A brief numerical description of a set of data.
27
votes
8answers
8k views
What are good basic statistics to use for ordinal data?
I have some ordinal data gained from survey questions. In my case they are Likert style responses (Strongly Disagree-Disagree-Neutral-Agree-Strongly Agree). In my data they are coded as 1-5.
I ...
27
votes
7answers
2k views
Graphical data overview (summary) function in R
I'm sure I've come across a function like this in an R package before, but after extensive Googling I can't seem to find it anywhere. The function I'm thinking of produced a graphical summary for a ...
15
votes
1answer
2k views
Empirical Relationship Between Mean, Median and Mode
For a unimodal distribution which is moderately skewed, we have the following empirical relationship between mean, mode and median:
(Mean-Mode) ~ 3(Mean-Median)
Could someone please explain how the ...
14
votes
2answers
397 views
Statistics, war stories, data intuition
I think it is fair to say statistics is an applied science so when averages and standard deviations are calculated it is because someone is looking to make some decisions based on those numbers. Part ...
8
votes
5answers
5k views
What does orthogonal mean in the context of statistics?
In other contexts, orthogonal means "at right angles" or "perpendicular".
What does orthogonal mean in a statistical context?
Thanks for any clarifications.
8
votes
2answers
261 views
Standard measure of clumpiness?
I am a lowly consumer of statistics, not a statistician. I hope this question is not ridiculous in some way, but I have searched around here and elsewhere and had no luck. It may just be that I don't ...
7
votes
1answer
5k views
How to 'sum' a standard deviation?
I have a monthly average for a value and a standard deviation corresponding to that average. I am now computing the annual average as the sum of monthly averages, how can I represent the standard ...
7
votes
1answer
1k views
Meta-analysis in R, using metafor package
How must I syntax the rma function from metafor package in order to get results in the following real-life example of a small meta-analysis?
(random-effect, ...
6
votes
2answers
263 views
What is the meaning of $\|a\|_p=\left(\sum _{i=1}^n \left|a_i(t)\right|{}^p\right){}^{\frac{1}{p}}$?
What is the meaning of $\|a\|_p=\left(\sum _{i=1}^n \left|a_i(t)\right|{}^p\right){}^{\frac{1}{p}}$?
This formula is called out on the fifth page of An Improved Data Stream Summary: The Count-Min ...
6
votes
2answers
496 views
The exact distribution of Wilcoxon rank-sum statistic U
The distribition of the rank-sum statistic U is assumed to be normal for large number of samples being considered. What is the exact distribution? I want to compare and sometimes fuse results from ...
6
votes
0answers
144 views
Finding a comparable Control group for a treatment group?
I have a treatment group of size 30 (30 schools in California) that used a math supplemental software. In a simple analysis, I'd like to compare students' average Math growth between our treatment ...
5
votes
4answers
9k views
What is the interpretation of interquartile range?
I have daily measurements of nitrogen dioxide for one year (365 days) and the interquartile (IQR) is 24 microgram per cubic meter. What does "24" mean in this context, apart from the definition of IQR ...
5
votes
2answers
779 views
Alternatives to using Coefficient of Variation to summarize a set of parameter distributions?
Background
I have a model with 17 parameters, and I currently use the coefficient of variation ($\text{CV}=\sigma/\mu$) to summarize the prior and posterior distributions of each parameter.
All of ...
5
votes
2answers
84 views
What are statistical methods for comparing different brackets
I am not particularly familiar with statistics and am looking at methods for analysing numbers that have been broken into different "brackets" or "groups" for different entities.
Consider three ...
5
votes
1answer
69 views
Measure of dispersion over unordered set
I'm looking for a measure of dispersion, such as standard deviation, that can be used when distributing to an unordered set.
Specifically: A bucket distribution assigns a non-negative value to each ...
5
votes
2answers
129 views
Predictive model & standardized variables
In a predictive model, I have standardized variables as predictors. Say I have to rescore the model on fresh data at some point in the future: do I use the means/stds as they were when I built the ...
