8.6 A large laboratory has four types of devices used to determine the pH of soil samples. The laboratory wants to determine whether there are differences in the average readings given by these devices. The lab uses 24 soil samples having known pH in the study and randomly assigns six of the samples to each device. The soil samples are tested, and the response recorded for each sample is the difference between the pH reading of the device and the known pH of the soil. These values, along with summary statistics, are given in the following table. Sample Device 1 2 3 4 5 6 A 2.307 2.294 .079 .019 2.136 2.324 B 2.176 .125 2.013 .082 .091 .459 C .137 2.063 .240 2.050 .318 .154 D 2.042 .690 .201 .166 .219 .407 Copyright 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 436 Chapter 8 Inferences About More Than Two Population Central Values a. Based on your intuition, is there evidence to indicate any difference among the mean differences in pH readings for the four devices? b. Run an analysis of variance to confirm or reject your conclusion in part (a). Use a 5 .05. c. Compute the p-value of the F test in part (b).
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
8.6 A large laboratory has four types of devices used to determine the pH of soil samples. The
laboratory wants to determine whether there are differences in the average readings given by
these devices. The lab uses 24 soil samples having known pH in the study and randomly assigns
six of the samples to each device. The soil samples are tested, and the response recorded for each
sample is the difference between the pH reading of the device and the known pH of the soil.
These values, along with summary statistics, are given in the following table.
Sample
Device 1 2 3 4 5 6
A 2.307 2.294 .079 .019 2.136 2.324
B 2.176 .125 2.013 .082 .091 .459
C .137 2.063 .240 2.050 .318 .154
D 2.042 .690 .201 .166 .219 .407
Copyright 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
436 Chapter 8 Inferences About More Than Two Population Central Values
a. Based on your intuition, is there evidence to indicate any difference among the
mean differences in pH readings for the four devices?
b. Run an analysis of variance to confirm or reject your conclusion in part (a).
Use a 5 .05.
c. Compute the p-value of the F test in part (b).
d. What conditions must be satisfied for your analysis in parts (b) and (c) to be valid?
e. Suppose the 24 soil samples have widely different pH values. What problems may
occur by simply randomly assigning the soil samples to the different devices?
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