How to estimate a confidence interval on a box plot?
I am new to the box plot graph and have a really hard time understanding it. And I've also just learned what a confidence interval is. I am unsure of whether you can or can't take a confidence interval of a box plot? If you can, how can you? Any advice to get a better understanding of box plots?
statistics
asked Feb 26 at 0:20
George Harrison
62110
bumped to the homepage by Community♦ 2 days ago
This question has answers that may be good or bad; the system has marked it active so that they can be reviewed.
add a comment |
I am new to the box plot graph and have a really hard time understanding it. And I've also just learned what a confidence interval is. I am unsure of whether you can or can't take a confidence interval of a box plot? If you can, how can you? Any advice to get a better understanding of box plots?
statistics
asked Feb 26 at 0:20
George Harrison
62110
bumped to the homepage by Community♦ 2 days ago
This question has answers that may be good or bad; the system has marked it active so that they can be reviewed.
Usually confidence intervals refer directly to population parameters (such as mean $mu,$ median $eta,$ or standard deviation $sigma$), rather than to graphical summaries of data (such as histograms and boxplots). However, graphical summaries can sometimes show confidence intervals of parameters. I discuss a couple of examples in my Answer.
– BruceET
Feb 26 at 1:05
add a comment |
I am new to the box plot graph and have a really hard time understanding it. And I've also just learned what a confidence interval is. I am unsure of whether you can or can't take a confidence interval of a box plot? If you can, how can you? Any advice to get a better understanding of box plots?
statistics
asked Feb 26 at 0:20
George Harrison
62110
I am new to the box plot graph and have a really hard time understanding it. And I've also just learned what a confidence interval is. I am unsure of whether you can or can't take a confidence interval of a box plot? If you can, how can you? Any advice to get a better understanding of box plots?
statistics
statistics
asked Feb 26 at 0:20
George Harrison
62110
asked Feb 26 at 0:20
George Harrison
62110
asked Feb 26 at 0:20
George Harrison
62110
asked Feb 26 at 0:20
George Harrison
62110
asked Feb 26 at 0:20
George Harrison
62110
62110
bumped to the homepage by Community♦ 2 days ago
This question has answers that may be good or bad; the system has marked it active so that they can be reviewed.
bumped to the homepage by Community♦ 2 days ago
This question has answers that may be good or bad; the system has marked it active so that they can be reviewed.
Usually confidence intervals refer directly to population parameters (such as mean $mu,$ median $eta,$ or standard deviation $sigma$), rather than to graphical summaries of data (such as histograms and boxplots). However, graphical summaries can sometimes show confidence intervals of parameters. I discuss a couple of examples in my Answer.
– BruceET
Feb 26 at 1:05
add a comment |
Usually confidence intervals refer directly to population parameters (such as mean $mu,$ median $eta,$ or standard deviation $sigma$), rather than to graphical summaries of data (such as histograms and boxplots). However, graphical summaries can sometimes show confidence intervals of parameters. I discuss a couple of examples in my Answer.
– BruceET
Feb 26 at 1:05
Usually confidence intervals refer directly to population parameters (such as mean $mu,$ median $eta,$ or standard deviation $sigma$), rather than to graphical summaries of data (such as histograms and boxplots). However, graphical summaries can sometimes show confidence intervals of parameters. I discuss a couple of examples in my Answer.
– BruceET
Feb 26 at 1:05
Usually confidence intervals refer directly to population parameters (such as mean $mu,$ median $eta,$ or standard deviation $sigma$), rather than to graphical summaries of data (such as histograms and boxplots). However, graphical summaries can sometimes show confidence intervals of parameters. I discuss a couple of examples in my Answer.
– BruceET
Feb 26 at 1:05
add a comment |
1 Answer
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The interquartile range (IQR), which is the height of the box in a boxplot (drawn vertically),
is related to the variability of the sample, but is not primarily intended
as an estimate of $sigma.$ (If data are normal, then this is sometimes done.)
Some computer programs show a nonparametric confidence interval (CI) for the population median. In Minitab this CI is indicated by a second, smaller, box.
In R statistical software the CI is indicated by 'notches' in the sides of
the main box.
If boxplots of two independent samples are shown side-by-side,
the notched CIs shown using R are constructed so that lack of overlap of the CIs indicates
statistically different population medians at the 5% level of significance.
Here is a boxplot from Minitab for a sample of size 50 from an exponential
population with mean 1. The vertical extent of the brown box is the CI for
the population median. [The population in this case has median $eta = 0.6931 < mu = 1;$ The sample median is $H = 0.790$ (the location of the horizontal bar within the boxes.]
The boxplots below are from R. Samples of size 50 are from two different exponential
distributions The non-overlapping notches indicate
that the samples come from populations with different medians.
Note: A characteristic of exponential samples is that they tend to have outliers
on the high side of the median because exponential populations are positively skewed. All three of the boxplots above happen to show at least one outlier
on the high side.
answered Feb 26 at 1:10
BruceET
35.2k71440
add a comment |
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The interquartile range (IQR), which is the height of the box in a boxplot (drawn vertically),
is related to the variability of the sample, but is not primarily intended
as an estimate of $sigma.$ (If data are normal, then this is sometimes done.)
Some computer programs show a nonparametric confidence interval (CI) for the population median. In Minitab this CI is indicated by a second, smaller, box.
