Question

Purpose, advantages, and limitations of: a.) Independent T-test, b.) Paired T-test, c.)Analysis of Variance, d.) Chi-Square Analysis, e.) Regression analysis

Answer 1

a)

Independent T-test:

The Independent Samples t Test compares the means of two independent groups in order to determine whether there is statistical evidence that the associated population means are significantly different. The Independent Samples t Test is a parametric test. This test is also known as: Independent t Test.

An independent samples t-test is a statistical method of comparing two samples in terms of their means.

Advantages:

Simplicity of Interpretation:

The output from an independent samples t-test tells you how different the mean of one sample is from the mean of the other group. It tells you the mean of each group, and the average difference between the groups. It also tells you whether this difference is statistically significant. Statistical significance is a measure of how likely differences as large as the ones in this sample are, if the two populations from which the samples are drawn have the same means,

Robustness:

The independent samples t-test assumes that the two populations are normally distributed (the bell-shaped curve) and have the same variance (the variance is a measure of how spread out a distribution is). However, the t-test is fairly robust to violations of the first assumption, and there are methods for using the t-test with two samples from populations with unequal variances.

Ease of Gathering Data:

The independent samples t-test requires very little data: Simply the values of subjects from each of two groups on some quantitative variable. The t-test is valid even with a small number of subjects, and requires only one value from each subject.

Ease of Calculation:

These days, even t-tests are nearly always done with the aid of a computer. But the formula for the independent samples t-test is simple, and this makes it easy to understand what is going on. This is especially appealing to people without much statistical training.

limitations:

You can examine the assumptions of t-test, so the limitations are clear. When data violates the assumptions, t-test might not have reliability. The assumption for a t-test is that the scale of measurement applied to the data collected follows a continuous or ordinal scale, such as the scores for an IQ test.

b)

Paired T - test:

A paired t-test is used to compare two population means where you have two samples in which observations in one sample can be paired with observations in the other sample. Before-and-after observations on the same subjects .

Advantages:

The Paired Sample t-test is an example of a repeated measures design.Repeated measures designs have the especially important advantage of being more powerful. Each person is used as his or her own control and so individual differences can be partialled out of the error term.

Limitations:

Therefore, the paired t-test should not be applied uncritically to method comparison data. Only when the graphical display suggests that a systematic constant difference, but not a systematic proportional difference, is involved should this test be applied.

c)

Analysis of Variance:

Analysis of variance (ANOVA) is an analysis tool used in statistics that splits an observed aggregate variability found inside a data set into two parts: systematic factors and random factors. The systematic factors have a statistical influence on the given data set, while the random factors do not.

Advantages:

It provides the overall test of equality of group means. It can control the overall type I error rate (i.e. false positive finding) It is a parametric test so it is more powerful, if normality assumptions hold true.

Limitations:

It assume the dataset is uniformly distributed with means of each sub-set data group to be equal.

Similarly, the variance and standard deviation of each sub-set data group is equal.

d)

Chi-Square Analysis:

chi-square test is used to determine whether there is a statistically significant difference between the expected frequencies and the observed frequencies in one or more categories of a contingency table.

Advantages:

Chi-square include its robustness with respect to distribution of the data, its ease of computation, the detailed information that can be derived from the test, its use in studies for which parametric assumptions cannot be met, and its flexibility in handling data from both two group and multiple.

Limitations:.

chi-square is highly sensitive to sample size. As sample size increases, absolute differences become a smaller and smaller proportion of the expected value. Generally when the expected frequency in a cell of a table is less than 5, chi-square can lead to erroneous conclusions.

e)

Regression analysis:

It is a powerful statistical method that allows you to examine the relationship between two or more variables of interest. While there are many types of regression analysis, at their core they all examine the influence of one or more independent variables on a dependent variable.

Advantages:

Regression analysis uses data, specifically two or more variables, to provide some idea of where future data points will be. The benefit of regression analysis is that this type of statistical calculation gives businesses a way to see into the future.

Limitations:

it is limited to the linear relationship

it is easily affected by outliers

regression solution will be likely dense (because no regularization is applied)

subject to over-fitting

regression solutions obtained by different methods (e.g. optimization, least-square, QR decomposition, etc.) are not necessarily unique.

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