5
votes
0answers
65 views
Aggregating all measurements per x-value in least-square fitting
We want to select one out of a given set of (continuous) functions that best matches a set of observations $\{(s_i,c_i) \mid 1 \leq i \leq N\} \subseteq\mathbb{N} \times \mathbb{N}$ (input size and ...
4
votes
3answers
3k views
Why is the arithmetic mean > median on a histogram skewed to the right?
I am fairly new to statistics.
Currently I am into (histograms) medians, arithmetic mean and all the general basics.
And I came accross the fact/rule that the arithmetic mean is (always) larger than ...
4
votes
4answers
481 views
Ratio of Range to IQR vs. Coefficient of Variation — which is the more useful robust measure?
For a given set of data, spread is often calculated either as the standard deviation or as the IQR (inter-quartile range).
Whereas a standard deviation is ...
4
votes
3answers
230 views
How to measure usage data across cohorts/segments?
Netflix and Google among others use customer usage (number of videos streamed or unique searches conducted) as a proxy for value, or for determining which version of a test is best. I am curious how ...
4
votes
1answer
525 views
Is this the correct way to calculate $MSE$ from $SS_{\text{treatment(s)}}$, $df_{\text{treatment(s)}}$, $F$?
As described in a few of my previous questions (here and there), I am interested in deriving summary statistics from statistics reported in the literature.
I would very much appreciate any advice ...
4
votes
1answer
215 views
Measure of variation around Median
Are there terms for measures of variation around the median? I know that we use "variance" for means of data but how can variance be defined for the median? Is there a similar statistic for median?
4
votes
1answer
2k views
How to generate nice summary table?
I want to have R display the data it gives me from the summary() function in a table so I can easily share this. I am currently just doing ...
4
votes
2answers
825 views
What summary statistics to use with categorical or qualitative variables?
Just to clarify, when I mean summary statistics, I refer to the Mean, Median Quartile ranges, Variance, Standard Deviation.
When summarising a univariate which is categorical or qualitative, ...
4
votes
3answers
153 views
How to describe the differences in skewed data with same median but statistically different distribution?
I am comparing length of stay after laparoscopic and open appendectomy in over 160000 patients. LOS is typically a skewed variable so I use the median and interquartile range and ranksum test to ...
4
votes
0answers
226 views
How does pooling and resampling affect variance of sample mean?
Suppose I have $N$ independent random variables $X_n$. I draw a sample of predetermined size $K_n$ from each of them. Denote the average of each sample $\bar{\hat{X}}_n$, and the total number of ...
3
votes
2answers
1k views
Analyzing Likert scales
The Likert scale I am analyzing has both positive and negative questions, but all the items are answered with 4 - strongly agree, 3 - agree, 2 - disagree and 4 - strongly disagree. For analysis, ...
3
votes
1answer
774 views
What are some ways to graphically display non-normal distributions in Excel?
The ultimate goal is to show users, at a glance, if their data is normally distributed.
The first attempt is a kludge that plots the data in a frequency graph. Then, the observed mean and standard ...
3
votes
3answers
441 views
Is there a way to optimize regression according to a specific criterion?
I am curious, is there a way to optimize a regression according to a specific statistic?
Let's say I am interested in a model with the best possible AIC statistic (or MSE or whatever measurement I ...
3
votes
1answer
135 views
Am I using the wrong statistical test?
I am using $\chi^2$ to analyze a set of data gathered over 4 time periods. The two variables are independent--each 'event' is categorized as 'good' or 'bad'. We want to prove that the intervention ...
3
votes
2answers
5k views
How to create an index
I have 5 categories, each category is divided into the subcategories low, medium and high. An object can belong to one or more of these categories with a number between 1 and 100 in each subcategory ...
3
votes
1answer
367 views
How to compare the variance from published summary statistics with own data?
I have compiled a very small set of summary data from the literature, and I wish to compare the variances between aspects of the literature-based data, and to some of my own data. The summary data ...
3
votes
1answer
528 views
Estimating misclassification rate from summary classification values
I'm trying to work out the misclassification rate in a published study, where the results do not include this value. However, I have the sensitivity, ...
