Comparing the means of two or more groups

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Comparing the means of two or more groups

Open in a separate window Note that the authors of this study also collected information on baseline mean arterial pressure and examined the 6-hour pressures in the context of these using a method known as analysis of covariance [ 1 ].

In practice this is a more appropriate analysis, but for illustrative purposes the focus here is on 6-hour mean arterial pressures only. It appears that the mean arterial pressure was 14 mmHg higher in the early goal-directed therapy group.

There is no overlap between the two confidence intervals and, because these are the ranges in which the true population values are likely to lie, this supports the notion that there may be a difference between the two groups.

However, it is more useful to estimate the size of any difference directly, and this can be done in the usual way. The only difference is in the calculation of the SE. In the paired case attention is focused on the mean of the differences; in the unpaired case interest is in the difference of the means.

Because the sample sizes in the unpaired case may be and indeed usually are different, the combined SE takes this into account and gives more weight to the larger sample size because this is likely to be more reliable.

The pooled SD for the difference in means is calculated as follows: The pooled SE for the difference in means is then as follows. This SE for the difference in means can now be used to calculate a confidence interval for the difference in means and to perform an unpaired t-test, as above.

The pooled SD in the early goal-directed therapy trial example is: If there were no difference in the mean arterial pressures of patients randomized to early goal-directed and standard therapy then the difference in means would be close to 0. However, the confidence interval excludes this value and suggests that the true difference is likely to be between 9.

To explore the likely role of chance in explaining this difference, an unpaired t-test can be performed. The null hypothesis in this case is that the means in the two populations are the same or, in other words, that the difference in the means is 0.

As for the previous two cases, a t statistic is calculated. Again, the larger the t statistic, the smaller the P value will be. In other words, it is extremely unlikely that a difference in mean arterial pressure of this magnitude would be observed just by chance.

This supports the notion that there may be a genuine difference between the two groups and, assuming that the randomization and conduct of the trial was appropriate, this suggests that early goal-directed therapy may be successful in raising mean arterial pressure by between 9.

As always, it is important to interpret this finding in the context of the study population and, in particular, to consider how readily the results may be generalized to the general population of patients with severe sepsis or septic shock.

Assumptions and limitations In common with other statistical tests, the t-tests presented here require that certain assumptions be made regarding the format of the data. The one sample t-test requires that the data have an approximately Normal distribution, whereas the paired t-test requires that the distribution of the differences are approximately Normal.

The unpaired t-test relies on the assumption that the data from the two samples are both Normally distributed, and has the additional requirement that the SDs from the two samples are approximately equal.

Formal statistical tests exist to examine whether a set of data are Normal or whether two SDs or, equivalently, two variances are equal [ 2 ], although results from these should always be interpreted in the context of the sample size and associated statistical power in the usual way.

However, the t-test is known to be robust to modest departures from these assumptions, and so a more informal investigation of the data may often be sufficient in practice.

If assumptions of Normality are violated, then appropriate transformation of the data as outlined in Statistics review 1 may be used before performing any calculations.

Similarly, transformations may also be useful if the SDs are very different in the unpaired case [ 3 ]. However, it may not always be possible to get around these limitations; where this is the case, there are a series of alternative tests that can be used.

Known as nonparametric tests, they require very few or very limited assumptions to be made about the format of the data, and can therefore be used in situations where classical methods, such as t-tests, may be inappropriate. These methods will be the subject of the next review, along with a discussion of the relative merits of parametric and nonpara-metric approaches.

Finally, the methods presented here are restricted to the case where comparison is to be made between one or two groups. This is probably the most common situation in practice but it is by no means uncommon to want to explore differences in means across three or more groups, for example lung function in nonsmokers, current smokers and ex-smokers.

This requires an alternative approach that is known as analysis of variance ANOVAand will be the subject of a future review.Multivariate: provides regression analysis and analysis of variance for multiple dependent variables by one or more factor variables or factor variables divide the population into groups.

investigate interactions between factors as well as the effects of individual factors. Methods of Comparing Images Compare Program The "compare" program is provided to give you an easy way to compare two similar images, to determine just how 'different' the images example here I have two frames of a animated 'bag', which I then .

ANALYSIS OF CONTINUOUS VARIABLES / 31 CHAPTER SIX ANALYSIS OF CONTINUOUS VARIABLES: COMPARING MEANS In the last chapter, we addressed the analysis of discrete variables. Much of the statistical analysis in medical research, however, involves the analysis of continuous variables (such as cardiac output, blood pressure, and heart rate) which can assume an infinite range .

Comparing the means of two or more groups

[The total df is always one fewer than the total number of data entries] Step Using the mean squares in the final column of this table, do a variance ratio test to obtain an F value.

F = Between treatments mean square / Residual mean square. Creation stories in the Bible Comparing/contrasting the two creation stories in Genesis. Sponsored link. Quotations showing three different interpretations of the Bible.

In this lesson when comparing two proportions or two means, we will use a null value of 0 (i.e. "no difference"). Although we can test for a specific difference, for example does the diet result in an average weight loss of more than 10 pounds.

Use SPSS to Compare Means