Question

Between-subject and within-subjects designs differ in several ways. What is the importance of a one-way between-subjects ANOVA, and what are you comparing? Please explain the processes and application of the one-way ANOVA between-subjects design.

You can also explain or define what a one-way ANOVA is and how it applies in research.

Answer 1

A one-way ANOVA evaluates the impact of a sole factor on a sole response variable. It determines whether all the samples are the same. The one-way ANOVA is used to determine whether there are any statistically significant differences between the means of three or more independent (unrelated) groups.In statistics, one-way analysis of variance (abbreviated one-way ANOVA) is a technique that can be used to compare means of two or more samples (using the F distribution). This technique can be used only for numerical response data, the "Y", usually one variable, and numerical or (usually) categorical input data, the "X", always one variable, hence "one-way".

Examples of when to use a one way ANOVA

Situation 1: You have a group of individuals randomly split into smaller groups and completing different tasks. For example, you might be studying the effects of tea on weight loss and form three groups: green tea, black tea, and no tea.
Situation 2: Similar to situation 1, but in this case the individuals are split into groups based on an attribute they possess. For example, you might be studying leg strength of people according to weight. You could split participants into weight categories (obese, overweight and normal) and measure their leg strength on a weight machine.

The data and statistical summaries of the data

One form of organizing experimental observations is with groups in columns:

ANOVA data organization, Unbalanced, Single factor

	Lists of Group Observations
1
2
3
	Group Summary Statistics	Grand Summary Statistics
# Observed							# Observed
Sum							Sum
Sum Sq							Sum Sq
Mean							Mean
Variance							Variance

Comparing model to summaries: and . The grand mean and grand variance are computed from the grand sums, not from group means and variances.

The hypothesis test[edit]

Given the summary statistics, the calculations of the hypothesis test are shown in tabular form. While two columns of SS are shown for their explanatory value, only one column is required to display results.

ANOVA table for fixed model, single factor, fully randomized experiment

Source of variation	Sums of squares	Sums of squares	Degrees of freedom	Mean square	F
	Explanatory SS	SS	DF	MS
Treatments			{\displaystyle J-1}
Error
Total

is the estimate of variance corresponding to of the model.

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