Indetermining if there indeed exists a significant departure from themean temperature for a particular date in a specified location, thepaper will use two descriptive statistics they include standarddeviation and standard error. Use of standard deviation is criticalgiven that through it, a researcher can then construct the t-static(Leys et al., 2013). The t-static constructed is then compared witht-critical that is got from the t-static table. If the studyestablished that, the value derived is higher than the t-criticalthen the null hypothesis is rejected. From this, the study thenreaches a conclusion that temperature of 70 degrees indeedsignificantly departures from the mean temperature. Nonetheless, ift-calculate is found to be less than t-critical then the studyconcludes that there is no significant departure from the averagetemperature.
Theuse of standard error is critical given that it assists inconstructing the confidence interval for the mean temperature(Thompson, 2011). From the construction, one can then infer that ifthe temperature of 70 is outside the confidence interval, then thestudy infers that there is a significant departure from the averagetemperature (Satorra & Bentler, 2011). Nonetheless, if thetemperature is within the confidence interval, then the studyconcludes that there is no significant departure from the average(Altman et al., 2013).
Thet and the z statistic are often used in finding out if there is alinear relationship between covariates (Muthén, 2011). The othertool that is also useful in the process is an analysis of variance(ANOVA) (Arias-Castro, Candès & Plan, 2011).
Whenstudying individuals, the repeated measure design is encouraged ashaving repeated measures ensure that the study operates within therequired integrity. Having a high integrity in the research translateto a reduction in standard error.
Altman,D., Machin, D., Bryant, T., & Gardner, M. (Eds.).(2013). Statisticswith confidence: confidence intervals and statistical guidelines.John Wiley & Sons.
Arias-Castro,E., Candès, E. J., & Plan, Y. (2011). Global testing undersparse alternatives: ANOVA, multiple comparisons and the highercriticism.TheAnnals of Statistics,2533-2556.
Leys,C., Ley, C., Klein, O., Bernard, P., & Licata, L. (2013).Detecting outliers: Do not use standard deviation around the mean,use absolute deviation around the median. Journalof Experimental Social Psychology,49(4),764-766.
Muthén,B. O. (2011). Mean and covariance structure analysis of hierarchicaldata. Departmentof Statistics, UCLA.
Satorra,A., & Bentler, P. (2011). Scaling corrections for statistics incovariance structure analysis. Departmentof Statistics, UCLA.
Thompson,S. B. (2011). Simple formulas for standard errors that cluster byboth firm and time. Journalof Financial Economics, 99(1),1-10.