The data analysis technique chosen will depend on the type of data collected and how it is prepared for analysis. Data can often be analyzed both qualitatively and quantitatively. Survey responses, for example, can be analyzed qualitatively by studying the meanings of the responses or quantitatively by studying the frequencies of the responses.

**Statistics**: is a study of quantitative data; a method of gaining inference from a large quantity of data; a method of interpreting measurements. The reason valid statistics are important is because "the world is full of variation, and sometimes it's hard to tell real differences from natural variation" (Biostatistics : the bare essentials).

"In order to determine whether or not numerical differences in observations are due to treatments, we need to know how much error was encountered within the experiment. Statistics allow us to quantify and assess this error (experimental error)...the two most important concepts of modern statistics: (1) to estimate the experimental error of treatments requires replication, and (2) to ensure an unbiased estimate of experimental error requires randomization of the treatments" (Statistics and agricultural research).

- arXiv-Statistics arXiv is an open archive for scholarly articles in various fields, including Statistics.
- Monthly Bulletin of Statistics Online Current monthly economic and social statistics for most countries and territories of the world. The statistics in this resource are obtained by the Statistics Division of the United Nations and the international statistical services from official sources in the countries.

Qualitative data analysis deals with non-numeric data, such as words, descriptions, images, objects, etc. **Content Analysis** is the most widely used technique in this field. It is employed to analyze documented and recorded communication. The information can be collected from written (books, newspapers, social media posts), oral (speeches and interviews) or visual (photographs and video) forms.

**Conversation Analysis**: analyzes the sequential organization and details of conversation, the moment-by-moment interchange. It focuses on how reality is constructed, rather than on what it is.

**Narrative Analysis**: focuses on "the story itself" in order to put together the "big picture." Narratives can typically be coded into four types of stories: *action tales*, *expressive tales*, *moral tales* and *rational tales*.

The 5 steps listed below outline "the different techniques that are shared by most approaches to qualitative data analysis:

- Documentation of the data and the process of data collection
- Organization/categorization of the data into concepts
- Connection of the data to show how one concept may influence another
- Corroboration/legitimization, by evaluating alternative explanations, disconfirming evidence, and searching for negative cases
- Representing the account (reporting the findings)" (Qualitative Data Analysis, (Ch. 10))

Descriptive Statistics is that branch of statistics which is concerned with describing the population under study. It summarizes the data, which is already known. Descriptive statistics are visual in form. Means, medians, variances, standard deviations, correlation, coefficients, etc. can be communicated via charts and graphs.

"Descriptive Statistics are used to present quantitative descriptions in a manageable form. In a research study we may have lots of measures. Or we may measure a large number of people on any measure. Descriptive statistics help us to simplify large amounts of data in a sensible way. Each descriptive statistic reduces lots of data into a simpler summary" (Research Methods Knowledge Base > Descriptive Statistics).

"Descriptive statistics convey two basic aspects of a sample: central tendency and dispersion. The former describes the most representative or common or central observation of the sample, and the latter how the sample is distributed around the common variate" (Statistics for Anthropology)

- Statistical methods used in the public health literature and implications for training of public health professionals Hayat MJ, Powell A, Johnson T, Cadwell BL (2017) Statistical methods used in the public health literature and implications for training of public health professionals. PLOS ONE 12(6): e0179032. https://doi.org/10.1371/journal.pone.0179032

**Inferential Statistics** makes statements about the population from which samples were obtained. It is the branch of statistics dealing with conclusions, generalizations, predictions, and estimations based on data from samples.

"With inferential statistics, you are trying to reach conclusions that extend beyond the immediate data alone. For instance, we use inferential statistics to try to infer from the sample data what the population might think. Or, we use inferential statistics to make judgments of the probability that an observed difference between groups is a dependable one or one that might have happened by chance in this study. Thus, we use inferential statistics to make inferences from our data to more general conditions; we use descriptive statistics simply to describe what’s going on in our data" (Research Methods Knowledge Base > Inferential Statistics).

There are many types of inferential statistics and which one(s) to use will be specific to the research design and sample characteristics. However, most inferential statistics are based on the principle that a test-statistic value is calculated on the basis of a particular formula.

- Statistical methods used in the public health literature and implications for training of public health professionals Hayat MJ, Powell A, Johnson T, Cadwell BL (2017) Statistical methods used in the public health literature and implications for training of public health professionals. PLOS ONE 12(6): e0179032. https://doi.org/10.1371/journal.pone.0179032

**Hypothesis Testing** is the use of statistics to determine the probability that a given hypothesis is true. The usual process of hypothesis testing consists of four steps:

1. The null (H0) and alternative (H1) hypotheses are stated.

2. The *level of statistical significance,** (criteria) is established for a decision .

3. Collect the sample / Compute the *test statistic*** and compare the produced ** p-value** to the criterion set in step 2.

- The
is the probability value.*p*-value- "P value is the probability, given that the null hypothesis is true, of obtaining data as extreme or more extreme than that observed" (Oxford Handbook of Medical Statistics)
- "The probability of any event can only vary between 0 and 1 (which correspond to 0 and 100%). If an event is certain to occur, it has a probability of 1; while, if it is certain the event will not occur, it has a probability of 0" (Statistics explained : an introductory guide for life scientists).