In R statistical software the CI is indicated by 'notches' in the sides of
the main box.
If boxplots of two independent samples are shown side-by-side,
the notched CIs shown using R are constructed so that lack of overlap of the CIs indicates
statistically different population medians at the 5% level of significance.
Here is a boxplot from Minitab for a sample of size 50 from an exponential
population with mean 1. The vertical extent of the brown box is the CI for
the population median. [The population in this case has median $eta = 0.6931 < mu = 1;$ The sample median is $H = 0.790$ (the location of the horizontal bar within the boxes.]
The boxplots below are from R. Samples of size 50 are from two different exponential
distributions The non-overlapping notches indicate
that the samples come from populations with different medians.
Note: A characteristic of exponential samples is that they tend to have outliers
on the high side of the median because exponential populations are positively skewed. All three of the boxplots above happen to show at least one outlier
on the high side.
answered Feb 26 at 1:10
BruceET
35.2k71440
add a comment |
The interquartile range (IQR), which is the height of the box in a boxplot (drawn vertically),
is related to the variability of the sample, but is not primarily intended
as an estimate of $sigma.$ (If data are normal, then this is sometimes done.)
Some computer programs show a nonparametric confidence interval (CI) for the population median. In Minitab this CI is indicated by a second, smaller, box.
In R statistical software the CI is indicated by 'notches' in the sides of
the main box.
If boxplots of two independent samples are shown side-by-side,
the notched CIs shown using R are constructed so that lack of overlap of the CIs indicates
statistically different population medians at the 5% level of significance.
Here is a boxplot from Minitab for a sample of size 50 from an exponential
population with mean 1. The vertical extent of the brown box is the CI for
the population median. [The population in this case has median $eta = 0.6931 < mu = 1;$ The sample median is $H = 0.790$ (the location of the horizontal bar within the boxes.]
The boxplots below are from R. Samples of size 50 are from two different exponential
distributions The non-overlapping notches indicate
that the samples come from populations with different medians.
Note: A characteristic of exponential samples is that they tend to have outliers
on the high side of the median because exponential populations are positively skewed. All three of the boxplots above happen to show at least one outlier
on the high side.
answered Feb 26 at 1:10
BruceET
35.2k71440
add a comment |
The interquartile range (IQR), which is the height of the box in a boxplot (drawn vertically),
is related to the variability of the sample, but is not primarily intended
as an estimate of $sigma.$ (If data are normal, then this is sometimes done.)
Some computer programs show a nonparametric confidence interval (CI) for the population median. In Minitab this CI is indicated by a second, smaller, box.
In R statistical software the CI is indicated by 'notches' in the sides of
the main box.
If boxplots of two independent samples are shown side-by-side,
the notched CIs shown using R are constructed so that lack of overlap of the CIs indicates
statistically different population medians at the 5% level of significance.
Here is a boxplot from Minitab for a sample of size 50 from an exponential
population with mean 1. The vertical extent of the brown box is the CI for
the population median. [The population in this case has median $eta = 0.6931 < mu = 1;$ The sample median is $H = 0.790$ (the location of the horizontal bar within the boxes.]
The boxplots below are from R. Samples of size 50 are from two different exponential
distributions The non-overlapping notches indicate
that the samples come from populations with different medians.
Note: A characteristic of exponential samples is that they tend to have outliers
on the high side of the median because exponential populations are positively skewed. All three of the boxplots above happen to show at least one outlier
on the high side.
answered Feb 26 at 1:10
BruceET
35.2k71440
The interquartile range (IQR), which is the height of the box in a boxplot (drawn vertically),
is related to the variability of the sample, but is not primarily intended
as an estimate of $sigma.$ (If data are normal, then this is sometimes done.)
Some computer programs show a nonparametric confidence interval (CI) for the population median. In Minitab this CI is indicated by a second, smaller, box.
In R statistical software the CI is indicated by 'notches' in the sides of
the main box.
If boxplots of two independent samples are shown side-by-side,
the notched CIs shown using R are constructed so that lack of overlap of the CIs indicates
statistically different population medians at the 5% level of significance.
Here is a boxplot from Minitab for a sample of size 50 from an exponential
population with mean 1. The vertical extent of the brown box is the CI for
the population median. [The population in this case has median $eta = 0.6931 < mu = 1;$ The sample median is $H = 0.790$ (the location of the horizontal bar within the boxes.]
The boxplots below are from R. Samples of size 50 are from two different exponential
distributions The non-overlapping notches indicate
that the samples come from populations with different medians.
Note: A characteristic of exponential samples is that they tend to have outliers
on the high side of the median because exponential populations are positively skewed. All three of the boxplots above happen to show at least one outlier
on the high side.
answered Feb 26 at 1:10
BruceET
35.2k71440
answered Feb 26 at 1:10
BruceET
35.2k71440
answered Feb 26 at 1:10
BruceET
35.2k71440
answered Feb 26 at 1:10
BruceET
35.2k71440
35.2k71440
add a comment |
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Usually confidence intervals refer directly to population parameters (such as mean $mu,$ median $eta,$ or standard deviation $sigma$), rather than to graphical summaries of data (such as histograms and boxplots). However, graphical summaries can sometimes show confidence intervals of parameters. I discuss a couple of examples in my Answer.
– BruceET
Feb 26 at 1:05