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- Knowledge Base

## 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.

## Prevent plagiarism. Run a free check.

## 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?

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- 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)

## What is your plagiarism score?

An official website of the United States government

## Practical recommendations for statistical analysis and data presentation in Biochemia Medica journal

## Sažetak

## Introduction

## Are key results included in the Abstract ?

## Below is the example for poorly written Results section of the Abstract :

## The following is the example for well written Results section of the Abstract:

## Is Statistical analysis section written well, accurate and comprehensive?

- What kind of data did they have (categorical or numerical)?
- How did they describe their data?
- Did they test their distributions for normality? The name of the normality test needs to be stated.
- How was statistical test chosen to test the possible differences and associations between their data?
- Which statistical test was used for analyzing their categorical data?
- Were the groups large enough to detect the expected effect?
- What was the level of significance in their analysis?
- Which statistical software did they use? The version of the software and complete information on the manufacturer of the statistical software must be provided.

## The following is the example for poorly written Statistical analysis subheading of the Materials and methods section:

## The following is the example for well written Statistical analysis subheading of the Materials and methods section:

## Key points to keep in mind when writing the Results section

When results are reported, authors need to make sure that:

- Their descriptive analysis is appropriate;
- They have presented their results with adequate precision and accurately;
- They have provided the measure of confidence for all estimates, if necessary and applicable;
- They have used correct statistical tests for their analysis;
- Their graphs and tables are informative;
- They have provided P value for all tests done in their work;
- They are not making any conclusions on the causal relationship unless their study is an experiment or a clinical trial.

## Is the descriptive analysis adequate?

## Are results presented with adequate precision and accurately?

Example for the flawed data presentation of the observations is provided in the Table 1a .

The example for erroneously presented results for observations in two groups (groups A and B).

- Age is usually expressed with years and only one decimal is allowed, if absolutely necessary. Only when children are studied, it makes sense to provide age in months and even days. Moreover, age is usually reported as median and range (min–max). So, instead of stating that average age was 55.905 ± 2.112 years, it needs to be stated that the average age was 56 (51–60) years.
- The mean and measure of dispersion (standard deviation) for all laboratory parameters needs to be presented with as many decimals as the results are usually reported on the laboratory test report. It is therefore improper to present the WBC data with three decimals, since this parameter is usually measured and reported with only one decimal. So, instead of stating that WBC number in group A was 13.177 (6.837–15.272) × 10 9 /L, authors should report that WBC was 13.2 (6.8–15.3) × 10 9 /L.
- Finally, due to the small number of subjects in both groups, the ratio of females in both groups needs to be provided as the number of the observations divided with the total number of subjects within the group (6/11 and 8/14 instead of 54.5% and 57.1%).

General rules when reporting frequencies are listed below:

- Percentages are not recommended if the number of subjects in the group is < 100. Instead, ratios should be used (for example, 0.67 instead of 67%).
- Percentages should be presented as whole numbers, without decimals. The exception are percentages < 10%, where one decimal place is allowed, only if necessary and applicable (for example, if percentage is 0.3%).
- For small samples (N < 30), the use of percentages and ratios is not recommended. When their sample size is small, authors are advised to present their data with the number of the observations divided with the total number of subjects within the group (for example, 3/11, instead of 27%).

Correct way to present data is provided in Table 1b .

The example for correctly presented results for observations in two groups (groups A and B).

Examples for flawed presentation of results.

Examples for correct presentation of results.

## Were correct statistical tests used for the analysis?

- Are data normally distributed?
- Are data numerical or categorical?
- How many groups do authors have?
- How big are the studied groups?
- Are the measurements independent?

- Normality is not tested and statistical test is used without the knowledge of the data distribution, or regardless to the sample size.
- Paired statistical test is not used, although dependent observations (for example, repeated measurements) are tested.
- Chi-square test is used even if total number of observations or the number of expected frequencies in the 2×2 table is low.
- Pearson’s coefficient of correlation is calculated even if one variable is measured using the ordinal scale or data distribution significantly deviates from normal distribution.
- Differences between three or more groups are tested with t-test, instead of tests like ANOVA or Kruskal-Walis test.

## Is P value provided for all tests done in the study?

## Data interpretation

Furthermore, statements like this are also discouraged:

- We have observed the difference between our study groups, although not statistically significant.
- Though not statistically significant, concentration of glucose was higher in females than in males.
- There was a trend towards higher values of marker X with increasing concentrations of marker Y. The observed association was unfortunately not statistically significant.

## Correlation analysis

## Conclusions on the causal relationship

Checklist for authors who submit their work to Biochemia Medica.

