摘要:Calculatethe test statistic and compare with the critical value. Also calculate theprobability of obtaining the sample value. Reject the null hypothesis if thesample value is outside the critical range or single value if it is a one-sidedtest.
higher powerthan the equivalent non-parametric test which is the Mann-Whitney U-test.However, the Mann-Whitney test is more robust in that it does not assume thatthe data is normally distributed.
It is a matter of weighing up the pros and cons. Ifnormality can be assumed then the independent samples t-test is best. If not,then the U-test should be used. Tests suchj as a histogram or Q-Q(quantile-quantile) plot can be used to check normality to help the decisionBland (2000).
Because the test is one-sided we would be looking for themale mean to be higher and the critical value to come from 0.05 in the one tailof the distribution. For the t test this would be looked up with n1 + n2 - 2degrees of freedom where n1 and n2 are the numbers of males and femalesrespectively.
It is also useful to work out a 95% confidence interval forthe population mean. This gives an idea of the spread of the estimate. Largersample sizes will reduce the confidence interval.
It was mentioned above that the inferences made are onlyvalid for the population being sampled and only so if the sample isrepresentative, which means selecting the sample from the whole population suchthat each member has equal probability of selection.
For the results to be reliable as Coolican (1990) says thatif a research finding can be repeated it is reliable. So, if the sample isrepeated the same result would indicate reliability.
Hypothesis 2: Taller children are heavier.
The null hypothesis is that there is no relationship betweenhow tall children are and how much they weigh. The alternative hypothesis isthat taller children are heavier, which is a one-sided test. That is, thealternative is not simply that there is a relationship, which would betwo-sided.
Both heights and weights are ratio data. This enables thedata to be examined by tests where normality is an underlying assumption.
In order to visually check the relationship a scatter graphis pretty well essential. This would give an idea of the strength and nature ofthe relationship. The relationship may not be linear as is often assumed. If sothen the scatter should show indication of a curve.
The strength of the relationship can be tested by using thePearson correlation coefficient ( r ). This is closely related to a regressionanalysis which would be fitting a straight line equation to the data withheight being the independent (x) variable and weight being dependent (y).
The correlation coefficient can be tested using a 1 sidedt-test. This has n-2 degrees of freedom, 28 in this case. The value of r wouldneed to be positive to indicate that taller children are heavier.
Analysis of the regression residuals can give us a lot moreinformation than simply carrying out a correlation calculation. See Bland(2000). They can be plotted to see whether they are normally distributed usinga histogram or Q-Q plot. Also, non-linearity should be apparent if this is thecase.
If the data shows a non-linear relationship then it would benecessary to transform the data using logs or other mathematical functions. Thetransformed variables would then need to be analyses for normality andlinearity.
According to Bland there is an alternative to the Pearsoncorrelation coefficient which does not assume that the data is normallydistributed. This is the Spearman Rank Correlation Coefficient. This is basedon the distribution of the ranks of the data and not the data
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