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Null-hypothesis for a Pearson Product Moment Correlation
Independence Question
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With hypothesis testing we are setting up a null-hypothesis –
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With hypothesis testing we are setting up a null-hypothesis – the probability that there is no effect or relationship –
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With hypothesis testing we are setting up a null-hypothesis – the probability that there is no effect or relationship – and then we collect evidence that leads us to either accept or reject that null hypothesis.
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As you may recall, a Pearson Product Moment Correlation or simply Pearson Correlation is a tool that makes it possible to statistically test the relationship between or (for the purposes of this presentation) the independence of two continuous variables.
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As you may recall, a Pearson Product Moment Correlation or simply Pearson Correlation is a tool that makes it possible to statistically test the relationship between or (for the purposes of this presentation) the independence of two continuous variables. By continuous we mean a number that can take any value between two points (e.g., weight between 150 to 250 pounds).
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Here is a template for writing a null-hypothesis for a Pearson Correlation:
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Here is a template for writing a null-hypothesis for a Pearson Correlation:
There is no statistically significant relationship between the [insert variable] and [insert variable].
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Here is a template for writing a null-hypothesis for a Pearson Correlation:
There is no statistically significant relationship between the [insert variable] and [insert variable].
With a question of independence, the null-hypothesis is what is sought after.
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Example 1
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ProblemYou have been asked to determine if student ACT scores and their Grade Point Averages (GPAs) are independent of one another.
Template for a Pearson Correlation Null-HypothesisThere is no statistically significant relationship between the [insert variable] and [insert variable].
Null-hypothesis for this ProblemThere is no statistically significant relationship between the [insert variable] and [insert variable].
3.8
2
2.90
3.311.5
0 4.00
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ProblemYou have been asked to determine if student ACT scores and their Grade Point Averages (GPAs) are independent of one another.
Template for a Pearson Correlation Null-HypothesisThere is no statistically significant relationship between the [insert variable] and [insert variable].
Null-hypothesis for this ProblemThere is no statistically significant relationship between the [insert variable] and [insert variable].
![Page 13: Null hypothesis for Pearson Correlation (independence)](https://reader034.vdocuments.site/reader034/viewer/2022052507/55847947d8b42abf538b5195/html5/thumbnails/13.jpg)
ProblemYou have been asked to determine if student ACT scores and their Grade Point Averages (GPAs) are independent of one another.
Template for a Pearson Correlation Null-HypothesisThere is no statistically significant relationship between the [insert variable] and [insert variable].
Null-hypothesis for this ProblemThere is no statistically significant relationship between the [insert variable] and [insert variable].
![Page 14: Null hypothesis for Pearson Correlation (independence)](https://reader034.vdocuments.site/reader034/viewer/2022052507/55847947d8b42abf538b5195/html5/thumbnails/14.jpg)
ProblemYou have been asked to determine if student ACT scores and their Grade Point Averages (GPAs) are independent of one another.
Template for a Pearson Correlation Null-HypothesisThere is no statistically significant relationship between the [insert variable] and [insert variable].
Null-hypothesis for this ProblemThere is no statistically significant relationship between [insert variable] and [insert variable].
![Page 15: Null hypothesis for Pearson Correlation (independence)](https://reader034.vdocuments.site/reader034/viewer/2022052507/55847947d8b42abf538b5195/html5/thumbnails/15.jpg)
ProblemYou have been asked to determine student ACT scores and their Grade Point Averages (GPAs) are independent of one another.
Template for a Pearson Correlation Null-HypothesisThere is no statistically significant relationship between the [insert variable] and [insert variable].
Null-hypothesis for this ProblemThere is no statistically significant relationship between [insert variable] and [insert variable].
![Page 16: Null hypothesis for Pearson Correlation (independence)](https://reader034.vdocuments.site/reader034/viewer/2022052507/55847947d8b42abf538b5195/html5/thumbnails/16.jpg)
ProblemYou have been asked to determine student ACT scores and their Grade Point Averages (GPAs) are independent of one another.
Template for a Pearson Correlation Null-HypothesisThere is no statistically significant relationship between the [insert variable] and [insert variable].
Null-hypothesis for this ProblemThere is no statistically significant relationship between student ACT Scores and [insert variable].
![Page 17: Null hypothesis for Pearson Correlation (independence)](https://reader034.vdocuments.site/reader034/viewer/2022052507/55847947d8b42abf538b5195/html5/thumbnails/17.jpg)
ProblemYou have been asked to determine student ACT scores and their Grade Point Averages (GPAs) are independent of one another.
Template for a Pearson Correlation Null-HypothesisThere is no statistically significant relationship between the [insert variable] and [insert variable].
