twice a your four levels of the water factor in the above EXPERIMENT has two factors: seed (with three levels) and the amount of water (withfour levels).

4 This creates 3 x 4 = 12 factor-level combinations, as represented by the cellsin the following table. The twelve combinations will be denoted by the letters A,.., DescriptionDetailed DescriptionA(1,1)Seed variety 1 and water level 1B(1,2)Seed variety 1 and water level 2C(1,3)Seed variety 1 and water level 3D(1,4)Seed variety 1 and water level 4E(2,1)Seed variety 2 and water level 1F(2,2)Seed variety 2 and water level 2G(2,3)Seed variety 2 and water level 3H(2,4)Seed variety 2 and water level 4I(3,1)Seed variety 3 and water level 1J(3,2)Seed variety 3 and water level 2K(3,3)Seed variety 3 and water level 3L(3,4)Seed variety 3 and water level 4 Your task will be to determine which of these twelve combinations produces the largestplants. As 24 pots are available, we shall have 2 pots for each treatment is an example of a two-factor EXPERIMENT with type and water level are two factors affecting the growth of the plants that can becontrolled.

5 However, some of the other factors cannot be controlled. For example, wecannot control the amount of light coming through the window. The ideal situation wouldbe for all 24 plants to receive the same amount of light, so any differences in plant growthwill be due to the two controlled factors of water and seed minimize the effect of uncontrollable factors, it is very important that the levels of thefactors are assigned at random to the experimental units, the pots, in the is a technique for assigning treatment combinations to experimental units(in this case, pots). We will use randomization to decide the arrangement of the 24 pots inthe window. Randomization gives each of the 24 pots an equal chance to be chosen toeach of the 12 the first step of randomization, it is necessary to assign labels to the experimentalunits.

6 Two digits are needed to label each of the 24 pots, so we use labels 01, 02, 03, ..,24..We assign the 24 pots to the twelve treatments, so that each treatment combination willbe assigned randomly to exactly two CombinationTreatment NumberA (1,1)1B (1,2)2C (1,3)3D (1,4)4E (2,1)5F (2,2)6G (2,3)7H (2,4)8I (3,1)9J (3,2)10K (3,3)11L (3,4)12 Now obtain a long sequence of random numbers between 1 and 12. The sequence can beobtained either from the table of random numbers (numbers different from the integersbetween 1 and 12 are disregarded) or by random number generation feature in thestatistical software (integer uniform distribution with possible values between 1 and 12).The first number in the sequence will assign a treatment combination to the first using the numbers until all the 24 pots have been assigned a treatmentcombination.

7 Remember that each treatment is to be used only twice. That is, after two 1shave appeared, skip over the remaining 1s. Use the figure below to record the treatment-combination assignments as they are NumberTreatment NumberRandom Numbers177244311114885101062211231212248 8010203222324 When you are finished, you should have 24 pots labelled as two 1s (A s), two 2s (Bs),..,two 12s (L s). The random assignment of the experimental units (24 pots) to thetreatment combinations is now data CollectionWe are now ready to plant the seeds. For each pot, make sure the proper treatmentcombination is being used. Label each pot with an identification tag that indicates theseed type and watering plan. Also, to minimize the effect of the uncontrollable factors,make the amount of soil and the position of the seed with regard to depth and distancefrom edge of pot as consistent as possible.

8 Use a balance the measure the amount of soilused and meter stick to measure depth and the pots in their locations. You should make sure that all 24 plants receiveapproximately the same amount of your plants according to the treatment combination assigned. Do not deviate fromyour set watering schemes, even if the plants do not appear about how height will be measured and stick with that rule. For example, if yourplant is of the droopy variety, then you might choose to straighten out the plant before theheight measurement is taken. If so, you should do this every time the height is collected data in millimeters are displayed in the table below:WATERING PLANHEIGHT12 3 41353738384139454323133393744404745 SEED33838343639374644 Straighten out the plantbefore the heightmeasurement is takenWe will store our data in an spss worksheet with the three variables: seed, water, andheight.

9 These data are available in the spss file located on the FTP server inthe Stat337 following is a description of the variables in the data file:ColumnName of VariableDescription of Variable1 SEEDSeed Variety (an integer from 1 to 3)2 WATERW ater level (an integer from 1 to 4)3 HEIGHTH eight of plant (in millimeters) Displaying DataWe will visualize the effects of seed type and watering plan on the plant growth byobtaining the plot of factor-level means versus watering plan by seed produces the following line chart of mean height versus watering plan by seed type:The lines in the graph are obtained by connecting the factor-level means for the fourwater levels. The plot indicates that the mean height increases with the water level for theseed type 1 and 2. On the other hand, the mean height decreased slightly from water level1 to level 2 and increased sharply at water levels 2 and 3.

10 The growth rate is uneven fordifferent combinations of seed type and amount of water. The graph indicates a lack ofadditivity (interaction) between the means for the different seeds when taken across thewater seed 2 produces the shortest plants under the watering plan 1 but it surpasses theother seeds under the watering plans 2, 3, and 4. It looks that the plants obtained from theseed need more water than the other of Mean Height vs. Watering Height48464442403836343230 SEED seed 3 does not perform well under the watering plan 2 and 3, somehow increasingthe frequency of watering and amount of water does not produce higher plants in strongest interaction effect is shown for the water level 1 with seeds 2 and 3. Thiscorresponds to the point where the above graph displays the greatest degree of Two-Way analysis of VarianceThe PLANT-GROWTH EXPERIMENT is an example of a factorial EXPERIMENT .