Section A (Types of t test)
A. Difference between one-tailed and two- tailed t test
One tailed and two tailed tests are part of hypothesis testing or significance testing, which is used to verify a claim or a hypothesis regarding a particular parameter in a particular population using the data obtained from a sample of that population. This involves verifying whether a statistic obtained matches with the statistic predicted by the null hypothesis, which is a statement made about the population, assumed to be true. (www.unc.edu., 2014)
When testing hypotheses, it is assumed that if the obtained statistic does not match that predicted by the null hypothesis significantly, then the null hypothesis is false and the alternative hypothesis which is the one we want to prove is true. Now, assuming that we want our alternate hypothesis to lead to a result in a particular direction such as either should be greater than or lesser than the value for the null hypothesis, we would want to use a one tailed test while if we are not sure about which directions, the statistical analysis for the alternate hypothesis leads to, we would go for the two tailed t-test.
Thus, the one tailed test is used to determine the significance of a data set, given that the outcome of the alternative hypothesis looked for should be mainly one outcome or not i.e., the values are positive or zero. The two-tailed test is used to determine the statistical significance when the hypothesis can take any of the possible directions i.e. The term tail is used to refer to the sloping end or the extremes of the normal distribution curve, which are usually small as the most of the data values are located in the middle region. Hence a one tailed test would be one half a bell curve and is used for asymmetric distributions while a two tailed test is used for normal distributions. (Chem.utoronto.ca, 2006)
The type of tailed test to be used, is dependent on the kind of experimental design. For example, in this research, “A paired sample 2 tailed t test was used to assess the annualized relapse rate during 18 months pre treatment with methotrexate to annualized relapse rate 18 months post treatment with methotrexate.” This makes sense, because the researchers are not sure about what they are expecting in the experiment, so for them any outcome would be significant and would affect the direction of their next experiment (Ncbi.nlm.nih.gov, 2014)
B. State two research hypotheses that can be tested using a one-tailed t test, and discuss why a one-tailed t test would be appropriate for those hypotheses.
One tailed t tests can be used where the investigators are looking for a particular outcome and so they are interested in outcomes which should be positive or zero. Any other is not meaningful for them. For example, such hypotheses as Usage of Vitamin D results in better bones is an example where such a test can be used. Another example of a hypothesis is when you want to determine that studying under light is more beneficial for eyes. In such cases, the alternative hypothesis would be true if the p <0.5 for one outcome.
State two research hypotheses that can be tested using a two-tailed t test, and discuss why a two tailed t test would be appropriate for those hypotheses
Two tailed t- tests can be used for studies where outcomes in any direction are deemed significant. This means that the statistical significance value p= 0.5 is split between the two outcomes. A two –tailed t test would follow a bell-shaped normal distribution curve.
Examples of such research hypotheses would be for e.g., study of the effect of an independent variable on two different dependent variables and determining the effect. Studying the effect of a drug before and after exposure to an infection for example would be such a hypothesis. Another would be: Vitamin D and Vitamin acts in opposite ways on skin health.
Chem.utoronto.ca. (2006). 1- vs 2-Tailed Tests. [online] Retrieved from: http://www.chem.utoronto.ca/coursenotes/analsci/StatsTutorial/12tailed.html [Accessed: 11 Apr 2014].
Ncbi.nlm.nih.gov. (2014). Treatment of neuromyelitis optica/neuromyelitis o... [BMC Neurol. 2014] - PubMed - NCBI. [online] Retrieved from: http://www.ncbi.nlm.nih.gov/pubmed/24628894 [Accessed: 11 Apr 2014].
www.unc.edu.. (2014). [online] Retrieved from: http://www.unc.edu/~blopes/files/stat11spring03/Files/HypothesisTesting.pdf [Accessed: 11 Apr 2014].
References Öien, R. F., Åkesson, N. N., & Forssell, H. H. (2013). Assessing quality of life in patients with hard-to-heal ulcers using the EQ-5D questionnaire. Journal Of Wound Care, 22(8), 442.
Summary of the study: The study aimed to assess the Health related Quality of life in a set of patients who were diagnosed with difficult to heal ulcers, starting from the baseline (zero point/no indications of healing) continuing via healing phases and un till 6months following healing. This assessment was carried out using a statistical instrument EQ-5D. Two objectives of using this instrument were to understand how effective is this instrument in studying the HRQoL in the selected patients and how much information it can contribute to a national dataset on Ulcer treatment issues. The study found out that there was a significant difference in the QoL of patients with unhealed open ulcers and those with healed ulcers. But the difference between the freshly healed and 6 months follow up were not that much different. In addition, the questionnaire highlighted that pain was significantly associated with the QoL outcomes but the instrument was found not useful enough to contribute to the Swedish Ulcer Registry.
1. Identify the null hypothesis and research/alternative hypotheses
The null hypothesis in this study is that there would be not much significant difference in the HRQoL of patients with fresh ulcers and closed ulcers with p value =0.05 being used as the boundary. The alternative hypothesis would be that there would be a significant difference in the quality of life of patients suffering from open wounds after a certain period of healing and this would be indicated by p values lesser than o.o5 (www.sagepub.com, n.d.)
2. The different kind of variables:
Some of the different variables used were Sex, age, length, ulcer size, ulcer healing, arterial circulation via ABPI, Pain is measured using VAS, ulcer duration, antibiotic treatment, sleep disturbances, mobility, Deep vein thrombosis incidences, effect of previous ulcers and comorbidites etc. (www.sagepub.com, n.d.)
1. Dependent Variable (DV) and it’s level of measurement.
Health related Quality of life measured through the use of a questionnaire EQ-5D which measures five dimensions of health of the patient and is a categorical variable. (Polsci.wvu.edu, 2014)
2. Independent Variable (IV) and it’s level of measurement.
The duration of healing of ulcer and the size of ulcers were the independent variables and these were continuous variables and hence they were assessed using appropriate measures.
3. The type of test, how appropriate it is, the type of data required and whether assumptions of the test were met
The tests were appropriately used. The two sample student’s t tests were used for the comparison of data obtained for the continuous variables. The Association between continuous variables were determined by linear regression. Comparison studies of the categorical variables obtained through the questionnaire instrument was carried out using Pearson’s c hi-squared tests.
4. Possible implication of the study.
Main finding is that there is a positive correlation between the improvement in ulcer condition i.e. ulcer healing and the patient’s quality of life. This improvement was measured by EQ-5D but the limitations of this are that the dimensions were limited by the fact that the research was self reported and hence there would be some variations. Also some critical dimensions were not taken into consideration such as depression and other issues.
Polsci.wvu.edu. (2014). Levels of Measurement. [online] Retrieved from: http://www.polsci.wvu.edu/duval/ps601/Notes/Levels_of_Measure.html#Tools of Inference [Accessed: 11 Apr 2014].
www.sagepub.com. (n.d.) Chapter8 Introduction to hypothesis testing. [online] Retrieved from: http://www.sagepub.com/upm-data/40007_Chapter8.pdf [Accessed: 11 Apr 2014].
www.sagepub.com. (n.d.) Appendices: Guide for selecting appropriate inferential and descriptive. [online] Retrieved from: http://www.sagepub.com/fitzgerald/study/materials/appendices/app_a.pdf [Accessed: 11 Apr 2014].