Question

The Independent Samples t Test can only compare the means for two (and only two) groups. It cannot make comparisons among more than two groups. If you wish to compare the means across more than two groups, you will likely want to run an ANOVA.

What is the main differences between an unpaired and paired t-test? Why would you want to limit the number of variables you are comparing? Why would you want to start with two groups and work your way through your variables, compared to running an ANOVA (Analysis of Variance)?

Answer 1

ANSWER:

Paired t-test:

A paired t-test (also known as a dependent or correlated t-test) is a statistical test that compares the averages/means and standard deviations of two related groups to determine if there is a significant difference between the two groups.

●       A significant difference occurs when the differences between groups are unlikely to be due to sampling error or chance.

●       The groups can be related by being the same group of people, the same item, or being subjected to the same conditions.

Paired t-tests are considered more powerful than unpaired t-tests because using the same participants or item eliminates variation between the samples that could be caused by anything other than what’s being tested.

Hypotheses of a paired t-test:

There are two possible hypotheses in a paired t-test.

●       The null hypothesis (H0) states that there is no significant difference between the means of the two groups.

●       The alternative hypothesis (H1) states that there is a significant difference between the two population means, and that this difference is unlikely to be caused by sampling error or chance.

Assumptions of a paired t-test:

●       The dependent variable is normally distributed

●       The observations are sampled independently

●       The dependent variable is measured on an incremental level, such as ratios or intervals.

●       The independent variables must consist of two related groups or matched pairs.

Unpaired t-test:

An unpaired t-test (also known as an independent t-test) is a statistical procedure that compares the averages/means of two independent or unrelated groups to determine if there is a significant difference between the two.

Hypotheses of an unpaired t-test:

The hypotheses of an unpaired t-test are the same as those for a paired t-test. The two hypotheses are:

●       The null hypothesis (H0) states that there is no significant difference between the means of the two groups.

●       The alternative hypothesis (H1) states that there is a significant difference between the two population means, and that this difference is unlikely to be caused by sampling error or chance.

Assumptions of an unpaired t-test:

●       The dependent variable is normally distributed

●       The observations are sampled independently

●       The dependent variable is measured on an incremental level, such as ratios or intervals.

●       The variance of data is the same between groups, meaning that they have the same standard deviation

●       The independent variables must consist of two independent groups.

Paired vs unpaired t-test:

The key differences between a paired and unpaired t-test are summarized below.

1. A paired t-test is designed to compare the means of the same group or item under two separate scenarios. An unpaired t-test compares the means of two independent or unrelated groups.
2. In an unpaired t-test, the variance between groups is assumed to be equal. In a paired t-test, the variance is not assumed to be equal.

ANOVA undertakes two assumotions:

1. It assume the dataset is uniformly distributed with means of each sub-set data group to be equal.
2. Similarly, the variance and standard deviation of each sub-set data group is equal.

In the real-world application, researchers investigate data from various sources (e.g. social media, news, web-forums, lab test) where uniform distribution may not be right to assume.

Hence, these assumptions becomes limitations to ANOVA so we dont consider to run ANOVA.

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