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Statistics problem

Give an example of an experiment or observational study that you could perform in your major field.

An example of a study I could perform that goes along with my major would be a study to know if there is a change in occupational stress across age groups. The variable of interest in this case would be occupational stress as measured by a scale based on a factor of age. Since this is only one factor a one-way ANOVA would be ideal for running this study.

The three groups in which the employees are divided include:

• Less than 40
• 40 to 55
• Above 55

These three groups are the levels of factor age – there are three levels here.

What kind of experimental design would you use and why? What would you measure? Lay out the important steps.

For this study, I would use True Experimental design. I would use this method because it is regarded as the most accurate form of experimental research among statisticians. It’s favored specifically because it tries to prove or disprove a hypothesis mathematically, through statistical analysis. For an experiment to be considered carried out with a true experimental design, the sample groups must be assigned randomly, there must be a viable control group, and only one variable can be manipulated and tested. With this design, we shall have multiple observations in the form of scores on Occupational Stress from a number of employees belonging to the three levels of factor age. We are interested to know whether all the levels i.e. age groups have equal stress on the average. It is necessary to use one-way ANOVA because there are three age groups but one factor. With this experimental design, there are multiple observations that can be measured in the form of scores or rankings as they relate to occupational stress. They can be taken from three age groups.

How would you sample and allocate the samples or, on the case of an observational study, collect data?

The difficulty with running an observational study is that the experimenter has no control over the control groups, making it impossible to randomize how subjects are allocated. This can create bias, or distract from the cause and effect relationships that might arise. It ultimately can create error in the research by implying connections where there aren’t any. Randomization balances and diversifies the external causal effects of the study, which is something that can’t be done in an observational study. Without an independent variable, a cause an effect result can’t be assumed without opening the study up to being significantly invalid.

If possible, propose alternative design, and  describe all the needed adjustment to the experiment.

A possible alternative design could be Quasi-experimental design. This method is often viewed as unreliable, but it still can be effective at measuring social variables. Quasi-experimental design entails selecting groups where a variable will be tested without any random pre-selection process. For example, to perform this experiment, the company would be arbitrarily divided by alphabetical selection or by departments instead of by age. After this slight change, the experiment would be run very similar to any other experiment.

After you decide a design, a measure, sample and collect data you run an Analysis of Variance. What are the null and alternative hypotheses your Analysis of Variance?

A non-significant result of the test statistic, specifically the F-statistic would show that age has no effect on stress in the work place. On the other hand, significance would imply that stress afflicts different age groups differently.

Null ANOVA Hypothesis H0: All the age groups have the same mean stress level. This value can also be displayed as μ1 = μ2 = μ3, where μ1, μ2, μ3, which would be the variables used to express the mean stress scores for the three different age groups.

The alternative hypothesis is:

H1: The mean stress of at least one age group is significantly different.

How do you know if a one way ANOVA is significant?

The most clear defining factor to know the one-way ANOVA is significant is by the null hypotheses being rejected. If the significance tests generate 95% or 99% likelihood that the results do not fit the null hypothesis, it’s rejected, in favor of the alternative. Otherwise, the null hypothesis is accepted. These are the only correct assumptions, and it is incorrect to reject, or accept, H1. Accepting the null hypothesis does not mean that it is true. It is still a hypothesis, and must conform to the principle of infallibility, in the same way that rejecting the null does not prove the alternative.

If you reject the null hypotheses in ANOVA, then what do you do?

If the null hypothesis is rejected, then it suggests there is a difference between the means of the age groups and this difference is significant.  It also means one will have to perform independent t-tests for each individuals case to identify the different level.

Assume we do a One-way ANOVA, and the overall ANOVA is significant. Further assume that the single treatment/factor has four levels. How many hypotheses tests are there?

If there are 3 or more levels (in this case k=4), then we usually need to follow-up on rejection of the overall null hypothesis. The follow-up will have to be with more exact hypotheses to distinguish which population group means show evidence of a difference.

The overall null hypothesis for one-way ANOVA with k groups is H0: μ1 = μ2 = μ3 = μ4

The alternative hypothesis is that “the population means are not all equal”.

In a two-way ANOVA, with treatments paint and location, and with three levels. What are the three main hypotheses tests to tell whether the overall ANOVA is significant?

A two-way ANOVA, can measure the significance of the main result for each factor. This is similar to a one-way ANOVA test, except, the interaction of results across different factors is also evaluated. In order to do this, a null and alternative hypothesis is setup, like in the one-way tests.

Hypotheses null 1: The means of observations grouped by paint for the three levels are the same.

Hypotheses null 2: The means of observations grouped by location for the three levels are the same.

Hypotheses null 3:  There is no interaction between the two factors paint and location.

Hypotheses alternative: There is at least one statistically significant difference among the groups.

Tell me: the greatest skateboarder of all time and the greatest Rock Band of all time.

The best Skateboarder of all time is James Craig. The best Rock band of all time is Radiohead.

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