3
votes
2answers
320 views
How do I estimate the parameters of a log-normal distribution from the sample mean and sample variance
Given the sample mean $\bar{x}$ and the sample variance $s^2$ of a random variable $X$, is it possible to estimate the shape $\sigma^2$ and log-scale $\mu$ of the log-normal distribution, with ...
3
votes
0answers
38 views
What type of tool/statistic should I use to inspect two misaligned time series of different granularity?
I have two separate time series, indexed by time in nanoseconds. They both measure the same thing but because they come about in two completely different ways, the number of observations they each ...
2
votes
4answers
291 views
Visualise and interpret large set of univariate skewed data
I am trying to find out answer for this simple question. I have data (list of numbers). I have 20000 numbers. smallest number is 100 and largest is 15000. I want to interpret this data, how it is ...
2
votes
2answers
121 views
How do I calculate the range that 90% of the values fall into
Given a series of values, I know that 68% of the values fall withing one standard deviation and that 95% fall withing 2 standard deviations, but how do I calculate the range whereby 90% percent of the ...
2
votes
1answer
78 views
A good summary measure on analyzing repeated measures of longitudinal data?
I have an interesting question on longitudinal data and I'm looking for a proper summary measure that enables me to answer my question of interest without knowing/using anything about correlated data. ...
2
votes
2answers
124 views
Determine range that contains given ratio of data points
I'd like to determine the "representative" range for a series of data points. For example, I'd like to know the range where 98% (or any other given ratio) of points are located. I could have used the ...
2
votes
3answers
443 views
Command-line tool to calculate basic statistics for stream of values
Is there any command-line tool that accepts the flow of numbers (in ascii format) from standard input and gives the basic descriptive statistics for this flow, such as min, max, average, median, RMS, ...
2
votes
2answers
731 views
Help with the Ljung-Box test for time independence of residuals
I fit a simple linear model y = bX to a data set today, and that produced 24 residuals (I have 24 data points, one for each year from 1984-2007). I would like to test the time-independence of the ...
2
votes
1answer
65 views
Advice on the statistical analysis of clinical data using summary statistics, t-tests, ANOVA, and linear regression
I need some help with the statistical analysis of a study of a particular surgery to remove a particular cancer. I am using the statistical program R to conduct my analysis. My data are saved in the ...
2
votes
1answer
59 views
Use of data on a website
I wanted to use some data for statistical analysis available on a company's website. The data is in the form of a time series. Am I allowed to publish my results and conclusions?
regards
Leo
2
votes
1answer
11 views
Macro and Micro Inter-Coder/Rater Agreement
I have a labeling task with 4 labels for which I'm using 2 coders/annotators/raters. This labeling effort leads to a confusion matrix like the one in
...
2
votes
2answers
199 views
Calculating the percentage change of 2 values
If I have two different percentages and I wanted to know the change, I would simply use the percentage change formula...but what if I want to compare two percentages that have different amounts:
Ex: ...
2
votes
1answer
176 views
How do I compare the accuracy of two measurement devices when one of them is the reference?
I'm currently trying to compare the measurement accuracy of two devices. However, I am using one of the devices as a "gold standard" to say something about the accuracy of the other device.
The ...
2
votes
1answer
73 views
Summary statistic for an error measurement
I have $n$ error measures that can be positive or negative values. Negative values are more important for my experiment than positive values. Of course, taking the mean of the $n$ values doesn't make ...
2
votes
1answer
1k views
Tukey's Hinges: Grouping Data
I am having trouble figuring out how to group data using the inter-quartile ranges calculated with a box and whiskers plot as well as looking at Tukey's Hinges. I understand the IQR and Tukey's hinges ...
2
votes
0answers
56 views
Sample vs. Population
I'm trying to analyse the performance of my server by collecting performance data using standard tools such as Windows Performance Monitor, and then putting this data on Excel for analysis.
When I ...
1
vote
1answer
213 views
Quantiles for non-normal cdf
When I compute the five-number summary on my sample, I obtain quantiles that differ from the quantiles I got from the empirical cdf, since they are not normally distributed data.
Can you help me in ...
