Notebook

Nov 15, 2024, 3:58 PM

vitamin.xlsx

Missing file

5. In a study of healthy subjects grouped by age (Younger: 19–50 years, Seniors: 65–75 years, and Longeval: 85–102 years), Herrmann et al. measured their vitamin B-12 levels (ng/L). All elderly subjects were living at home and able to carry out normal day-to-day activities. The data set in “vitamin” shows vitamin B-12 levels for 50 subjects in the young group, 92 seniors, and 90 subjects in the longeval group. Is the data normally distributed? May we conclude, on the basis of these data, that the populations represented by these samples differ with respect to vitamin B-12 levels?

To determine if the data is normally distributed and if the populations differ with respect to vitamin B-12 levels, we can perform the following steps:

Normality Test: We can use the Shapiro-Wilk test to check for normality of the vitamin B-12 levels within each group.
ANOVA Test: If the data is normally distributed, we can use ANOVA to test if there are significant differences in vitamin B-12 levels between the groups.
Kruskal-Wallis Test: If the data is not normally distributed, we can use the Kruskal-Wallis test as a non-parametric alternative to ANOVA.

Let's start by checking the normality of the data using the Shapiro-Wilk test.

The B12 column is currently of type object, which suggests that there might be non-numeric values or formatting issues. Let's clean the data by converting the B12 column to numeric values and handling any potential errors.

There is one missing value in the B12 column after conversion. We will remove this row to ensure accurate analysis.

Let's proceed by removing the missing values and then perform the Shapiro-Wilk test for normality on each group.

The Shapiro-Wilk test results for normality are as follows:

Group 1 (Younger): Statistic = 0.676, p-value = 4.03e-09
Group 2 (Seniors): Statistic = 0.856, p-value = 5.32e-08
Group 3 (Longeval): Statistic = 0.538, p-value = 2.31e-15

The p-values for all groups are less than 0.05, indicating that the data is not normally distributed in any of the groups.

Since the data is not normally distributed, we will use the Kruskal-Wallis test to determine if there are significant differences in vitamin B-12 levels between the groups.

The Kruskal-Wallis test results are as follows:

Statistic: 15.455
p-value: 0.00044

The p-value is less than 0.05, indicating that there are significant differences in vitamin B-12 levels between the groups.

Conclusion: Based on the Kruskal-Wallis test, we can conclude that the populations represented by these samples differ with respect to vitamin B-12 levels.

If you have any more questions or need further analysis, feel free to ask!

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