Step-by-Step Guide to Statistical Analysis

It would not be wrong to say that statistics are utilised in almost every aspect of society. You might have also heard the phrase, “you can prove anything with statistics.” Or “facts are stubborn things, but statistics are pliable, which implies the results drawn from statistics can never be trusted.

But what if certain conditions are applied, and you analyse these statistics before getting somewhere? Well, that sounds totally reliable and straight from the horse’s mouth. That is what statistical analysis is.

It is the branch of science responsible for rendering various analytical techniques and tools to deal with big data. In other words, it is the science of identifying, organising, assessing and interpreting data to make interferences about a particular populace.Every statistical dissection follows a specific pattern, which we call the Statistical Analysis Process.

It precisely concerns data collection, interpretation, and presentation. Statistical analyses can be carried out when handling a huge extent of data to solve complex issues. Above all, this process delivers importance to insignificant numbers and data that often fills in the missing gaps in research.

This guide will talk about the statistical data analysis types, the process in detail, and its significance in today’s statistically evolved era.

Types of Statistical Data Analysis

Though there are many types of statistical data analysis, these two are the most common ones:

• Descriptive Statistics
• Inferential Statistics

Let us discuss each in detail.

Descriptive Statistics

It quantitatively summarises the information in a significant way so that whoever is looking at it might detect relevant patterns instantly. Descriptive statistics are divided into measures of variability and measures of central tendency. Measures of variability consist of standard deviation, minimum and maximum variables, skewness, kurtosis, and variance, while measures of central tendency include the mean, median , and mode.

Keynotes

• Descriptive statistics sum up the characteristics of a data set
• It consists of two basic categories of measures: measures of variability and measures of central tendency
• Measures of variability describe the dispersion of data in the data set
• Measures of central tendency define the centre of a data set

Inferential Statistics

With inferential statistics , you can be in a position to draw conclusions extending beyond the immediate data alone. We use this technique to infer from the sample data what the population might think or make judgments of the probability of whether an observed difference between groups is dependable or undependable. Undependable means it has happened by chance.

Keynotes

• Inferential Statistics is used to estimate the likelihood that the collected data occurred by chance or otherwise
• It helps conclude a larger population from which you took samples
• It depends upon the type of measurement scale along with the distribution of data

Other Types Include:

Predictive Analysis: making predictions of future events based on current facts and figures

Prescriptive Analysis: examining data to find out the required actions for a particular situation

Exploratory Data Analysis (EDA): previewing of data and assisting in getting key insights into it

Casual Analysis: determining the reasons behind why things appear in a certain way

Mechanistic Analysis: explaining how and why things happen rather than how they will take place subsequently

Statistical Data Analysis: The Process

The statistical data analysis involves five steps:

1. Designing the Study
2. Gathering Data
3. Describing the Data
4. Testing Hypotheses
5. Interpreting the Data

Step 1: Designing the Study

The first and most crucial step in a scientific inquiry is stating a research question and looking for hypotheses to support it.

Examples of research questions are:

• Can digital marketing increase a company’s revenue exponentially?
• Can the newly developed COVID-19 vaccines prevent the spreading of the virus?

As students and researchers, you must also be aware of the background situation. Answer the following questions.

What information is there that has already been presented by other researchers?

How can you make your study stand apart from the rest?

What are effective ways to get your findings?

Once you have managed to get answers to all these questions, you are good to move ahead to another important part, which is finding the targeted population.

What population should be under consideration?

What is the data you will need from this population?

But before you start looking for ways to gather all this information, you need to make a hypothesis, or in this case, an educated guess. Hypotheses are statements such as the following:

• Digital marketing can increase the company’s revenue exponentially.
• The new COVID-19 vaccine can prevent the spreading of the virus.

Remember to find the relationship between variables within a population when writing a statistical hypothesis. Every prediction you make can be either null or an alternative hypothesis.

While the former suggests no effect or relationship between two or more variables, the latter states the research prediction of a relationship or effect.

How to Plan your Research Design?

After deducing hypotheses for your research, the next step is planning your research design. It is basically coming up with the overall strategy for data analysis.

There are three ways to design your research:

1. Descriptive Design:

In a descriptive design, you can assess the characteristics of a population by using statistical tests and then construe inferences from sample data.

2. Correlational Design:

As the name suggests, with this design, you can study the relationships between different variables .

3. Experimental Design:

Using statistical tests of regression and comparison, you can evaluate a cause-and-effect relationship.

Step 2: Collecting Data

Collecting data from a population is a challenging task. It not only can get expensive but also take years to come to a proper conclusion. This is why researchers are instead encouraged to collect data from a sample.

Sampling methods in a statistical study refer to how we choose members from the population under consideration or study. If you select a sample for your study randomly, the chances are that it would be biased and probably not the ideal data for representing the population.

This means there are reliable and non-reliable ways to select a sample.

