**Introduction to Statistical Analysis **

The term “statistical analysis” refers to the use of quantitative data to investigate trends, patterns, and relationships. Scientists, governments, businesses, and other organizations use it as a research tool.
Statistical analysis necessitates careful planning from the outset of the research process in order to obtain meaningful conclusions. You’ll need to decide on your research design, sample size, and sampling technique, as well as explain your hypothesis.
After you’ve collected data from your sample, you may use descriptive statistics to arrange and summarize it. You may next use inferential statistics to explicitly test hypotheses and make population estimates. Finally, you can put your findings into context and generalize them.
This article provides students and researchers with a practical introduction to statistical analysis. Using two study examples, we’ll walk you through the steps. The first looks into the possibility of a cause-and-effect link, whereas the second looks into the possibility of a correlation between variables.
**Step 1: Make a list of your hypotheses and make a plan for your study.**

You must first describe your hypotheses and set out your research design in order to collect valid data for statistical analysis.
**Statistical Hypotheses Writing**

Often, the purpose of research is to look into a link between factors in a population. You start with a hypothesis and then test it through statistical analysis.
A statistical hypothesis is a method of formally expressing a population prediction. You can break down every research hypothesis into null and alternative hypotheses that you can test with data from a sample.
The null hypothesis always predicts that there will be no effect or relationship between variables, whereas the alternative hypothesis expresses your study prediction of an effect or link.
**Creating A Research Design**

The total strategy for data collecting and analysis is referred to as a study design. It establishes the statistical tests that will be used to test your hypothesis in the future.
To begin, choose whether your study will be descriptive, correlational, or experimental. Experiments have a direct impact on variables, whereas descriptive and correlational research only assess them.
- Statistical tests of comparison or regression are what you can use in an experimental design to analyze a cause-and-effect connection (e.g., the influence of meditation on test scores).
- With a correlational design, you can use correlation coefficients and significance tests to investigate correlations between variables (for example, parental income and GPA) without making any assumptions about causality.
- Using statistical tests to derive inferences from sample data, you can analyse the features of a population or phenomenon (e.g., the prevalence of anxiety in US college students) in a descriptive design.

- You evaluate the group-level results of individuals who undergo different treatments (e.g., those who undertook a meditation exercise vs. those who did not) in a between-subjects design.
- A within-subjects design compares repeated measures from participants who have completed all of the study’s treatments (e.g., scores from before and after performing a meditation exercise).
- One variable you can change between subjects while another you can change within subjects in a factorial design.

**Variables are exact.**

You should operationalize your variables and establish exactly how you will measure them while creating a research design.
It’s crucial to think about the level of measurement of your variables while doing statistical analysis because it tells you what sort of data they contain:
- Groupings you can present using categorical data. These can be nominal (for example, gender) or ordinal (for example, age) (e.g. level of language ability).
- Quantitative data is a representation of quantity. These can be on an interval scale (for example, a test score) or a ratio scale (for example, a weighted average) (e.g. age).

**Step 2: Collect data from a representative sample**

**Sample vs. Population**

In most circumstances, collecting data from every person of the population you’re studying is too difficult or expensive. Instead, you’ll gather information from a sample.
As long as you utilize acceptable sampling practices, statistical analysis permits you to apply your conclusions beyond your own sample. A sample that is representative of the population should be your goal.
For statistical analysis, sampling is put to use.
There are two major methods for choosing a sample.
**Probability sampling**: every member of the population has a probability of being chosen at random for the study.**Non-probability sampling**: some people are more likely to be chosen for the study than others based on factors like convenience or voluntary self-selection.

- Your sample is representative of the population to whom your findings are being applied.
- Your sample is biased in a systematic way.

**Make a suitable sampling procedure.**

Decide how you’ll recruit participants based on the resources available for your study.
- Will you have the resources to publicize your research extensively, including outside of your university?
- Will you be able to get a varied sample that represents the entire population?
- Do you have time to reach out to members of hard-to-reach groups and follow up with them?

**Calculate an appropriate sample size.**

Decide on your sample size before recruiting people by looking at prior studies in your field or utilizing statistics. A sample that is too tiny may not be typical of the entire sample, while a sample that is too large will be more expensive than necessary.
There are numerous sample size calculators available on the internet. Depending on whether you have subgroups or how rigorous your investigation should be, different formulas are employed (e.g., in clinical research). A minimum of 30 units or more each subgroup is required as a rule of thumb.
To utilize these calculators, you must first comprehend and input the following crucial elements:
- The risk of rejecting a true null hypothesis that you are ready to incur is called the significance level (alpha). It is commonly set at 5%.
- Statistical power is the likelihood that your study will discover an impact of a specific size if one exists, which is usually around 80% or higher.
- Predicted impact size: a standardized estimate of the size of your study’s expected result, usually based on similar studies.
- The standard deviation of the population: an estimate of the population parameter based on past research or a pilot study of your own.

**Step 3: Use descriptive statistics to summarize your data.**

After you’ve gathered all of your information, you may examine it and create descriptive statistics to summarize it.
**Examine your information.**

You can inspect your data in a variety of methods, including the ones listed below:
- Using frequency distribution tables to organize data from each variable.
- To see the distribution of replies, use a bar chart to display data from a key variable.
- Using a scatter plot to visualize the relationship between two variables.

**Calculate central tendency measures.**

The location of the majority of the values in a data set, you can describe by measures of central tendency. There are three main measurements of central tendency that you can mention frequently:
- The most prevalent response or value in the data set is the mode.
- When you arrange data set from low to high, the median is the value in the exact middle.
- The sum of all values divided by the number of values is the mean.

**Calculate the variability measurements.**

Variability measures reveal how evenly distributed the values in a data set are. There are four main metrics of variability:
- The highest value of data set minus the lowest value is called the range.
- The range of the data set’s middle half is interquartile range.
- The average distance between each value in your data collection and the mean is standard deviation.
- The square of the standard deviation is the variance.

**Step 4: Use inferential statistics to test hypotheses or create estimates.**

A statistic is a number that describes a sample, whereas a parameter is a number that characterizes a population. You can draw conclusions about population parameters using inferential statistics based on sample statistics.
To make statistical inferences, researchers frequently use two major methodologies (simultaneously):
- Estimation is the process of determining population parameters using sample statistics.
- Hypothesis testing is a formal procedure for employing samples to test research assumptions about the population.

**Estimation**

From sample statistics, you may derive two sorts of population parameter estimates:
- A point estimate is a number that indicates your best approximation of a parameter’s exact value.
- An interval estimate is a set of numbers that represents your best guess as to where the parameter is located.

**Testing Hypotheses**

You can test hypotheses regarding links between variables in the population using data from a sample. Hypothesis testing begins with the premise that the null hypothesis is true in the population, and statistical tests are used to determine whether or not the null hypothesis can be rejected.
If the null hypothesis were true, statistical tests would establish where your sample data would fall on an expected distribution of sample data. The results of these tests you attain in form of two categories:
- A test statistic indicates how far your data deviates from the test’s null hypothesis.
- A p value indicates how likely it is that you obtain your results if the null hypothesis is true in the population.

- Comparison tests look for differences in outcomes across groups.
- Correlation tests look at how variables are related without assuming causation.