Biostatistics Homework: Analysis of Variance and Regression

This biostatistics assignment solution addresses key concepts in statistical analysis. Question 1 classifies data types as nominal, ratio, and ordinal. Question 2 analyzes a distribution, determining median, mode, and range. Question 3 explores the application of chi-square tests to determine if there is a gender difference and if waist circumference is a significant factor with regards to the number of remaining teeth. Question 4 differentiates between ANOVA and Chi-square, presenting p-values for various variables. Question 5 delves into multiple regression analysis, interpreting the R-squared value, assessing the model's significance, deriving a regression equation, and providing a calculation based on given input values. The solution references key statistical methodology resources and provides a comprehensive understanding of statistical tests and their interpretations.

BIOSTATISTICS
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Question 1
1) Gender – Nominal
2) Blood Type – Nominal
3) Number of Children – Ratio
4) Serum potassium level – Ratio
5) Age in Categories – Ordinal
Question 2
1) The median of the distribution is 7 hours.
2) The mode of the distribution is 8 hours as it has the largest frequency.
3) The range of the distribution is 11 hours obtained from the difference of 15 hours (highest
value) and 4 hours (minimum value)
4) The answer is 29.7% as is evident from the table.
Question 3
1) Gender difference does not exist in the three groups as the chi-square test statistic in this
context has come out as 4.03 which is not significant and hence does not point towards any
significant difference for the two genders (Flick, 2015).
2) It is apparent from the given table that waist circumference is a significant factor with
regards to the number of remaining teeth as the chi square statistic derived in this regards is
statistically significant even at 0.1% level of significance. Typically a higher number of
remaining teeth would be witnessed for those having abnormal waist circumference (Hair,
Wolfinbarger, Money, Samouel & Page, 2015).
Question 4

The key difference between ANOVA and Chi-square is that the former is used for continuous
numerical variables unlike Chi-square which is used for categorical variables only (Hillier,
2016).
The various p values as a result of the ANOVA test are indicated below.
 Age (years) where p value = 0.000
 Education (years) where p value = 0.000
 Monthly income where p value = 0.459
 Number of Chronic Illness where p value = 0.000
Question 5
2) The R square value of 0.348 implies that 34.8% of the variation in the dependent variable
(Incws) can be accounted for jointly by the variation in the independent variables
(Educ_yr,hours, sex, age) (Hillier, 2016).
3) From the ANOVA table, the significance of the multiple regression model is established as
the p value corresponding to the F statistic of 5.019 is lesser than the underlying level of
significance. This implies that there does exist at least one slope coefficient in the given
multiple regression model which is significant and hence cannot be assumed as zero. (Flick,
2015).
4) The regression equation derived on the basis of the output provided is indicated below.
Incws = -39061.2 + 2785.736*educ_yr +341.835*age -8893.049*sex + 844.966*hours
5) The given input values are substituted in the above equation as indicated below.
INCWS = -39061.2 + 2785.736*8+341.835*51 -8893.049*0 + 844.966*2 = 2348.205

References
Flick, U. (2015). Introducing research methodology: A beginner's guide to doing a research
project New York: Sage Publications.
Hair, J. F., Wolfinbarger, M., Money, A. H., Samouel, P., & Page, M. J. (2015). Essentials of
business research methods New York: Routledge.
Hillier, F. (2016). Introduction to Operations Research.New York: McGraw Hill
Publications.