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# ST311 Applied Statistics I Assignment Sample NUI Galway Ireland

ST311 Applied Statistics I course covers fundamental statistical concepts and methods with applications. The course is designed to provide students with a sound understanding of basic statistics and its application in solving problems in various fields. The topics covered in this course include exploratory data analysis, probability, random variables, and probability distributions, sampling distributions, estimation, hypothesis testing, regression, and correlation. These concepts and methods are illustrated using real data from a variety of fields.

This course is an introduction to statistics with an emphasis on applications in the natural and social sciences. The goal of this course is to provide students with the statistical tools and techniques they need to critically analyze data. By the end of the course, students should have a good understanding of the basic concepts of statistics and be able to apply these concepts to real-world data sets.

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In this section, we are describing some assigned activities. These are:

### Assignment Activity 1: Demonstrate various non-parametric testing procedures:

Non-parametric methods are statistical methods that make no assumptions about the underlying distribution of the data. These methods are often used when the data is not normally distributed, or when the nature of the relationship between variables is not known. Non-parametric methods are sometimes referred to as distribution-free methods.

The following list of non-parametric tests includes some of the most commonly used tests.

• Wilcoxon Signed-Rank Test: This test is used to compare two sets of data that are related to each other (e.g., before and after treatment). It is a non-parametric alternative to the paired t-test.
• Mann-Whitney U Test: This test is used to compare two independent sets of data. It is a non-parametric alternative to the independent t-test.
• Kruskal-Wallis H Test: This test is used to compare more than two independent sets of data. It is a non-parametric alternative to the one-way ANOVA.
• Chi-Square Test: This test is used to compare two or more categorical variables. It tests the null hypothesis that the variables are independent of each other.
• Fisher’s Exact Test: This test is used to compare two or more categorical variables. It is a more powerful alternative to the chi-square test, but it can only be used when the data are small (e.g., less than 30).

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### Assignment Activity 2: Identify the suitability of parametric methods and their non-parametric alternative test method:

Parametric methods are statistical methods that make assumptions about the underlying distribution of the data. These methods are often used when the data is normally distributed, or when the nature of the relationship between variables is known. Parametric methods are sometimes referred to as distribution-based methods.

The following list of parametric tests includes some of the most commonly used tests.

• t-Test: This test is used to compare two sets of data that are related to each other (e.g., before and after treatment). It can be used with either paired or independent data.
• ANOVA: This test is used to compare more than two sets of data. It can be used with either independent or dependent data.
• Regression: This test is used to examine the relationship between one or more independent variables and a dependent variable.
• Correlation: This test is used to examine the relationship between two variables.

The non-parametric alternatives to these tests are the Wilcoxon signed-rank test, the Mann-Whitney U test, the Kruskal-Wallis H test, and the chi-square test. These tests can be used when the data is not normally distributed or when the nature of the relationship between variables is not known.

### Assignment Activity 3: Discuss the advantages and disadvantages of parametric and non-parametric testing:

There are both advantages and disadvantages to using parametric and non-parametric methods.

Parametric methods are more powerful than non-parametric methods, which means that they can detect small effects that might be missed by a non-parametric test. However, parametric methods are also more likely to produce false positives (i.e., results that show an effect when there is none).

Non-parametric methods are less powerful than parametric methods, but they are more robust. This means that they are less likely to produce false positives. However, non-parametric methods are also more likely to produce false negatives (i.e., results that show no effect when there is one).

In general, parametric methods should be used when the data is normally distributed and the nature of the relationship between variables is known. Non-parametric methods should be used when the data is not normally distributed or when the nature of the relationship between variables is not known.

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### Assignment Activity 4: Define the power of a test and interpret its meaning in applications, formulate the power function and sketch power curves:

The power of a statistical test is the probability that the test will detect an effect when there is one. The power of a test increases as the size of the effect increases. The power of a test also increases as the sample size increases.

The power function is used to calculate the power of a statistical test. It takes as input the size of the effect, the sample size, and the alpha level. The power function can be used to calculate the power of a test before the data is collected (i.e., prior power). It can also be used to calculate the power of a test after the data has been collected (i.e., post-hoc power).

The power curve is a graphical representation of the power function. It shows how the power of a test varies as the size of the effect and the sample size change. Power curves can be used to choose an appropriate sample size for a study.

### Assignment Activity 5: Carry out parametric and non-parametric testing procedures with the use of software:

Assuming that you have two sets of data that you would like to compare, the first step is to decide which type of test you will use. If the data is normally distributed and the nature of the relationship between variables is known, then a parametric test should be used. If the data is not normally distributed or if the nature of the relationship between variables is not known, then a non-parametric test should be used.

Once you have decided which type of test to use, the next step is to collect the data. Once the data has been collected, it can be entered into a statistical software program. There are many different statistical software programs available, but some popular ones include SPSS, SAS, and R.

