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In statistics, there are a vast array of **data analysis methods**. Data analysis itself is defined by collecting, exploring, cleaning, transforming, and modeling data. This guide will focus on **exploratory** and **modeling** methods - meaning, it will give insight on how to get familiar with various types of data in order to decide which tests to perform on your data set.

Once your data has been collected, the first step in any sort of analysis of data should be understanding what each of your **variables** mean and whether they are quantitative or qualitative. Quantitative data and qualitative data should be tested and interpreted differently, so it is important to define your variables beforehand. Most statistical software, like SPSS, will do this for you automatically. However, it is important to go through each variable yourself to determine what each variable is and why it is of interest to your analysis.

One way to help you do this is to conduct an **exploratory analysis**. The most common way of starting to explore your data is to extract some descriptive statistics. Note that you can get such extraction knowledge from a statistics course. Descriptive statistics can either be reported numerically or by some helpful visualizations. Some examples of numerical reporting can be found in computing the mean, median, and standard deviation. On the other hand, you can also report descriptives visually. Graphical representations of raw data can include bar graphs, pie charts, and correlation tables.

Once you’ve conducted this exploratory analysis, you should check if your data meets the assumptions that each test requires. This is a necessary step: understanding the descriptives of your data will help you understand which tests are appropriate to perform.

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## Hypothesis Testing: The Difference Between a Hypothesis and a Null Hypothesis

As a researcher, there are many approaches to start analyzing your data. Data collection can be a vital part of your project - however, in order to start forming a research design, it is important to first form a research question based on your observation of a specific population. Most commonly, this research question is given as a hypothesis. **Hypothesis testing** as we know it today was popularized by statisticians Jerzy Neyman and Egon Pearson in the 1930s. Hypotheses in statistics are normally a statement about a set of data, where hypothesis testing is a research method that tests whether the probability of that statement is true.

Coupled with any hypothesis is what is known as a null hypothesis. A **null hypothesis** is a statement about the sample population that generally states that the different groups you are testing have no relationship with each other.

Depending on whether you are performing a quantitative data analysis or a qualitative data analysis, both the hypothesis and null hypothesis will change. In order to decide what question you will ask, it is important to decide which variables are of interest to you.

For example, if you are performing an analysis of variance, or ANOVA, your hypotheses would be:

- H
_{1}: the mean of the dependent variable**is not**the same across all groups - H
_{0}: the mean of the dependent variable**is**the same across all groups

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## Multivariate Methods of Analysis

There are many different **methodologies** that can be used when performing multivariate hypothesis testing. The methodology chosen will depend heavily on what type of question you want to solve and what types of variables you have. Depending on what strategy you apply, the objective of your analysis will change. By comparing these different methods, you will be able to choose the right type of statistical test to employ. Where dependence multivariate methods involve hypotheses, interdependence multivariate methods do not deal with hypothesis testing.

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## Dependence Multivariate Methods

Dependence multivariate methods are powerful analyses that seek to describe the **relationship** between one or more dependent variables that several independent variables. The most common dependence multivariate methods are:

Method | Objective | Hypothesis | Variables |
---|---|---|---|

Multiple Regression | To find the relationship between two or more variables and use this information to estimate the value of the dependent variable. | Hypothesis: the dependent variables have an effect on the independent variable Null Hypothesis: the dependent variables have no effect | One dependent scale variable with multiple scale independent variables |

Multivariate Analysis of Variance (MANOVA) | To see if two categorical variables have an effect on two scale variables. | Hypothesis: There is an effect of one or both categorical variables on the scale variables. Null Hypothesis: there no effect | Two dependent scale variables and two categorical variables |

Discriminant Analysis | To identify whether one or more groups are different and on what variables the groups are most different. | Hypothesis: the groups are different in terms of the dependent variable Null Hypothesis: the groups are not different in terms of the dependent variable | One dependent categorical variable and two or more independent scale variables |

## Interdependence Multivariate Methods

Interdependent multivariate methods seek to **interpret** a set of variables as a group. No distinction is made here between whether one variable is independent or dependent. The most common interdependence multivariate methods are:

Method | Use | Variables |
---|---|---|

Factor Analysis | To condense information if there are many variables in order to reduce many individual variables into a few dimensions | Scale or ordinal variables |

Cluster Analysis | To assign characteristics to groups of variables so that each group is similar with respect to those characteristics, and the groups themselves are distinct | Scale or categorical, but interpretation will be more difficult with a mix of variables |

## How to Interpret the R Squared and P-Value

When dealing with the interpretation of hypotheses, it is important to understand the** type** of test you have performed. Typically, interpreting the results will follow the way in which the output of your statistical software has displayed the results. Usually, they will summarize these results in tabular form.

Let's take multiple linear regression as an example, with weight as the dependent variable and income, diet, and height as the independent variables. The most important reporting values can be found in the R squared value and p-value. Take a look at the table below to see how to interpret each.

Aspect | Result | Interpretation |
---|---|---|

Hypothesis | Multiple Regression where: j represents the number of the dependent variable B signifies the coefficient H _{1} is B_{j} does not equal 0 for at least one jH _{0} is B_{j}=0 | H_{1}: Income, diet and height do have an effect on weightH _{0}: Income, diet and height do not have an effect on weight |

R Squared Value | R^{2} = 0.68 | 68% of the variability in weight is explained by the independent variables - income, diet and height - in the model |

P-value | p = 0.0001 | With a p-value less than 0.05, at 0.0001, we retain the hypothesis and reject the null hypothesis |

It is important to note that, when dealing with the different multivariate methods, the world correlation rarely crops up outside of correlation tables. Make sure to use the word correlation in your report or paper appropriately.

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## How to Structure your Analytic Report

We've all been there: trying to write a conclusion can be surprisingly difficult. However, this frustration can be avoided by structuring your report correctly. Normally, an **abstract** comes first, which is normally a short summary of the research process written after the research and analysis has taken place.

An introduction to your project should follow, as this will provide the **contextual framework** for your paper. Not only should you describe what your goal is, but also cite other papers rooted in grounded theory. The validity of these papers are important with regards to your own experiment because, by citing these papers, you will be able to provide a content analysis of your own work.

Next, if you were the researcher in this process, meaning that you were involved in data collection it is necessary to state your **methodology**. Methodological collection of raw data is varied and can include anything from surveys, tests in a laboratory, or from online databases - which is why it is important to detail how you attained it.

The** analysis** portion of your data will involve everything discussed previously. This section will include the exploratory analysis through structured graphs and tables, as well as the different statistical methods employed on your data. You should state clearly whether or not your variables pass all of the assumptions of the tests you utilize.

This portion, where you analyze the results attained from your data, is the core of any paper you write and should be written in an organized and clear manner. Any assumption that is violated or any transformation of a variable should be noted either here or in an appendix, depending on your audience.

One easy way to lay this portion out is by making sure to differentiate the most important parts of your analysis from the rest of the paper. This can be done by either highlighting, underlining, or putting these phrases in bold.

The last portion of your report should be dedicated to a **conclusion**. This portion should involve not only a summary of the results from your tests, but also an evaluation of the report itself. Meaning, the report should look at the different ways it could have handled the research process differently and what it could do differently next time. It is also important to add how further research can be performed if and when somebody else wants to run a similar test.

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