4. Make a decision based on the probability. The sample is compared with the null hypothesis’ parameters, and a conclusion is reached about which hypothesis to accept. The decision to reject or retain the H0 is called *significance*.***

When testing a hypothesis, two errors may be committed: 1) Rejection of the null hypothesis when in fact it is true (type I error), or 2) Failure to reject a false null hypothesis (type II error).

Definitions:

*"*Level of significance*, or *significance level*, refers to a criterion of judgment upon which a decision is made regarding the value stated in a null hypothesis. The criterion is based on the probability of obtaining a statistic measured in a sample if the value stated in the null hypothesis were true. The most commonly used significance level is 5%, (0.05).

**The *test statistic* is a mathematical formula that allows researchers to determine the likelihood of obtaining sample outcomes if the null hypothesis were true. The value of the test statistic is used to make a decision regarding the null hypothesis.

****Significance*, or *statistical significance*, describes a decision made concerning a value stated in the null hypothesis. When the null hypothesis is rejected, we reach significance. When the null hypothesis is retained, we fail to reach significance" (Introduction to hypothesis testing, (Ch. 8).

- The ASA Statement on p-Values: Context, Process, and Purpose Ronald L. Wasserstein & Nicole A. Lazar (2016) The ASA Statement on p-Values: Context, Process, and Purpose, The American Statistician, 70:2, 129-133, DOI: 10.1080/00031305.2016.1154108
- Reporting p Values Huber, W. (2019). Reporting p Values. Cell Systems, 8(2), 170–171. doi:https://doi.org/10.1016/j.cels.2019.03.001

Note: A **test statistic** is a quantity, derived from the sample, used to determine how well the model/means fits the data.

**Parametric Tests** (regression, comparison and correlation) are used where a Normal distribution of variables is assumed (think "bell-shaped curve":

**Regression Models**are used to test cause-and-effect relationships.**Simple Regression**is used to estimate the relationship between two quantitative variables.- The Coefficient of Determination (or R2 value) is the test statistic used to evaluate the goodness-of-fit of the model. R
^{2 }= 1 - unexplained variation / total variation

- The Coefficient of Determination (or R2 value) is the test statistic used to evaluate the goodness-of-fit of the model. R
**Multiple Linear Regression**is used to describe relationships between two or more independent variables and one dependent variable.**Logistic Regression**is similar to multiple linear regression, except the response/outcome variable is binary ("0" or "1") which is used to represent "Yes" or "No." "Pass" or "Fail," for example.

**Comparison Tests**are used to look for differences among group means. Expected outputs will be the t-value, degrees of freedom, p-value**T-tests**are used to compare the means of two groups. To chose which t-test to use, ask whether the groups being compared derive from a single population or two different ones, and whether you want to test the difference in a specific direction. The(or*t*-value*t*-statistic) is the test statistic used to determine whether the null hypothesis is supported or rejected.**ANOVA & MANOVA:**Analysis of variance (**ANOVA**) is the statistical procedure of comparing the means of a variable across several groups (more than two groups). ANOVA uses**F-tests**to assess the equality of the means. The**F****-value**(of*F*-statistic) is the ratio of two variances (between group variation to within group variation). Used as the test statistic, the larger the value, the more likely it is that the variation associated with the independent variable is real and not due to chance. Multivariate analysis of variance (**MANOVA**) is used to compare means of several variables simultaneously across several groups (more than two groups).

**Correlation Tests**check whether two variables are related without assuming cause-and-effect relationships.**Pearson'**is used to express the correlation between two variables X and Y.*r*- Looking for an association between two
*categorical*variables? A**Chi-squared test**(or**X**) "calculates the frequencies that would be expected if there were no association (i.e. null hypothesis is true)" (Oxford handbook of medical statistics).^{2}

**Rank Correlation Tests:**Assumptions for these tests (Spearman or Kendall) are that variables can be ranked and the relationship between the variables either increases or decreases. Use in place of regression and correlation tests.- "
**Kruskal-Wallis Test**is a nonparametric approach to the*one-way ANOVA*. The procedure is used to compare three or more groups on a dependent variable that is measured on at least an ordinal level" (Comprehensive Clinical Psychology). **Wilcoxon Rank-Sum Test**is the nonparametric version of the*independent t-test*, commonly used for the comparison of two groups of nonparametric data.- Use the
**Wilcoxon Signed Rank Test**(or**Wilcoxon Matched Pairs Test**) for a repeated measure design where the same sujects are evaluated under two different conditions.

To communicate the information of your research, the data will often need to be described in numeric and tabular form. But graphics can allow for data to be displayed in a visual/pictorial form that facilitates more insight into the data.

"Three Basic Principles for Graphical Presentation--Always remember 3 principles in illustrating the results

- Heading or title: Each figure should have clearly defined heading / title
- Simplicity: Presentation of data should be simple to understand
- Honesty: If possible always give the sample size with results" (Handbook of basic statistical concepts : for scientists and pharmacists)

Another consideration, from an accessibility standpoint, would be color and font choice and consistency.

Delve into the world of research with the ** Researcher's Bootcamp**. In these sessions you will learn how to create a search string, use reliable research resources, find law and legislation, and use reference managers to keep your research organized. The session order is as follows:

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4. Reference Managers