## Conclusions

Potential conflict of interest

## An evaluation of the quality of statistical design and analysis of published medical research: results from a systematic survey of general orthopaedic journals

BMC Medical Research Methodology volume 12 , Article number: 60 ( 2012 ) Cite this article

Published between 1 st January 2005 and 1 st March 2010 (study start date)

No more than one paper from any single research group

## Study design

## Experimental unit

## Sample size

## Missing data

Subjective assessments and blinding

## Statistical methods

## Analysis methods

## Parametric versus non-parametric tests

## Multiple comparisons

## Presentation of results

Article CAS PubMed Google Scholar

Article PubMed PubMed Central Google Scholar

Web of Knowledge. [ http://wok.mimas.ac.uk/ ]

Altman DG, Bland JM: Units of analysis. BMJ. 1874, 1997: 314-

Missing data analysis. [ http://missingdata.lshtm.ac.uk/ ]

Bland M: An introduction to medical statistics. 2003, Oxford: OUP

Article CAS PubMed PubMed Central Google Scholar

Bland M: How to upset the Statistical Referee. [ http://www-users.york.ac.uk/~mb55/talks/upset.htm ]

BMJ Statistics Notes Series. [ http://openwetware.org/wiki/BMJ_Statistics_Notes_series ]

## Pre-publication history

## Author information

Warwick Medical School, University of Warwick, Coventry, CV2 2DX, UK

Nick R Parsons, Juul Achten & Matthew L Costa

University Hospitals Coventry and Warwickshire NHS Trust, Coventry, UK

You can also search for this author in PubMed Google Scholar

## Corresponding author

Correspondence to Nick R Parsons .

## Additional information

The authors declare that they have no competing interests.

## Authors’ contributions

## Electronic supplementary material

Additional file 1: statistical questionnaire.(doc ), rights and permissions.

## About this article

DOI : https://doi.org/10.1186/1471-2288-12-60

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## BMC Medical Research Methodology

## Trending now

## Table of Contents

## Master Tools You Need For Becoming an AI Engineer

## Types of Statistical Analysis

Given below are the 6 types of statistical analysis:

## Descriptive Analysis

## Inferential Analysis

## Predictive Analysis

## Prescriptive Analysis

## Exploratory Data Analysis

## Causal Analysis

## Importance of Statistical Analysis

- The statistical analysis aids in summarizing enormous amounts of data into clearly digestible chunks.
- The statistical analysis aids in the effective design of laboratory, field, and survey investigations.
- Statistical analysis may help with solid and efficient planning in any subject of study.
- Statistical analysis aid in establishing broad generalizations and forecasting how much of something will occur under particular conditions.
- Statistical methods, which are effective tools for interpreting numerical data, are applied in practically every field of study. Statistical approaches have been created and are increasingly applied in physical and biological sciences, such as genetics.
- Statistical approaches are used in the job of a businessman, a manufacturer, and a researcher. Statistics departments can be found in banks, insurance businesses, and government agencies.
- A modern administrator, whether in the public or commercial sector, relies on statistical data to make correct decisions.
- Politicians can utilize statistics to support and validate their claims while also explaining the issues they address.

## Boost Your AI and Machine Learning Career

## Benefits of Statistical Analysis

- It can help you determine the monthly, quarterly, yearly figures of sales profits, and costs making it easier to make your decisions.
- It can help you make informed and correct decisions.
- It can help you identify the problem or cause of the failure and make corrections. For example, it can identify the reason for an increase in total costs and help you cut the wasteful expenses.
- It can help you conduct market analysis and make an effective marketing and sales strategy.
- It helps improve the efficiency of different processes.

## Statistical Analysis Process

Given below are the 5 steps to conduct a statistical analysis that you should follow:

- Step 1: Identify and describe the nature of the data that you are supposed to analyze.
- Step 2: The next step is to establish a relation between the data analyzed and the sample population to which the data belongs.
- Step 3: The third step is to create a model that clearly presents and summarizes the relationship between the population and the data.
- Step 4: Prove if the model is valid or not.
- Step 5: Use predictive analysis to predict future trends and events likely to happen.

## Statistical Analysis Methods

## Standard Deviation

## Hypothesis Testing

## Sample Size Determination

## Statistical Analysis Software

## Statistical Analysis Examples

The weights of 5 pizza bases in cms are as follows:

Calculation of Mean = (9+2+5+4+12)/5 = 32/5 = 6.4

Calculation of mean of squared mean deviation = (6.76+19.36+1.96+5.76+31.36)/5 = 13.04

Standard deviation = √13.04 = 3.611

## Career in Statistical Analysis

## Become Proficient in Statistics Today

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## What Is Statistical Modeling?

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Understanding Statistical Process Control (SPC) and Top Applications

A Complete Guide on the Types of Statistical Studies

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What is Data Analysis? Methods, Process and Types Explained

A Complete Guide to Get a Grasp of Time Series Analysis

## Statistics Research Paper Writing Guide + Examples

## How to write a statistics research paper

You can learn them by following this short guide:

## Start by proper research:

It can also serve as a springboard for later argumentation or present the central idea.

