A study was conducted to compare three methods of measuring concentration of certain type of chemical pollutants in a lake. The data is given in Table 1 below. Compute SS(between) and SS(within). Compute SS(total), and explain the relationship between SS(between), SS(within), and SS(total). Compute MS(between), MS(within), and F statistic. Based on your computations, are there significant differences in the mean pollutant concentrations among the three methods? Table 1. Amount of concentration of a chemical pollutant in a lake using three different measuring methods Method 1 Method 2 Method 3 10.96 10.88 10.73 10.77 10.75 10.79 10.90 10.80 10.78 10.69 10.81 10.82 10.87 10.70 10.88 10.6 10.82 10.81
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.
- A study was conducted to compare three methods of measuring concentration of certain type of chemical pollutants in a lake. The data is given in Table 1 below.
- Compute SS(between) and SS(within).
- Compute SS(total), and explain the relationship between SS(between), SS(within), and SS(total).
- Compute MS(between), MS(within), and F statistic.
- Based on your computations, are there significant differences in the mean pollutant concentrations among the three methods?
Table 1. Amount of concentration of a chemical pollutant in a lake using three different measuring methods
Method 1
Method 2
Method 3
10.96
10.88
10.73
10.77
10.75
10.79
10.90
10.80
10.78
10.69
10.81
10.82
10.87
10.70
10.88
10.6
10.82
10.81
- Monoamine oxidase (MAO) is an enzyme that is thought to play a role in the regulation of behavior. To see whether different categories of patients with schizophrenia have different levels of MAO activity, researchers collected blood specimens from 42 patients and measured the MAO activity in the platelets. The results are partially summarized in the accompanying tables.
Table 2. Summary measures for the MAO activity in the blood of 42 patients as categorized according to the type of schizophrenia.
Diagnosis
Mao activity
Mean
SD
No. of patients
Chronic undifferentiated schizophrenia
9.81
3.62
18
Undifferentiated with paranoid features
6.28
2.88
16
Paranoid schizophrenia
5.97
3.19
8
Table 3. ANOVA table for Lab Exercise 10.2
Source
df
Sum of squares
Mean square
statistic
Between
XX
136.12
68.06
XX
Within
XX
418.25
10.72
Total
XX
554.37
- How many degrees of freedom are there for the ANOVA test?
- Compute the value of statistic.
- The p-value for the test is 0.004. If , what is your conclusion regarding the null hypothesis?
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