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Types of T-test

TYPES OF T-TEST 6

Name of the student

Name of the institution

Differences between Two-tailed and One-tailed T Test

There are two alternative ways of testing statistical significance ofdata set the two-tailed and one-tailed t tests. Two-tailed tests areapplicable where the test statistic assumes both negative andpositive values. On the other hand, one-tailed t tests are applicableonly where the test statistic is positive or zero (Jekel, 2007).One-tailed tests are applied on testing statistical significance forsingle-tailed asymmetric distributions. A good example of suchdistributions is the Chi-squired distribution that measures goodnessof fit. As well, the one-tailed tests are applied in testingstatistical significance for one side of a two- tailed distribution.For instance, one tailed t-tests can be applied in testingstatistical significance in the normal distribution that is used inestimating location (Black, 2011). When using a significance level of0.05, for instance, all of the alpha in a one tailed-test will beused to test significance in one direction only and the otherdirection will be disregarded.

One-tailed test is applicable in the following null hypotheses

  1. A flipping coin is biased towards tails.

  2. Chemotherapy in the treatment of breast cancer will lead to better results than chance

A one-tailed test is appropriate for the above hypotheses since testsare carried out only in one direction. In the first hypothesis,getting data for “all tails” would be regarded as highlysignificant. On the other hand, getting results for “all heads”would be regarded as not significant at all. No test for significanceis conducted to determine whether the flipping coin is biased towardsthe heads. The same also applies to the second hypothesis. Gettingdata for “all positive results” would be regarded as highlysignificant. On the other hand, getting results for “all negativeresults” would be regarded as not significant at all. Thus, bothhypotheses focus on testing significance in one direction only. Thisexplains the fact that a one-tailed test is suitable for the twohypotheses (Ruxton &amp Neuhäuser, 2010).

On the other hand, two-tailed tests are only applicable in two-taileddistributions. The two-tailed test considers statistical significancein both directions. For instance, when using a significance level of0.05, 0.025 will be used to test significance in one direction andanother 0.025 will be applied in the other direction (Veney, Kros, &ampRosenthal, 2009).

Two-tailed test can be applied in the following null hypotheses

  1. A flipping coin is biased towards either tails or heads.

  2. Chemotherapy in the treatment of breast cancer will lead to better or worse results than chance.

In the above cases, test for statistical significance is conducted intwo directions. In the first hypothesis, getting data for “alltails” or “all head” would be regarded as highly significant.In the second case, getting data for “positive results” or“negative results” would be regarded as highly significant. Sincethe test for significance is needed for both directions, thetwo-tailed test is more appropriate in both cases (Veney, Kros, &ampRosenthal, 2009).

Article applying T-test Analysis

T-test has been applied in the article written by Maher et al.(2007). The article examines the relationship between type ofchildcare prior to the entry into kindergarten and the possibility ofdeveloping obesity after the entry into kindergarten. The studyutilizes a sample of 15 691 children entering kindergarten for thefirst time. The researchers tested the impacts of the influence ofincome and ethnicity on the possibility of developing obesity amongthe children. The results of the study showed that by the time ofentry into kindergarten, 12% of the children included in the studywere obese. Children in primary child care (under the care of family,neighbor or friend) before the entry were more likely to developobesity after entry into kindergarten than children who were in othertypes of childcare. Latino children were more likely to developobesity than White children. In conclusion, the results of the studyshowed significant association between primary care and obesity amongthe children. In addition, the results showed significant associationbetween child’s ethnicity and the possibility of developing obesity(Maher et al., 2007).

The Null Hypotheses

The null hypotheses in the study are

  1. Null hypotheses: There is significant association between primary care and obesity among the children entering kindergarten for the first time.

Alternative Hypotheses: There is not significant association betweenprimary care and obesity among the children entering kindergarten forthe first time

  1. Null hypotheses: There is significant association between child’s ethnicity and the possibility of developing obesity among the children entering kindergarten for the first time.

Alternative Hypotheses: There is no significant association betweenchild’s ethnicity and the possibility of developing obesity amongthe children entering kindergarten for the first time.

Dependent variable (DV)

The DV in the study is the dichotomous variable on whether a child isobese or not. The DV was measured at 5% level of significance.

The Independent Variable (IV)

The IV in the study is type of child-care arrangement. The IV wasmeasured at 5% level of significance.

Type of Data and Assumptions

The study required quantitative data in order to allow forstatistical analysis. The researchers made several assumptions duringthe research. To start with, they assumed that a child’s ethnicbackground and type of care influence the quality of child carereceived. As well, the researchers made assumptions that all childrenin the same type of childcare setting or those sharing similar ethnicbackground receive similar care. All the above assumptions were met.

References

Black, K. (2011). Business Statistics: For Contemporary DecisionMaking. London: John

Wiley &amp Sons

Jekel, J. F. (2007). Epidemiology, Biostatistics, and PreventiveMedicine. London: Elsevier

Health Sciences

Maher, E. J., Li, G., Carter, L. &amp Johnson, B. D. (2007).Preschool Child Care Participation and

Obesity at the Start of Kindergarten. Pediatrics, 122 ( 2),322 -330

Ruxton, G. D. &amp Neuhäuser, M. (2010). When should we useone-tailed hypothesis testing?

Methods in Ecology and Evolution, 1(2), 114-117

Sawilowsky , S. S. (207). Real Data Analysis. New York, NY:IAP

Veney, J. E., Kros, J. F. &amp Rosenthal, D. A. (2009). Statisticsfor Health Care Professionals:

Working With Excel. California: John Wiley &amp Sons