## Finding journal articles on statistics research paper

## Writing body paragraphs

What are some common criticisms/counterpoints?

## Write your paper

And there you have it: statistics research paper.

## Write perfect conclusion

- Introduction – this section is often called the “literature review” and it contains a brief overview of your topic, including noteworthy definitions and facts. This discussion usually includes information regarding the shortcomings of prior research in this area, if there are any..
- Methodology – this section includes a description of how you obtained (gathered) your data; examples would include surveys, interviews or usage logs..
- Data – if you did not collect data yourself, then consider presenting a chart from an existing source that will help readers understand your results..
- Summary & Discussion – here you’ll present the most important numerical findings related to your study..
- Conclusions & Recommendations – be sure to make recommendations based on your findings.
- References – provide a list of pertinent sources from which you obtained information and ideas..
- Data Analysis – this section is usually presented as a subsection of the data section. Here you’ll report how you analyzed your data, including all calculations and inferences..
- Appendices – this is an optional section in which to place tables that provide detailed information about your study..
- Acknowledgments – it’s always nice to thank someone for their help (in this case, by providing a list of everyone who contributed to the project)..
- Related Reading – refer interested parties to other journal articles, books or websites related to this material for further reading..
- Tables – these are necessary in order to present your results. They also summarize large amounts of information in a small amount of space..
- Figures – Graphs and charts provide data in an easy to understand manner.
- Graphs – A graph is a visual representation of data..
- Charts – A chart is a graphical display of numerical comparisons. It can be useful for showing the relationship between two or more things, such as trends over time.
- List Of Participants – this is a list of everyone who helped you with the project.
- Certificate Of Approval – every department or institute has its own rules about what must be included here: usually some statement saying that your research followed ethical standards and was approved by the proper authorities..

## Statistics research paper outline template

As you begin each portion make sure to refer back to this outline.

- Problem statement
- Introduction/background
- Materials and methods discussion & results
- Data analysis plan/approach
- Discussion (use subheadings if necessary)
- Conclusion and recommendations

- Introduction – background information about the topic, relevance of particular issue, significance of data to the problem; 1-2 paragraphs
- Problem statement – state what problem was studied and why – this must be in your initial set of literature review sources (statistics research paper citations); 1 paragraph. State briefly how it relates to overall field or area of study;
- Objectives – list primary and secondary objectives that you were trying to achieve during the course of writing a stats paper; separate each with period. Do not use more than 2 levels of sub-objectives when doing outline.
- Materials & methods – explain your data gathering process (for collection of raw statistics), how you set up the experiment when doing statistical hypothesis testing, and any other relevant information concerning the creation of a statistics research paper; 2-3 paragraphs
- Data analysis/results – state how you analyzed data collected (tables, graphs, charts etc.) that is not available in published works or articles for stats research paper; 2-3 paragraphs
- Discussion section – this is important! Don’t forget to discuss results presented in data analysis/results section as well as recap your problem statement; 3-4 paragraphs. Discussion of main results is an important part of a research paper; don’t forget to include one! Defend your hypothesis (if applicable) and describe its importance. Also compare with other studies done on similar topics; present similarities & differences in data collection methods & outcome measurements used vs others. Take time to explain how each area is different.
- Conclusion & recommendations: In your research paper conclusion , reiterate the significance of your hypothesis; based on results it is either confirmed, disconfirmed or weakened/strengthened. Also indicate what you would like to do now that this is done (if not requested in guidelines) – future research, more studies should be done using same methods etc. Give an indication of how long each study might take and who can benefit from its findings. If needed you also have space here to discuss any recommendations for future work (suggestions are good but don’t sound too pushy).
- References: The references section is usually under a separate heading that includes title & author of the paper/book, date of publication and page numbers. In your bibliography, various books & articles, including editions & versions if needed, that were used as sources when doing your research paper or study (will likely contain other authors’ articles you read).
- Appendices – tables, figures, charts, appendices with raw data, etc. The appendices – anything else that was created during statistical analysis while writing stats research paper can go here (you may need extra sheets of paper if there are too many graphs etc. to include as part of the main text)

## Statistics research writing tips:

- “This paper will investigate…”
- “The objective of this study is…”
- “It is not found if…”
- “There have been a few studies concerning..”
- “As there has been much debate about…”
- “No prior study exists that.”

- Now, state your results and findings, including the statistical analysis if necessary (such as significance or not).
- Write only what was found using charts or graphs, tables, and numbers that back up your claims about the study.
- Check all your spelling and grammar again.
- Pay attention to commas, semicolons and spaces.
- Use a spell checker if possible or ask someone else to proof-read it for you.

