Question

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Q1. What is the Concept of One-Way ANOVA; assumptions, when to use it, and its applications?

Q2. what is the concept of Parametric vs NonParametric

Answer 1

Answer :

Q1.

Concept of One way ANOVA:

The one-way analysis of variance (ANOVA) is used to determine whether there are any statistically significant differences between the means of three or more independent (unrelated) groups.The one-way ANOVA compares the means between the groups you are interested in and determines whether any of those means are statistically significantly different from each other. Specifically, it tests the null hypothesis:

where µ = group mean and k = number of groups. If, however, the one-way ANOVA returns a statistically significant result, we accept the alternative hypothesis (HA), which is that there are at least two group means that are statistically significantly different from each other. At this point, it is important to realize that the one-way ANOVA is an omnibus test statistic and cannot tell you which specific groups were statistically significantly different from each other, only that at least two groups were. To determine which specific groups differed from each other, you need to use a post hoc test.

Assumptions:

• Normality – That each sample is taken from a normally distributed population
• Sample independence – that each sample has been drawn independently of the other samples
• Variance Equality – That the variance of data in the different groups should be the same
• Your dependent variable – here, “weight”, should be continuous – that is, measured on a scale which can be subdivided using increments (i.e. grams, milligrams)

When we use :

The one-way analysis of variance (ANOVA) is used to determine whether there are any statistically significant differences between the means of more than two independent (unrelated) groups (although you tend to only see it used when there are a minimum of three, rather than two groups).

Application:

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.

2.One real-life application of analysis of variance is the recommendation of a fertilizer against others for the improvement of a crop yield.

Q 2.

Concept of paramatric vs nonparamatric :

In the literal meaning of the terms, a parametric statistical test is one that makes assumptions about the parameters (defining properties) of the population distribution(s) from which one's data are drawn, while a non-parametric test is one that makes no such assumptions. In this strict sense, "non-parametric" is essentially a null category, since virtually all statistical tests assume one thing or another about the properties of the source population(s).

For practical purposes, you can think of "parametric" as referring to tests, such as t-tests and the analysis of variance, that assume the underlying source population(s) to be normally distributed; they generally also assume that one's measures derive from an equal-interval scale. And you can think of "non-parametric" as referring to tests that do not make on these particular assumptions. Examples of non-parametric tests include

• the various forms of chi-square tests
• the Fisher Exact Probability test
• the Mann-Whitney Test
• the Wilcoxon Signed-Rank Test
• the Kruskal-Wallis Test
• and the Friedman Test

Non-parametric tests are sometimes spoken of as "distribution-free" tests, although this too is something of a misnomer.

Advantage of non-parametric test is, Nonparametric tests are more robust than parametric tests. In other words, they are valid in a broader range of situations (fewer conditions of validity).

Advantage of parametric test is,

The advantage of using a parametric test instead of a nonparametric equivalent is that the former will have more statistical power than the latter. In other words, a parametric test is more able to lead to a rejection of H0. Most of the time, the p-value associated to a parametric test will be lower than the p-value associated to a nonparametric equivalent that is run on the same data.

In the parametric test, the test statistic is based on distribution. On the other hand, the test statistic is arbitrary in the case of the nonparametric test. Measurement level of parametric test is interval or ratio whereas measurement level of non-parametric test is nominal or ordinal. Measure of central tendency for parametric test is mean and for non - parametric test is median. For parametric test information about population is completely know and in non parametric test information about population is unavailable. Correlation test for parametric is Pearson and for non-parametric is spearman.

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