Once the data has been entered into the statistical software program, the next step is to run the test. The results of the test will typically include a p-value. The p-value is used to determine whether or not the results are statistically significant. If the p-value is less than 0.05, then the results are considered to be statistically significant.

The results of the test will also typically include a confidence interval. The confidence interval is used to give a range of values that are likely to contain the true value of the population parameter. For example, if the results of a test showed that the mean score on a test was 95 with a confidence interval of 90-100, this would mean that there is a 95% chance that the true population means the score is between 90 and 100.

Finally, the results of the test will also typically include an effect size. The effect size is used to measure the magnitude of the difference between the two groups. For example, if the results of a test showed that the mean score on a test was 95 for group 1 and 100 for group 2, then the effect size would be 5. This means that group 2 scored 5 points higher, on average than group 1.

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### Assignment Activity 6: Calculate and interpret correlations between variables and make inferences about relationships:

A correlation is a statistical measure of the relationship between two variables. Correlations can be positive or negative. A positive correlation means that as one variable increases, the other variable also increases. A negative correlation means that as one variable increases, the other variable decreases.

Correlations can be used to predict the values of one variable based on the values of another variable. For example, if there is a positive correlation between test scores and study hours, then we would expect that students who study more would tend to get higher grades on the test.

Correlations can also be used to infer causation. However, it is important to remember that correlation does not necessarily imply causation. That is, just because two variables are correlated does not necessarily mean that one variable is causing the other. There are many other possible explanations for why two variables might be correlated.

To calculate a correlation, you will need to have two sets of data. The first set of data is the independent variable and the second set of data is the dependent variable. The independent variable is the variable that you are using to predict the dependent variable. For example, if you are trying to predict test scores, then the independent variable would be study hours and the dependent variable would be test scores.

### Assignment Activity 7: Interpret and use the output from variable selection procedures to choose adequate models, including the best subsets procedure and step-wise.

There are a variety of variable selection procedures that you can use to choose which variables to include in your model. The best subsets procedure and step-wise procedures are two methods that are often used in statistics.

The best subsets procedure involves looking at all possible models that include a certain number of predictors and selecting the model that has the best fit according to some criterion. The step-wise procedure starts with a model that includes no predictors and then adds or removes individual predictors from the model until the criteria for adding or removing predictors are met.

Both of these methods have their advantages and disadvantages. The best subsets procedure is comprehensive but can be computationally intensive, while the step-wise procedure is less comprehensive but can be more efficient.

Once you have selected a model, you will need to interpret the output to choose the best model for your data. The output from the best subsets procedure and the step-wise procedure will typically include some measure of fits, such as R-squared or adjusted R-squared. You will also want to look at the p-values for the individual predictors to determine which predictors are statistically significant.

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### Assignment Activity 8: Carry out the regression analysis with the use of software, R.

Before carrying out a regression analysis, it is important to understand what this technique is and how it can be used to benefit your business or organization. Regression analysis is a statistical tool used to help identify relationships between different variables. This information can then be used to make predictions about future events.

R is a popular programming language for statistical computing and data science. It’s easy to use and has a wide range of packages available for carrying out regression analysis. In this article, we’ll show you how to carry out a regression analysis using R software.

First, you’ll need to install the required packages. You can do this by running the following code in your R terminal:

install.packages(“package_name”)

Next, you’ll need to load the packages into your R session. You can do this by running the following code:

library(package_name)

Now that the required packages are installed and loaded, we can start carrying out our regression analysis. We’ll use the built-in mtcars dataset for this example. The mtcars dataset contains information on various car models and their fuel efficiency.

We’ll start by taking a look at the data using the head() function:

This gives us the first six rows of the data. We can see that there are 11 variables in the dataset, including mpg (miles per gallon), cyl (number of cylinders), and disp (displacement).

### Assignment Activity 9: Compile a statistical report, i.e. prepare a typed document that introduces the statistical research question being explored, describes the data collection method applicable to the research, describes relevant features of the sample data obtained and outlines conclusions from the inferential statistical analysis carried out using the sample data, incorporating output and plots from statistical software.

The purpose of this study is to explore the link between diet and the risk of developing Alzheimer’s Disease. The data for this research was collected by surveying participants about their dietary habits and then analyzing whether or not they developed Alzheimer’s Disease.

The results of the study indicate that there is a significant correlation between consuming unhealthy foods and developing Alzheimer’s Disease. Participants who reported eating fast food, processed food, or sugary drinks at least three times per week were more likely to develop Alzheimer’s Disease than those who did not report eating these foods. These results suggest that a healthy diet may help reduce the risk of developing Alzheimer’s Disease.

Based on the results of this study, it is recommended that further research be conducted to confirm these findings. Additionally, it would be beneficial to explore other potential risk factors for Alzheimer’s Disease.

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