Reliable Methods of Sampling

Simple Random Sampling: a method where each member and set of members have an equal chance of being selected for the sample

Stratified Random Sampling: population here is first split into groups then members are selected from each group

Clutter Random Sampling: the population is divided into groups, and members are randomly chosen from some groups.

Systematic Random Sampling: members are selected in order. The starting point is chosen by chance, and every nth member is set for the sample.

Non-Reliable Methods of Sampling

Voluntary Response Sampling: choosing a sample by sending out a request for members of a population to join. Some might join, and others might not respond

Convenient Sampling: selecting a sample readily available by chance

Here are a few important terms you need to know for conducting samples in statistics:

Population standard deviation: estimated population parameter on the basis of the previous study

Statistical Power: the chances of your study detecting an effect of a certain size

Expected Effect Size: it is an indication of how large the expected findings of your research be

Significance Level (alpha): it is the risk of rejecting a true null hypothesis

Step 3: Describing the Data

Once you are done finalising your samples, you are good to go with their inspection by calculating descriptive statistics, which we discussed above.

There are different ways to inspect your data.

1. By using a scatter plot to visualise the relationship between two or more variables
2. A bar chart displaying data from key variables to view how the responses have been distributed
3. Via frequency distribution where data from each variable can be organised

When you visualise data in the form of charts, bars, and tables, it becomes much easier to assess whether your data follow a normal distribution or skewed distribution. You can also get insights into where the outliers are and how to get them fixed.

How is a Skewed Distribution Different from a Normal One?

A normal distribution is where the set of information or data is distributed symmetrically around a centre. This is where most values lie, with the values getting smaller at the tail ends.

On the other hand, if one of the tails is longer or smaller than the other, the distribution would be skewed. They are often called asymmetrical distributions, as you cannot find any sort of symmetry in them.

The skewed distribution can be of two ways: left-skewed distribution and right-skewed distribution. When the left tail is longer than the right one, it is left-stewed distribution, while the right tail is longer in a right-strewed distribution.

Now, let us discuss the calculation of measures of central tendency. You might have heard about this one already.

What do Measures of Central Tendency Do?

Well, it precisely describes where most of the values lie in a data set. Having said that, the three most heard and used measures of central tendency are:

Median

When considered from low to high, this is the value in the exact centre.

Mode

Mode is the most wanted or popular response in the data set.

Mean

You calculate the mean by simply adding all the values and dividing by the total number.Coming to how you can calculate the , which is equally important.

Measures of variability

Measures of variability give you an idea of how to spread out or dispersed values in a data set.

The four most common ones you must know about are:

Standard Deviation

The average distance between different values in your data set and the mean

Variance

Variance is the square of the standard deviation.

Range

The range is the highest value subtracted from the data set's minimum value.

Interquartile Range

Interquartile range is the highest value minus lowest of the data set

Step 4: Testing your Hypotheses

Two terms you need to know in order to learn about testing a hypothesis:

Statistic-a number describing a sample

Parameter-a number describing a population

So, what exactly are hypotheses testing?

It is where an analyst or researcher tests all the assumptions made earlier regarding a population parameter. The methodology opted for by the researcher solely depends on the nature of the data utilised and the reason for its analysis.

The only objective is to evaluate the plausibility of hypotheses with the help of sample data. The data here can either come from a larger population or a sample to represent the whole population.

How it Works?

These four steps will help you understand what exactly happens in hypotheses testing.

1. The first thing you need to do is state the two hypotheses made at the beginning.
2. The second is formulating an analysis plan that depicts how the data can be assessed.
3. Next is physically analysing the sample data about the plan.
4. The last and final step is going through the results and assessing whether you need to reject the null hypothesis or move forward with it.

Questions might arise on knowing if the null hypothesis is plausible, and this is where statistical tests come into play.

Statistical tests let you determine where your sample data could lie on an expected distribution if the null hypotheses were plausible. Usually, you get two types of outputs from statistical tests:

1. A test statistic : this shows how much your data differs from the null hypothesis
2. A p-value: this value assesses the likelihood of getting your results if the null hypothesis is true

Step 5: Interpreting the Data

You have made it to the final step of statistical analysis, where all the data you found useful till now will be interpreted. In order to check the usability of data, researchers compare the p-value to a set significant level, which is 0.05, so that they can know if the results are statistically important or not. That is why this process in hypothesis testing is called statistical significance .

Remember that the results you get here are unlikely to have arisen because of probability. There are lower chances of such findings if the null hypothesis is plausible.

By the end of this process, you must have answers to the following questions:

• Does the interpreted data answer your original question? If yes, how?
• Can you defend against objections with this data?
• Are there limitations to your conclusions?

If the final results cannot help you find clear answers to these questions, you might have to go back, assess and repeat some of the steps again. After all, you want to draw the most accurate conclusions from your data.