The following table was presented in an article summarizing a study to compare a new drug to a standard drug and to a placebo. Characteristic*New DrugStandard DrugPlacebopAge, years45.2 (4.8)44.9 (5.1)42.8 (4.3)0.5746% Female51%55%57%0.1635Annual Income, $000s59.5 (14.3)63.8 (16.9)58.2 (13.6)0.4635% with Insurance87%65%82%0.0352Disease Stage 0.0261 Stage I35%18%33% Stage II42%37%47% Stage III23%51%20% *Table entries and Mean (SD) or % 1. Are there any statistically significant differences in the characteristics shown among the treatments? Justify your answer. 2. Consider the test for differences in age among the new drug compared to the placebo (two variables). Write the hypotheses and the formula of the test statistic used (No computations required – formula only).

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Description: The following table was presented in an article summarizing a study to compare a new drug to a standard drug and to a placebo. Characteristic*New DrugStandard DrugPlacebopAge, years45.2 (4.8)44.9 (5.1)42.8 (4.3)0.5746% Female51%55%57%0.1635Annual Inc

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Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 30PPS

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The following table was presented in an article summarizing a study to compare a new drug to a standard drug and to a placebo.

Characteristic*	New Drug	Standard Drug	Placebo	p
Age, years	45.2 (4.8)	44.9 (5.1)	42.8 (4.3)	0.5746
% Female	51%	55%	57%	0.1635
Annual Income, $000s	59.5 (14.3)	63.8 (16.9)	58.2 (13.6)	0.4635
% with Insurance	87%	65%	82%	0.0352
Disease Stage				0.0261
Stage I	35%	18%	33%
Stage II	42%	37%	47%
Stage III	23%	51%	20%

*Table entries and Mean (SD) or %

1. Are there any statistically significant differences in the characteristics shown among the treatments? Justify your answer.

2. Consider the test for differences in age among the new drug compared to the placebo (two variables). Write the hypotheses and the formula of the test statistic used (No computations required – formula only).

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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