WK 5 dis Data

Comparison of Means

Last week we focused on comparing the means of two groups and used the independent samples t test and the Mann Whitney U test

This week we challenge that by adding additional comparisons

Once you have three groups to compare, you actually have 3 possible comparisons

Practice-Focused question

Is there a difference in perceived satisfaction with the RRT process by activating nurses when compared by RRT type (cardiac, respiratory, or neurology)?

One-Way anova

Uses the F statistic

Provides a p value that encompasses all possible combinations, but does not indicate by itself where those statistically significant findings occur.

Allows for “post hoc” multiple comparisons that do provide that focus

Has multiple assumptions associated with it. Most notably: data must be “normally distributed”

Sample size is large enough and passes the four tests of normality. Observations are all independent (that is, in this sample there were no patients who had both cardiac and respiratory components……..RRTs were classified as one or the other of the three groups.

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Anova Measurement

Rapid Response Team (RRT) analysis with 75 RRTs

Activating nurse completed a survey with seven questions indicating their level of satisfaction with the RRT (1= very dissatisfied, 5=very satisfied)

Scores were summed yielding a total score on all seven questions and averaged across the entire sample

The highest possible score (very satisfied) was 35 and the lowest possible score was 7.

RRTs were described as cardiac, respiratory, neurology or other.

There were 42 cardiac, 12 respiratory and 21 neurology RRTs in the sample. There were no RRTs described in the other category.

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ANOVA Results

Cardiac M: 30.0238 SD 6.42210

Respiratory M: 31.00 SD 3.30289

Neurology M: 13.9524 SD 12.92082

Now there is a lot of information in these results, most of which you do not see mentioned in a published study that used ANOVA. Sometimes, you see the F statistic (28.104). In Salkind & Frey, you can learn how to actually do an ANOVA in excel, which is for your information. In this course we are most concerned about understanding the basic elements of the test, and how to interpret.

So, the F statistic is accompanied by the all-important p value in the table above, and as you can see, it is indicating a statistically significant result. With a p value of <.001 we can be confident that the differences are not due to chance, and more likely to some factor. But the ANOVA level of significance does NOT tell us WHERE those differences are. Is it between cardiac and respiratory, or cardiac and neurology, or between respiratory and neurology? Three groups, three possible comparisons.

Now a one-way ANOVA test is used when there is more than one comparison (that would be two groups, and an independent samples t test). As we have three groups, we also have three comparisons. So, a post hoc test helps to fathom out just where those comparisons are located.

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Post hoc: scheffe

As you can see, the Scheffe post hoc test, computes the difference in the means, and then calculates the significance level. (Behind the scenes in the statistical software, there are actually several independent samples t tests that make these 2-group comparisons.)

Note the lack of statistical significance between cardiac and respiratory. That is likely because the difference was so small, less than a point. You would need a huge sample, far greater than 75 cases to be able to see this statistically. But notice that the difference between cardiac and neurology is much bigger and the p value is also statistically significant (p<.001). Finally, notice that the difference between respiratory and neurlogy is also statistically significant (also with a p value of < .001).

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RRT project small sample

N=25

Data did not meet the normality assumption

A nonparametric test is needed

Kruskal-Wallis

Measurement mechanisms: 7-item survey completed by activating nurses

Three types of RRTs: cardiac (n=14), respiratory (n=3), neurology (n=7), other (n=1) for a total of (N=25)

Much smaller sample, but practice-focused question was the same. Is there a difference by RRT type in activating nurse satisfaction?

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Differences in means

Cardiac: M=30.0714 SD 5.71724

Respiratory: M=29.6667 SD=3.05505

Neurology: M=28.2857 SD=10.33948

Is there a difference in the means? WOW they are very close……only fractional differences.

The small sample indicates that the data are likely to violate the assumptions of the ANOVA test. So let’s, use the nonparametric equivalent, the Kruksal-Wallis test.

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The statistical software discounts the one case in the “all other” category and compares cardiac, respiratory, and neurology. The H statistic used in the statistical software was 2.059 with 3 degrees of freedom and an asymtotic significance level of .560. As this result is far greater than the accepted .05 level of significance, there is no point in going any farther. The difference in the means is not statistically significant.

Degrees of freedom has to do with (essentially) an estimate of the sample size. In this case, all four groups are counted yielding 3 degrees of freedom (1-#of groups).

Salkind and Frey 5th edition has a good explanation of effect size (the magnitude of the difference) on pp243-246.

Read about the word asymptotic on page 183.

Now, because the sample size is so very small, the student took pains to explain that with a small between the groups, she would have needed a huge sample, in fact over 250 in order to see whether this small difference was statistically significant or not.

Thus, this very small dataset exhibits a very likely case of a type II error, when significance was not found, but it may, in fact, be there.

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Turgut & Yildez (2023)Table 3

N=200 PICU nurses

Professional grief and posttraumatic growth measured against a number of characteristics in nurses.

ANOVA used to determine the impact of duration of work in the unit against professional grief

There will be differences between the way professional grief is experienced based on tenure (duration of work in the PICU unit).

Professional grief & duration of work in the unit