Three different corrosion-resistant coatings are being considered for use on iron pipes. Ten pieces of pipe are marked off in six equal segments. For each pipe, two segments received coating A, two received coating B, and the remaining two received coating C. The pipes were placed in a corrosive environment for a period of time; then the depth of the deepest pit (in mm) caused by corrosion was measured for each segment on each pipe. The effect of interest is the coating; the pipe is a blocking factor, and there were two replications on each pipe. The following sums of squares were calculated: sum of squares for blocks = 11.2, sum of squares for treatments = 4.8, sum of squares for interactions = 18.4, total sum of squares = 44.7. a) Construct an ANOVA table. You may give ranges for the P-values. b) Are the assumptions for a randomized complete block design satisfied? Explain. c) Does the ANOVA table provide evidence that mean pit depth differs among coatings? Explain.
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.
Three different corrosion-resistant coatings are being considered for use on iron pipes. Ten
pieces of pipe are marked off in six equal segments. For each pipe, two segments received
coating A, two received coating B, and the remaining two received coating C. The pipes
were placed in a corrosive environment for a period of time; then the depth of the deepest
pit (in mm) caused by corrosion was measured for each segment on each pipe. The effect of
interest is the coating; the pipe is a blocking factor, and there were two replications on each
pipe. The following sums of squares were calculated: sum of squares for blocks = 11.2, sum
of squares for treatments = 4.8, sum of squares for interactions = 18.4, total sum of squares
= 44.7.
a) Construct an ANOVA table. You may give
b) Are the assumptions for a randomized complete block design satisfied? Explain.
c) Does the ANOVA table provide evidence that
Explain.
Trending now
This is a popular solution!
Step by step
Solved in 6 steps with 5 images
