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RSCH 8210 Quantitative Reasoning And Analysis
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RSCH 8210 Quantitative Reasoning And Analysis
1 Download4 Pages / 909 Words
Course Code: RSCH8210
University: Walden University
MyAssignmentHelp.com is not sponsored or endorsed by this college or university
Country: United States
Question:
How are the results of the test calculated
Answer:
Summary
Assumptions of the test
The test assumes mutual exclusivity within the observations; one case is assumed to only fall in one cell of the table (Choi , Blume , & Dupont, 2015).
The test assumes directional hypothesis (predicts either negative association or positive association but not both)
Assumes that samples are randomly drawn, that is, each observation has equal chance of being included in the sample.
The test makes an assumption in regard to the Independence of variables being tested.
Calculation of the fisher’s test results
The Fisher probability is calculated using the following formula;
Where ‘a,’ ‘b,’ ‘c’ and ‘d’ in this formula are the individual frequencies related to the 2 X 2 contingency table, while ‘N’ refers to the total frequency.
Interpretation of the test results
The test checks whether there is association between two variables (Corcoran, Senchaudhuri, Mehta, & Patel, 2005). When the null hypothesis is rejected then the results indicate that there is association between two variables. Otherwise accepting the null hypothesis implies that no significant association between variables.
P-value
P-value refers to the marginal level of significance within the Fisher’s statistical hypothesis test that represents the probability of the occurrence of association between two variables. The value is compared with the set level of significance and it is a measure of whether the null hypothesis should be rejected or accepted. If the computed p-value is less than the level of significance then the null hypothesis is rejected. However, if the computed p-value is greater than the level of significance then the null hypothesis is accepted and not rejected.
Alternative hypothesis
This is a statement that advises or suggests that there is a significant association between two variables as a researcher or an investigator may expect (Lombardi & Hurlbert, 2009).
Null hypothesis
Final assignment
# This is an individual assignment in which cooperation is not permitted.# Reference all sources.# # In the exact Fisher test below, describe:# 1. Assumptions of the test# 2. How are the results of the test calculated# 3. Interpretation of the test results# 4. In context of Fisher test, meaning of:# …. p-value# …. alternative hypothesis# …. null hypothesis# …. true odds ratio# …. 95 percent confidence interval# …. sample estimate: odds ratio##——————————————tea.tasting <- matrix(c(16,16,8,24),nrow=2)colnames(tea.tasting) <- c('Tasted Tea First', 'Tasted Milk First')rownames(tea.tasting) <- c('True Tea First', 'True Milk First')print(tea.tasting)fisher.test(tea.tasting)
# > print(tea.tasting)# Tasted Tea First Tasted Milk First# True Tea First 16 8# True Milk First 16 24## > fisher.test(tea.tasting)# # Fisher’s Exact Test for Count Data# # data: tea.tasting# p-value = 0.06968# alternative hypothesis: true odds ratio is not equal to 1# 95 percent confidence interval:# 0.9284922 10.0255982# sample estimates:# odds ratio # 2.94678
significant association between two variables as a researcher or an investigator may expect (Stockburger, 2007).
True odds ratio
This refers to a true population association measure that is between an outcome and an exposure. The ratio (true odds ratio) is used to represent the odds that a given or a particular outcome will occur based on certain exposure, compared to the odds of the outcome occurring in the control group which could be in the absence of that exposure (Holcomb, 2001).
95 percent confidence interval
This refers to a range of values that a researcher can be 95% certain contains the true population mean (Lee, 2017).
Sample estimate: odds ratio
This refers to a sample association measure that is between an outcome and an exposure but in a sample not in a population group. The ratio (true odds ratio) is mainly used to represent the odds that a given or a particular outcome will occur based on certain exposure, compared to the odds of the outcome occurring in the control group which could be in the absence of that exposure.
Interpreting the presented results
The given study sought to test whether the true odds ratio is equal to 1. Fisher’s exact test was performed and results showed the p-value to be 0.06968 (a value greater than 5% level of significance), we therefore failed to reject the null hypothesis at 5% significance level and concluded that the true odds ratio was equal to 1. The 95% confidence interval also showed that the true odds ratio was between 0.9284922 10.0255982. As can be seen, 1 is within the given range hence from the 95% confidence interval we can conclude that the odds ratio is not different from 1 since 1 is included in the range. The sample estimates of the odds ratio is 2.94678 which is also within the given range hence leading to non-rejection of the null hypothesis. The odds ratio which is given as 2.94678 means that it almost 3 times more for the outcome in the Tasted Tea First as compared to the outcome in the Tasted Milk First.
References
Choi , L., Blume , J. D., & Dupont, W. D. (2015). Elucidating the Foundations of Statistical Inference with 2 x 2 Tables. 10(4). doi:10.1371/journal.pone.0121263
Corcoran, C. D., Senchaudhuri, P., Mehta, C. R., & Patel, N. R. (2005). Exact Inference for Categorical Data. Encyclopedia of Biostatistics. doi:10.1002/0470011815.b2a10019
Holcomb, W. (2001). An odd measure of risk: Use and misuse of the odds ratio. Obstetrics & Gynecology, 98(4), 685–688. doi:10.1016/S0029-7844(01)01488-0
Lee, D. K. (2017). Alternatives to P value: confidence interval and effect size. Korean Journal of Anesthesiology, 69(6), 555–562.
Lombardi, C. M., & Hurlbert, S. H. (2009). Misprescription and misuse of one-tailed tests. Austral Ecology, 34, 47–468. doi:10.1111/j.1442-9993.2009.01946.x
Stockburger, D. W. (2007). Hypothesis and hypothesis testing. Encyclopedia of Measurement and Statistics.
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