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## The Beginner's Guide to Statistical Analysis | 5 Steps & Examples

## Table of contents

## Writing statistical hypotheses

- Null hypothesis: A 5-minute meditation exercise will have no effect on math test scores in teenagers.
- Alternative hypothesis: A 5-minute meditation exercise will improve math test scores in teenagers.
- Null hypothesis: Parental income and GPA have no relationship with each other in college students.
- Alternative hypothesis: Parental income and GPA are positively correlated in college students.

## Planning your research design

- In an experimental design , you can assess a cause-and-effect relationship (e.g., the effect of meditation on test scores) using statistical tests of comparison or regression.
- In a correlational design , you can explore relationships between variables (e.g., parental income and GPA) without any assumption of causality using correlation coefficients and significance tests.
- In a descriptive design , you can study the characteristics of a population or phenomenon (e.g., the prevalence of anxiety in U.S. college students) using statistical tests to draw inferences from sample data.

- In a between-subjects design , you compare the group-level outcomes of participants who have been exposed to different treatments (e.g., those who performed a meditation exercise vs those who didn’t).
- In a within-subjects design , you compare repeated measures from participants who have participated in all treatments of a study (e.g., scores from before and after performing a meditation exercise).
- In a mixed (factorial) design , one variable is altered between subjects and another is altered within subjects (e.g., pretest and posttest scores from participants who either did or didn’t do a meditation exercise).
- Experimental
- Correlational

## Measuring variables

- Categorical data represents groupings. These may be nominal (e.g., gender) or ordinal (e.g. level of language ability).
- Quantitative data represents amounts. These may be on an interval scale (e.g. test score) or a ratio scale (e.g. age).

## Sampling for statistical analysis

There are two main approaches to selecting a sample.

- Probability sampling: every member of the population has a chance of being selected for the study through random selection.
- Non-probability sampling: some members of the population are more likely than others to be selected for the study because of criteria such as convenience or voluntary self-selection.

If you want to use parametric tests for non-probability samples, you have to make the case that:

- your sample is representative of the population you’re generalizing your findings to.
- your sample lacks systematic bias.

## Create an appropriate sampling procedure

Based on the resources available for your research, decide on how you’ll recruit participants.

- Will you have resources to advertise your study widely, including outside of your university setting?
- Will you have the means to recruit a diverse sample that represents a broad population?
- Do you have time to contact and follow up with members of hard-to-reach groups?

## Calculate sufficient sample size

To use these calculators, you have to understand and input these key components:

- Significance level (alpha): the risk of rejecting a true null hypothesis that you are willing to take, usually set at 5%.
- Statistical power : the probability of your study detecting an effect of a certain size if there is one, usually 80% or higher.
- Expected effect size : a standardized indication of how large the expected result of your study will be, usually based on other similar studies.
- Population standard deviation: an estimate of the population parameter based on a previous study or a pilot study of your own.

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## Inspect your data

There are various ways to inspect your data, including the following:

- Organizing data from each variable in frequency distribution tables .
- Displaying data from a key variable in a bar chart to view the distribution of responses.
- Visualizing the relationship between two variables using a scatter plot .

## Calculate measures of central tendency

- Mode : the most popular response or value in the data set.
- Median : the value in the exact middle of the data set when ordered from low to high.
- Mean : the sum of all values divided by the number of values.

## Calculate measures of variability

- Range : the highest value minus the lowest value of the data set.
- Interquartile range : the range of the middle half of the data set.
- Standard deviation : the average distance between each value in your data set and the mean.
- Variance : the square of the standard deviation.

Researchers often use two main methods (simultaneously) to make inferences in statistics.

- Estimation: calculating population parameters based on sample statistics.
- Hypothesis testing: a formal process for testing research predictions about the population using samples.

You can make two types of estimates of population parameters from sample statistics:

- A point estimate : a value that represents your best guess of the exact parameter.
- An interval estimate : a range of values that represent your best guess of where the parameter lies.

## Hypothesis testing

- A test statistic tells you how much your data differs from the null hypothesis of the test.
- A p value tells you the likelihood of obtaining your results if the null hypothesis is actually true in the population.

Statistical tests come in three main varieties:

- Comparison tests assess group differences in outcomes.
- Regression tests assess cause-and-effect relationships between variables.
- Correlation tests assess relationships between variables without assuming causation.

## Parametric tests

- A simple linear regression includes one predictor variable and one outcome variable.
- A multiple linear regression includes two or more predictor variables and one outcome variable.

- A t test is for exactly 1 or 2 groups when the sample is small (30 or less).
- A z test is for exactly 1 or 2 groups when the sample is large.
- An ANOVA is for 3 or more groups.

The z and t tests have subtypes based on the number and types of samples and the hypotheses:

- If you have only one sample that you want to compare to a population mean, use a one-sample test .
- If you have paired measurements (within-subjects design), use a dependent (paired) samples test .
- If you have completely separate measurements from two unmatched groups (between-subjects design), use an independent (unpaired) samples test .
- If you expect a difference between groups in a specific direction, use a one-tailed test .
- If you don’t have any expectations for the direction of a difference between groups, use a two-tailed test .

