Statistics Calculating ANOVAs Solutions 2022

STATISTICS
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Homework 4
An example of ratio data is height of students. An example of ordinal data is grades of
students classified in A, B,C & D based on performance. An example of nominal data is
gender. The data type appropriate for a t test would be ratio since it has numerical values.
For t test, we need mean and standard deviation which are sensible only for a ratio data.
A hypothesis which can be examined using t test is whether the performance of boys and girls
of a given class tend to differ significantly. A suitable hypothesis to be tested using ANOVA
is to compare the performance of three sections of Grade 8 in a science exam.
Independent measures are those where the values of the respective datasets are independent
of each other. On the contrary, dependent measures are those where the respective values
tend to be dependent on one another.
The descriptive statistics that would be helpful are mean and standard deviation since these
are used to determine the test statistic and hence useful for hypothesis testing. Descriptive
statistics normally indicate the key characteristics of the sample data. The t test and ANOVA
tend to present information about the population characteristics which descriptive statistics do
not provide.
Calculating ANOVAs
Problem 1
Null Hypothesis: μSingle = μTwin = μTriple
Alternative Hypothesis: Atleast one of the above means is different from the other two
Level of significance = 0.05
The output obtained from Excel is pasted below.