Lab Report Statistical Analysis on Genetic Data - Rayana Rankoussi (1)

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Rayana Rankoussi Lab Report : Statistical Analysis on Genetic Data 02/15/2024 Table 4-1 served as the basis for the subsequent data analysis and calculations in the following tables. It contained essential information derived directly from the provided Ears of Corn. Unlike other tables, there was no predetermined or expected data on this table; it primarily functioned as a repository for raw data collected during the experiment. Table 4-2, much like its predecessor, played a fundamental role in shaping the subsequent tables' data and calculations. It operated as a compilation of information gathered directly from the provided Ears of Corn. Similar to Table 4-1, this table did not include any expected data, focusing solely on presenting the collected data in a structured format for further analysis in the subsequent tables. 4-3a For this table the expected value was 64, I was able to reach this conclusion by dividing the total corn count by how many specific values there were: 256 total corn / 4 values. The observed values were off by a bit, for instance, Red and Smooth had an observed total of 70 In table 4-3a, the total number of counted corn was 256. After calculations were done, it was seen that table 4-3a categorized itself into a 1:1:1:1 ratio; with the expected value becoming 64:64:64:64 of an equal value of red smooth, red wrinkled, yellow smooth and yellow wrinkled corn. Although the data of expected and observed were not completely equal in number, the observed values were very close or less than the expected data. This statement is true because when it comes to “failing to reject” a table, usually the observed data is either less than the expected data or either equal to/very close. Hence,we chose to fail to reject. 4-3b Similarly in 4-3b, the total count of the small sample of corn was 30. To determine the expected values, I divided the total count by the number of categories, resulting in an expected 1:1:1:1 ratio for red smooth, red wrinkled, yellow smooth, and yellow wrinkled corn, with each category ideally having 7.5 instances. However, the observed values deviated slightly. Despite minor discrepancies, the observed values closely approximated or were less than the expected values. Typically, when "failing to reject" a table, the observed data is either less than or very close to the expected data. This lack of significant difference suggests no effects to reject, acknowledging the possibility of errors in data collection such as miscounting or miscalculating. Comparing the differences in 4-3 a & b, it is seen that the bigger the sample the more close to accurate the data was. The overall decision to fail to reject both tables is significant enough to say the data was both very close to our expectations. For example the Yellow and Smooth data was off by a calculated 3.07. The total chi-square for the large sample was 2.37 vs the small

Rayana Rankoussi Lab Report : Statistical Analysis on Genetic Data 02/15/2024 sample was 3.96. This evidence further reasons how the larger sample is more accurate to the expected data. 4-4a The results conducted in this table were based off of Ear #2 ( large sample) . The total value for the corn counted was 242, and to get the expected we used the ratio 9:3:3:1 and put them over the total of 16 and then multiplied by the total according to each value; for instance, I multiplied 128 observed Red and Smooth by 9/16 since the ratio stated 9 Red and Smooth. The data I compiled left me with very similar results and each value sort of matched what was expected. The null hypothesis was failed to reject because the data was not far off. The chi-square for this table was a 2.13. 4-4b For this table we had a different situation which actually led to rejecting the data. The priori chi- square test conducted left us with an expected value of 60.5 and the observed value was far off in this case. Although the sample was large the ratio of 1:1:1:1 was far off from the ratio that we observed. The null hypothesis was the REjected due to a chi-square total of 114.2 which is significantly less than 0.01 on the table of chi-square values. There could have been the possibility of errors in data collection such as miscounting and/or miscalculating that could have brought this rejection. The difference in probabilities could be looked at in a number of ways but when it comes to viewing the differences in probabilities obtained for correct versus false hypotheses, Table 4-4a had included a correct-expected ratio whereas Table 4-4b included false hypotheses for a false

Rayana Rankoussi Lab Report : Statistical Analysis on Genetic Data 02/15/2024 ratio. We expected to "Fail to reject" table 4-4b and "Reject" table 4-4a, by the end it was the complete opposite case. 4-5 This table was a contingency chi-square analysis of data, the null hypothesis I accumulated was: “The number of bead colors and bag number are independent of each other. The expected data was found by taking the column total and multiplying it by the row total and dividing that number by the Group Total. There is a different expected value for each observed value. The expected values were far off from our observations so we proceeded to Reject. There could have been a number of reasons as to why we would reject but the most common mistake I tink was made in the miscalculations as the table was very big and had high chances for error. As well, there could have been a simple mistake of miscounting the data we received.

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Rayana Rankoussi Lab Report : Statistical Analysis on Genetic Data 02/15/2024 4-6a For this contingency table the null hypothesis was: “The texture and color are independent from each other of Corn Ear #1”. This null hypothesis was failed to reject due to the expected value we collected; the collection of data was the same as stated in table 4-5 and this time the data was more accurate to what we had observed. The chi square value was 1.62 with a chi-square table value of around 0.20-0.10 further explaining how the table failed to reject.

Rayana Rankoussi Lab Report : Statistical Analysis on Genetic Data 02/15/2024 4-6b The last table was a contingency chi-square analysis of Corn Ear #2, the expected values were found the same as the previous two tables: the column total and multiplying it by the row total and dividing that number by the Group Total. These values were different for each observed value and left us with almost the same values as observed. The null hypothesis was: “The texture and the color are independent from each other of Corn Ear #2. The chi-square value was 0.48 which is significantly low, giving us a probability around 50-30%. All of these results posed as a reason to Fail to Reject the null hypothesis.

Rayana Rankoussi Lab Report : Statistical Analysis on Genetic Data 02/15/2024

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