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.
Your study’s design also determines whether you’ll compare participants on a group or individual basis, or both.
- 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).
Many factors you can measure with varying degrees of accuracy. Age data, for example, can be categorical or quantitative (8 years old) (young). If a variable has the code numerically (for example, level of agreement from 1 to 5), that means it’s categorical.
Choosing proper statistics and hypothesis testing requires determining the measurement level. With quantitative data, you can generate a mean score, but not with categorical data.
In a research project, you’ll frequently collect data on relevant participant characteristics in addition to measures of your variables of interest.
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.
In theory, a probability sampling method should be used for highly generalizable conclusions. Random selection eliminates sampling bias and assures that the data from your sample is representative of the entire population. When data is acquired via probability sampling, parametric tests can be utilized to establish strong statistical judgments.
In practice, however, obtaining the optimal sample is unusual. Non-probability samples are more likely to be skewed, but they are also considerably easier to recruit and gather data from. Non-parametric tests are better suited to non-probability samples, but they yield weaker population inferences.
If you want to apply parametric tests with non-probability samples, you must show that:
- Your sample is representative of the population to whom your findings are being applied.
- Your sample is biased in a systematic way.
Keep in mind that external validity means you can only extrapolate your findings to people who share your sample’s characteristics. Results from Western, Educated, Industrialized, Rich, and Democratic samples (for example, college students in the United States) aren’t always transferable to non-WEIRD groups.
If you use parametric tests on data from non-probability samples, make sure to explain in your discussion section how far your results can be generalized.
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.
You may analyze whether your data has a skewed or normal distribution and whether there are any outliers or missing data by visualizing it in tables and graphs.
A normal distribution describes how your data is symmetrically distributed about a central point where the majority of the values are found, with values falling off at the ends.
A skewed distribution, on the other hand, is asymmetric, with more values on one end than the other. It’s vital to remember the shape of the distribution since skewed distributions should only be utilized with a few descriptive statistics.
Extreme outliers can also provide misleading statistics, therefore dealing with these values may require a systematic strategy.
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.
Only one or two of these measurements may be applicable depending on the form of the distribution and the level of measurement.
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.
For skewed distributions, the interquartile range is the best measure, while standard deviation and variance provide the most information for normal distributions.
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.
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.
It’s advisable to utilize both point and interval estimates in your work if your goal is to deduce and present population features from sample data.
Because there is always some degree of inaccuracy in estimation, you should include a confidence interval as an interval estimate to demonstrate the variability around a point estimate.
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.
There are three types of statistical tests:
- Comparison tests look for differences in outcomes across groups.
- Correlation tests look at how variables are related without assuming causation.
The statistical test you choose is on the basis of your research questions, research strategy, sampling method, and data characteristics.
Step 5: Analyze your findings
Interpreting your findings is the final step in statistical analysis.
The importance of statistics
The main criterion for drawing conclusions in hypothesis testing is statistical significance. To determine if your results are statistically significant or not, you compare your p value to a predetermined significance level (typically 0.05).
If the null hypothesis is true in the population, such a finding has a very small likelihood of occurring.
Size of the effect
A statistically significant result does not always imply that the research has meaningful real-world applications or therapeutic implications.
The effect size, on the other hand, demonstrates the practical relevance of your findings. For a complete view of your results, include effect sizes with your inferential statistics. If you’re writing an APA paper, you should also include interval estimates of effect sizes.
Errors in judgement
Type I and Type II errors occur when study conclusions are incorrect. A Type I error is when the null hypothesis you cannot accept when it is actually true, while a Type II error is when the null hypothesis is when you cannot accept it when the hypothesis is untrue.
By setting an optimal significance level and guaranteeing high power, you can reduce the chance of these errors. However, there is a trade-off between the two faults, necessitating a delicate balancing act.
Statistics: Frequentist vs. Bayesian
Frequentist statistics has always emphasized null hypothesis significance testing and always begins with the assumption of a true null hypothesis.
However, in recent decades, Bayesian statistics has gained prominence as a viable alternative. Using past research, you regularly update your hypotheses depending on your expectations and findings in this method.
Rather of deciding whether or not to reject the null hypothesis, the Bayes factor examines the relative strength of evidence for the null and alternative hypotheses.
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