The final step of statistical analysis is interpreting your results.

## Statistical significance

## Effect size

## Decision errors

## Frequentist versus Bayesian statistics

## Is this article helpful?

- Descriptive Statistics | Definitions, Types, Examples
- Inferential Statistics | An Easy Introduction & Examples
- Choosing the Right Statistical Test | Types & Examples

## More interesting articles

- Akaike Information Criterion | When & How to Use It (Example)
- An Easy Introduction to Statistical Significance (With Examples)
- An Introduction to t Tests | Definitions, Formula and Examples
- ANOVA in R | A Complete Step-by-Step Guide with Examples
- Central Limit Theorem | Formula, Definition & Examples
- Central Tendency | Understanding the Mean, Median & Mode
- Chi-Square (Χ²) Distributions | Definition & Examples
- Chi-Square (Χ²) Table | Examples & Downloadable Table
- Chi-Square (Χ²) Tests | Types, Formula & Examples
- Chi-Square Goodness of Fit Test | Formula, Guide & Examples
- Chi-Square Test of Independence | Formula, Guide & Examples
- Coefficient of Determination (R²) | Calculation & Interpretation
- Correlation Coefficient | Types, Formulas & Examples
- Frequency Distribution | Tables, Types & Examples
- How to Calculate Standard Deviation (Guide) | Calculator & Examples
- How to Calculate Variance | Calculator, Analysis & Examples
- How to Find Degrees of Freedom | Definition & Formula
- How to Find Interquartile Range (IQR) | Calculator & Examples
- How to Find Outliers | 4 Ways with Examples & Explanation
- How to Find the Geometric Mean | Calculator & Formula
- How to Find the Mean | Definition, Examples & Calculator
- How to Find the Median | Definition, Examples & Calculator
- How to Find the Mode | Definition, Examples & Calculator
- How to Find the Range of a Data Set | Calculator & Formula
- Hypothesis Testing | A Step-by-Step Guide with Easy Examples
- Interval Data and How to Analyze It | Definitions & Examples
- Levels of Measurement | Nominal, Ordinal, Interval and Ratio
- Linear Regression in R | A Step-by-Step Guide & Examples
- Missing Data | Types, Explanation, & Imputation
- Multiple Linear Regression | A Quick Guide (Examples)
- Nominal Data | Definition, Examples, Data Collection & Analysis
- Normal Distribution | Examples, Formulas, & Uses
- Null and Alternative Hypotheses | Definitions & Examples
- One-way ANOVA | When and How to Use It (With Examples)
- Ordinal Data | Definition, Examples, Data Collection & Analysis
- Parameter vs Statistic | Definitions, Differences & Examples
- Pearson Correlation Coefficient (r) | Guide & Examples
- Poisson Distributions | Definition, Formula & Examples
- Probability Distribution | Formula, Types, & Examples
- Quartiles & Quantiles | Calculation, Definition & Interpretation
- Ratio Scales | Definition, Examples, & Data Analysis
- Simple Linear Regression | An Easy Introduction & Examples
- Skewness | Definition, Examples & Formula
- Statistical Power and Why It Matters | A Simple Introduction
- Student's t Table (Free Download) | Guide & Examples
- T-distribution: What it is and how to use it
- Test statistics | Definition, Interpretation, and Examples
- The Standard Normal Distribution | Calculator, Examples & Uses
- Two-Way ANOVA | Examples & When To Use It
- Type I & Type II Errors | Differences, Examples, Visualizations
- Understanding Confidence Intervals | Easy Examples & Formulas
- Understanding P values | Definition and Examples
- Variability | Calculating Range, IQR, Variance, Standard Deviation
- What is Effect Size and Why Does It Matter? (Examples)
- What Is Kurtosis? | Definition, Examples & Formula
- What Is Standard Error? | How to Calculate (Guide with Examples)

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Descriptive analysis answers the question, “what happened?”

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Prescriptive analysis answers the question, “what should we do about it?”

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Whereas Camus perceives ideology as secondary to the need to address a specific historical moment of colonialism, Fanon perceives a revolutionary ideology as the impetus to reshape Algeria's history in a direction toward independence.

- In text-by-text , you discuss all of A, then all of B.
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As a girl raised in the faded glory of the Old South, amid mystical tales of magnolias and moonlight, the mother remains part of a dying generation. Surrounded by hard times, racial conflict, and limited opportunities, Julian, on the other hand , feels repelled by the provincial nature of home, and represents a new Southerner, one who sees his native land through a condescending Northerner's eyes.

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The data analysis report isn’t quite like a research paper or term paper in a class, nor like aresearch article in a journal. It is meant, primarily, to start an organized conversation between you and your client/collaborator.

Structuring your essay according to a reader's logic means examining your thesis and anticipating what a reader needs to know, and in what sequence, in order to grasp and be convinced by your argument as it unfolds. The easiest way to do this is to map the essay's ideas via a written narrative.

The frame of reference may consist of an idea, theme, question, problem, or theory; a group of similar things from which you extract two for special attention; biographical or historical information. The best frames of reference are constructed from specific sources rather than your own thoughts or observations.