Experimental Design and Analysis - Assignment Example

Experimental Design and Analysis Data for the “plasters” experiment undertaken in week 2 (7/10/14) are available on Moodle. Eliminate one of the rows of data (i.e. one plaster type for one person) at random and specify in your response which one was removed. Describe the experimental design, draw up a skeleton/dummy ANOVA table for the remaining data, describe how the experiment was undertaken (giving sufficient detail that it could be repeated by someone not present in the class) and what the response variable was, detail any hypotheses, undertake the analysis and draw conclusions. In the light of these results how could you improve the experiment? Limit your text to no more than 500 words. State the word count. [40%] The experiment was done such that it was intended to find out the degree of adhesity of different types of plasters. There were 4 plasters tested, namely, A, B, C and D. each of these have a different degree of being adhesive and this is what the experiment was set out to establish. In that respect, the experiment was founded upon the concept that depending on the degree of adhesiveness of a plaster, it gets to pull out different numbers of hair from the skin of an individual. This is the attribute that was used to design the experiment and it led to a remarkable result that is indeed plausible. Different people were used in the experiment in an effort to ascertain the results. The human skin is made up of some hair particles that can come out readily in the event that the skin is subjected to the throngs of a plaster that has adequate level of adhesive strength. As such, the different plasters were glued on the skin of an individual one after the other. Starting with the plaster A, on to B, then C and finally D, the plasters were stuck on the skin of an individual. In each case, the plasters were pulled out in a half and an observation made on the effect that the plaster had on the skin. Each of the plasters was observed to have a different effect on the skin of an individual. It was made sure that the portion of the skin where the plaster was suck had hair and in that regard the effect on the hair was observed. Some of the plasters had the effect of pulling out fewer hair particles than others. The number of hair hat was pulled out by each of the plasters was then counted. This was recorded against the plaster type for each individual. Different instances of the experiment were conducted such that for each instance, different numbers of individuals took part in the experiment. In most of the instances, there was just one individual taking part in the experiment and in that respect different portions of his skin with hair were stuck with different plaster types and the result was recorded on a spreadsheet. In other instances, 4 or 5 different people took part in the experiment and the different types of plasters were stuck on their skin hence the number of hair that was pulled out was counted. The result was recorded in a spreadsheet. The number of people who took part in the experiment in each different case is known as the block and it was recorded on the spreadsheet as such. The result was then tallied using the ANOVA spreadsheet command and the most adhesive plaster was hence established. (Word count: 460) Anova: Single Factor SUMMARY Groups Count Sum Average Variance Column 1 5 15 3 2.5 Column 2 5 21700 4340 18228000 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 47023923 1 47023923 5.159526 0.05277 5.317655 Within Groups 72912010 8 9114001 Total 1.2E+08 9         2. (a) An experiment is to be conducted on six experimental treatments coded A,B,C,D,E,L. The experiment will have five replicates, but the block size cannot be as large as six. Devise two alternative Balanced Incomplete Block designs for this scenario. In each case present a randomized plan for the design and a skeleton ANOVA table. Which design would you recommend and why? One of the block design would be having a regular number of people taking part in the experiment at the same time. In this design, the key is that the design is geared towards having a plain platform of students that are taking part for each repeated instance. This ensures that all the conditions are similar in each case as the space and the time factors are kept constant. Another design is that which have the block varying for each of the different cases. In this design, the key is that a varied number of people taking part in the experiment for each of the different cases implies that the experiment has the flexibility f varying the different elements and facets for each of the case and hence there is a test of what the result would be in the event that the different scenario is applied. It gave a platform where all the different possibilities were explored and hence a compact and comprehensive attribute of the experiment was established. I would choose the first design based on the fact that this design is very effective for the case of having the experiment well managed and outlined to give it the possibility of being non redundant. This design is effective in th event that high profile level of accuracy is desired and hence it is the way to go given that in all experiments, the success of the attribute is getting accurate inference. (Word count: 243) Block design (VWXYZ) 1 2 1 V X 2 V X 3 V Y 4 X Z 5 W Y 6 Y Y 7 V Z 8 V W 9 W X 10 Z W (b) An experiment is planned to look at the effects of climbing 1, 2, 3, 4 and 5 flights of stairs on the pulse rates of a sample of 10 students. However, the European Court of Human Rights has decreed that no student can be expected to do more than 3 of these activities. Consequently a balanced incomplete block design is required. Devise such a design, generate a randomisation and draw up a skeleton ANOVA table. Does an alternative Balanced Incomplete Block design exist? Limit your text to no more than 300 words. State the word count. [40%] In this experiment the number of students who took part in the experiment was also varied such that for each case, there was a given number of students who took part in the experiment. Te experiment was intended to establish the manner in which the pulse rate of the different students was affected by climbing up a fleet of stairs. The difference in this case was the fact that the key component was to ensure that for each case, the number of students that took part in the experiment for each repetitive period was as minimum as possible. His is the block number of students. The key was to keep the block as low as possible. It hence implies that in most of the instances it was desired to have the number of students taking part being just 1. In order to get effective inference though, it is necessary that the block is not just 1. This is because it aids in the process of comparison. It gives a platform where each of the students taking part in the experiment is subjected to the same conditions such as weather and other environmental factors. This leads to perfect inference. Hence an alternative Balanced Incomplete Block design sure does exist. It is through this balance that the experiment was conducted. This made it possible to have a limited number of students taking part in the experiment as the block and hence led to an effective aura of abiding by the laid out legislations. (Word Count: 251) Anova: Single Factor SUMMARY Groups Count Sum Average Variance Column 1 5 15 3 2.5 Column 2 5 180 36 554.5 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 2722.5 1 2722.5 9.775583 0.014088 5.317655 Within Groups 2228 8 278.5 Total 4950.5 9         3. Devise a Latin Square experiment for a classroom situation with a minimum of four treatments. Describe clearly how the experiment will be run, what the response variable will be, draw up an example randomisation and skeleton ANOVA table. Comment on your design. Limit your text to no more than 300 words. State the word count. [20%] One key design in this regard is a platform where all the students would be subjected to the same conditions for the same period of time and the same intensity of all accolades be well instigated upon the students. In that regard, the students shall be able to showcase an equal level of reaction and that is precisely the case that is desired. The fact that the stage shall be level for all te different variables to be effected in a different fashion implies that the students shall be able to react in the natural manner that they would otherwise not react like if they were subjected to a varying kind of platform. A keen analysis of the data is hence easily possible as the expected outcome is linear kind of result that is only seen where the students act in unison. It is very easy to detect any form of difference that takes place in the scenario given that each of the students are expected to work in a similar fashion. Any difference is very easily and very clearly seen and hence addressed effectively. This is expected to give a visual result that tells the entire adage in a plain nutshell. The experiment is poised to be a huge success as it works on a four prong attribute that is the most effective from the experimental divide. It is precisely the case that leads to the most accurate results. (Word Count: 240) Anova: Single Factor SUMMARY Groups Count Sum Average Variance Column 1 7 28 4 4.666667 Column 2 7 385 55 466.6667 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 9103.5 1 9103.5 38.62871 4.48E-05 4.747225 Within Groups 2828 12 235.6667 Total 11931.5 13         Bibliography Kendall, M. G., Stuart, A., Ord, J. K., Arnold, S. F., & OHagan, A. (1994). Kendalls advanced theory of statistics. London: Edward Arnold. Yule, G. U., & Kendall, M. G. (1950). An introduction to the theory of statistics. London: Charles Griffin. Hays, W. L. (1981). Statistics. 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