Null-hypothesis for this ProblemThere is no statistically significant relationship between student ACT Scores and [insert variable].
![Page 18: Null hypothesis for Pearson Correlation (independence)](https://reader034.vdocuments.site/reader034/viewer/2022052507/55847947d8b42abf538b5195/html5/thumbnails/18.jpg)
ProblemYou have been asked to determine student ACT scores and their Grade Point Averages (GPAs) are independent of one another.
Template for a Pearson Correlation Null-HypothesisThere is no statistically significant relationship between the [insert variable] and [insert variable].
Null-hypothesis for this ProblemThere is no statistically significant relationship between student ACT Scores and Grade Point Averages.
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Null-hypothesis for this ProblemThere is no statistically significant relationship between student ACT Scores and Grade Point Averages.
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Example 2
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ProblemUsing validated measures for each, you have been asked to determine if depression and a sense of belonging are independent of one another. Template for a Pearson Correlation Null-HypothesisThere is no statistically significant relationship between the [insert variable] and [insert variable].
Null-hypothesis for this ProblemThere is no statistically significant relationship between the [insert variable] and [insert variable].
![Page 22: Null hypothesis for Pearson Correlation (independence)](https://reader034.vdocuments.site/reader034/viewer/2022052507/55847947d8b42abf538b5195/html5/thumbnails/22.jpg)
ProblemUsing validated measures for each, you have been asked to determine if depression and a sense of belonging are independent of one another.
Template for a Pearson Correlation Null-HypothesisThere is no statistically significant relationship between the [insert variable] and [insert variable].
Null-hypothesis for this ProblemThere is no statistically significant relationship between the [insert variable] and [insert variable].
![Page 23: Null hypothesis for Pearson Correlation (independence)](https://reader034.vdocuments.site/reader034/viewer/2022052507/55847947d8b42abf538b5195/html5/thumbnails/23.jpg)
ProblemUsing validated measures for each, you have been asked to determine if depression and a sense of belonging are independent of one another.
Template for a Pearson Correlation Null-HypothesisThere is no statistically significant relationship between the [insert variable] and [insert variable].
Null-hypothesis for this ProblemThere is no statistically significant relationship between [insert variable] and [insert variable].
![Page 24: Null hypothesis for Pearson Correlation (independence)](https://reader034.vdocuments.site/reader034/viewer/2022052507/55847947d8b42abf538b5195/html5/thumbnails/24.jpg)
ProblemYou have been asked to determine if a relationship exists between depression and sense of belonging using validated measures for each.
Template for a Pearson Correlation Null-HypothesisThere is no statistically significant relationship between the [insert variable] and [insert variable].
Null-hypothesis for this ProblemThere is no statistically significant relationship between [insert variable] and [insert variable].
![Page 25: Null hypothesis for Pearson Correlation (independence)](https://reader034.vdocuments.site/reader034/viewer/2022052507/55847947d8b42abf538b5195/html5/thumbnails/25.jpg)
ProblemUsing validated measures for each, you have been asked to determine if depression and a sense of belonging are independent of one another.
Template for a Pearson Correlation Null-HypothesisThere is no statistically significant relationship between the [insert variable] and [insert variable].
Null-hypothesis for this ProblemThere is no statistically significant relationship between depression scores and [insert variable].
![Page 26: Null hypothesis for Pearson Correlation (independence)](https://reader034.vdocuments.site/reader034/viewer/2022052507/55847947d8b42abf538b5195/html5/thumbnails/26.jpg)
ProblemUsing validated measures for each, you have been asked to determine if depression and a sense of belonging are independent of one another.
Template for a Pearson Correlation Null-HypothesisThere is no statistically significant relationship between the [insert variable] and [insert variable].
Null-hypothesis for this ProblemThere is no statistically significant relationship between depression scores and [insert variable].
![Page 27: Null hypothesis for Pearson Correlation (independence)](https://reader034.vdocuments.site/reader034/viewer/2022052507/55847947d8b42abf538b5195/html5/thumbnails/27.jpg)
ProblemUsing validated measures for each, you have been asked to determine if depression and a sense of belonging are independent of one another.
Template for a Pearson Correlation Null-HypothesisThere is no statistically significant relationship between the [insert variable] and [insert variable].
Null-hypothesis for this ProblemThere is no statistically significant relationship between depression scores and sense of belonging scores.
![Page 28: Null hypothesis for Pearson Correlation (independence)](https://reader034.vdocuments.site/reader034/viewer/2022052507/55847947d8b42abf538b5195/html5/thumbnails/28.jpg)
Null-hypothesis for this ProblemThere is no statistically significant relationship between depression scores and sense of belonging scores.