Design a basic study, or use your research idea, in which you could analyze your
ID: 3219002 • Letter: D
Question
Design a basic study, or use your research idea, in which you could analyze your data using a t-test. How would you conduct the study and why? Who are your subjects? What are your independent and dependent variables? How would you report your results? Now design a basic study, or use your research idea, in which you could analyze your data using an ANOVA. Who are your subjects? What are your independent and dependent variables? How would you report your results? How could you redesign the study as a repeated-measures ANOVA? How could you redesign the study as an ANCOVA?Explanation / Answer
What is a one-sample t-test ?
A one-sample t-test helps determine whether (the population mean) is equal to a hypothesized value (the test
mean). The test uses the standard deviation of the sample to estimate (the population standard deviation). If the difference between the sample mean and the test mean is large relative to the variability of the sample mean, then is unlikely to be equal to the test mean.
When to use a one-sample t-test ?
Use a one-sample t-test when continuous data are available from a single random sample.
The test assumes the population is normally distributed. However, it is fairly robust to violations of this assumption, provided the observations are collected randomly and the data are continuous, unimodal, and reasonably symmetric.
Why use a one-sample t-test ?
A one-sample t-test can help answer questions such as:
For example,
The logic of hypothesis testing
All hypothesis testing follows the same steps:
1 Assume H0 is true.
2 Determine how different the sample is from what is expected under the above assumption.
3 If the sample is sufficiently unlikely under the assumption that H0 is true, then reject H0.
Making a decision
To make a decision, choose the significance level, (alpha), before the test:
• If P is less than or equal to , reject H0.
• If P is greater than , fail to reject H0. (Technically, you never accept H0, you simply fail to reject it.)
What is an independent two-sample t-test ?
An independent two-sample t-test helps determine whether two population means are different. The test uses the sample standard deviations to estimate for each population. If the difference between the sample means is large relative to the estimated variability of the sample means, then the population means are unlikely to be the same.
You can also use an independent two-sample t-test to evaluate whether the means of two populations are different
by a specific amount.
When to use an independent two-sample t-test ?
Use an independent two-sample t-test with continuous data from two independent random samples. Samples are
independent if observations from one sample are not related to the observations from the other sample. For example, the strengths of pellets from supplier A’s process are not influenced by the strengths of supplier B’s pellets; thus, samples are independent.
The test also assumes that the data come from normally distributed populations. However, it is fairly robust to
violations of this assumption, provided the observations are collected randomly and the data are continuous, unimodal,and reasonably symmetric.
Why use an independent two-sample t-test ?
An independent two-sample t-test can help answer questions such as:
For example,
What is one-way ANOVA ?
The one-way ANOVA (analysis of variance) procedure is a generalization of the independent samples t-test. Unlike the t-test, however, you can use one-way ANOVA to analyze the means of more than two groups (samples) at once.
The basic logic behind ANOVA is that within-group variation is due only to random error.
When to use one-way ANOVA ?
Use one-way ANOVA (also called single-factor ANOVA) when you have continuous response data for two or more
fixed levels of a single factor.
Before accepting the results of an ANOVA, you must verify that the following assumptions about the errors are valid for your data. They must:
Why use one-way ANOVA ?
One-way ANOVA can help answer questions such as:
For example,
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