## Statistics Research Topics

Wondering what to write a research paper on statistics and probability about?

A statistician collects, computes and analyzes numerical data to summarize information.

If you are looking for a statistics research paper topic ideas you’ve come to the right place!

## Statistics Research Topics – Probability

## Statistics Research Topics – Descriptive statistics

For example mean, median and mode are measures of central tendency and dispersion.

Descriptive statistics is also necessary for analyzing real-life situations.

It provides information that’s useful for making business decisions.

## Statistics Research Topics – Testing significance of relationships (correlation)

## Statistics – Research Paper – Sampling

The main idea behind sampling is to reduce information loss by minimizing unnecessary information.

## Statistics Research Topics – Hypothesis testing

## Statistics – Research Paper – Analysis of variance (ANOVA)

## Statistics Research Topics – Confidence intervals

It helps shows how much uncertainty exists within estimates for a single population parameter.

This is done by adding and subtracting margins of error to the original estimation..

## Statistics – Research Topics – Non-parametric tests

Some examples of these tests includes 1 rank sum test, sign test etc…

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## How can Tutlance help me get my statistics essay done?

## Can you help me come up with a good statistics research paper template?

## Can you help me write a business statistics research paper?

Read more about business statistics assignment help , psychology statistics homework help .

## Can you provide an example of a probability and statistics research paper?

Other kinds of examples of research papers in probability and statistics include:

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## Probability and statistics research paper examples

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## Effective Use of Statistics in Research – Methods and Tools for Data Analysis

## Role of Statistics in Biological Research

## 1. Establishing a Sample Size

## 2. Testing of Hypothesis

## 3. Data Interpretation Through Analysis

## Types of Statistical Research Methods That Aid in Data Analysis

## 1. Descriptive Analysis

## 2. Inferential Analysis

## 3. Predictive Analysis

## 4. Prescriptive Analysis

## 5. Exploratory Data Analysis

## 6. Causal Analysis

## 7. Mechanistic Analysis

## Important Statistical Tools In Research

## 1. Statistical Package for Social Science (SPSS)

## 2. R Foundation for Statistical Computing

## 3. MATLAB (The Mathworks)

## 4. Microsoft Excel

## 5. Statistical Analysis Software (SAS)

## 6. GraphPad Prism

## Use of Statistical Tools In Research and Data Analysis

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How to write data analysis in a research paper.

## Step 1: Plan your hypothesis and research design

## Analyzing statistical hypotheses

## How to plan your research design

## Measuring variables

## Step 2: Obtain data from a representative sample

## Step 3: Analyze and summarize your data

## Step 4: Analyze hypotheses and make inferences using inferential statistics

## Step 5: Interpret your results

Interpreting your findings is the final step of our statistical analysis.

Analysing data and interpreting the results requires practice and guidance

## Organization

## Problem Overview

- Provide a description of the problem.
- Are you attempting to answer a substantive question?
- It doesn’t have to be long, but it should be clear.

## Data Analysis and Model Approach

- Was your approach to addressing the question data-driven? If so, how?
- Be specific in describing your approach.

## The results of the Data Analysis

## The Substantive Conclusions

- What conclusions did you draw from this analysis?
- Is there an answer to the question you set out to address?

## Factors to consider when analyzing your research data

## Leave a Reply Cancel reply

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## Other stories

## Statistical Analysis

From: Olives and Olive Oil in Health and Disease Prevention , 2010

## Related terms:

## Statistical Methods

## 5.3.3.3 Estimation of Areal Averages

## Assessing Available Information

Edward E. Whang , Stanley W. Ashley , in Surgical Research , 2001

## e. Statistics

## Speech Recognition: Statistical Methods

L.R. Rabiner , B.-H. Juang , in Encyclopedia of Language & Linguistics (Second Edition) , 2006

## Statistical Analysis for Experimental-Type Designs

## What Is Statistical Analysis?

## Writing a Protocol

## Statistical Analysis for Security and Supervision

## The Collection of Data

Operational considerations include the following:

What programs, tasks, or actions consume our efforts?

Why are we engaged in these activities?

How can we show our activities are efficient and effective?

Strategic considerations include the following:

What goals represent the next horizon?

What must we do to support that direction?

## Imaging Physics

In Primer of Diagnostic Imaging (Fifth Edition) , 2011

## Statistical testing

Statistical Methods to Test Hypotheses

## Preclinical Evaluation of Carcinogenicity Using Standard-Bred and Genetically Engineered Rodent Models

## Statistical Clustering

J.A. Hartigan , in International Encyclopedia of the Social & Behavioral Sciences , 2001

## Mechanisms and Risks of Decompression

Richard D. Vann , in Bove and Davis' Diving Medicine (Fourth Edition) , 2004

## IMAGES

## VIDEO

## COMMENTS

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