How can I compare mean of subpopulation with mean of entire population? I want to compare mean of specific method with mean of all methods in a proficiency testing(PT) program.  A PT program is a program in which an organisation which executes PT, sends samples to multiple participants and ask them to measure some characteristics in sent sample. After a deadline participants send their results to PT provider. Provider analyse results in all and different groups. Groups are those who used same methods for measuring that characteristic.
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It is possible to compare a variable, for example age, between an entire group of patients and a subgroup of patients (a part of the entire group)?
108714
I have a feeling this may have been asked elsewhere, but not really with the type of basic description I need.  I know non-parametric relies on the median instead of the mean to compare... something.  I also believe it relies on "degrees of freedom"(?) instead of standard deviation.  Correct me if I'm wrong, though.  I've done pretty good research, or so I'd thought, trying to understand the concept, what the workings are behind it, what the test results really mean, and/or what to even do with the test results; however, no one seems to ever venture into that area.  For the sake of simplicity let's stick with the Mann-Whitney U-test, which I've noticed is quite popular (and also seemingly misused and overused too in order to force one's "square model into a circle hole").  If you'd like to describe the other tests as well feel free, although I feel once I understand one, I can understand the others in an analogous way towards various t-tests etc.  Let's say I run a non-parametric test with my data and I get this result back:  2 Sample Mann-Whitney - Customer Type         Test Information         H0: Median Difference = 0        Ha: Median Difference ≠ 0         Size of Customer    Large   Small Count                    45    55 Median                    2     2  Mann-Whitney Statistic: 2162.00  p-value (2-sided, adjusted for ties):   0.4156     I'm familiar with other methods, but what is different here?  Should we want the p-value to be lower than .05?  What does the "Mann-Whitney statistic" mean?  Is there any use for it?  Does this information here just verify or not verify that a particular source of data I have should or should not be used?  I have a reasonable amount of experience with regression and the basics, but am very curious about this "special" non-parametric stuff - which I know will have it's own shortcomings.  Just imagine I'm a fifth grader and see if you can explain it to me.
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I have two groups of independent samples whose means I want to compare. The data comes from a distinctly non-normal distribution. (Unimodal, but heavily right skewed).    Let's say that one group (Group A) has 14,000 observations and that another group (Group B) has 700 observations. Thus each group has a decent amount of observations (we are not talking about 2000 versus 5 here).   I am of the opinion that this strong unbalance in the group sizes will not make the Mann-Whitney-Wilcoxon Test any less applicable, however a colleague is suggesting that we randomly sample 700 observations from Group A so that our group sizes are perfectly balanced. He feels that the unbalance of the groups is making the test fail to find the "correct" result. (Where correct result means "result he wants," i.e. that the two groups are statistically significantly different).   As I said, I think that having highly unequal groups does not cause the Mann-Whitney-Wilcoxon Test to somehow stop working.   As far as I understand it, I do believe that the size of the smaller group will have implications for the power of our test, but even there, I am thinking that we probably have at least a decently sufficient sample size for Group B.   Will this highly unbalanced data somehow invalidate my analysis?
53538
I have built and tested a computer application, which involved two participant groups (Group-A with existing knowledge of databases and Group-B without knowledge of databases). I was required to apply statistical tests to determine if the perception and rating given to the application was same among both groups (based on the data recorded in the form of questionnaires). The participants from both groups filled out questionnaires (with 10 questions to rate based on Likert scales) to rate the system based on their experience during testing it.   Is the use of statistical tests (histograms, means, skewness and kurtosis), used for measuring the differences of data / rating / perception between both groups appropriate? What I am trying to see is that if / how much participants' ratings in group A differ from the ratings given by the participants in group-B, for each question of the questionnaire.
36705
I applied a survey consisting of 12 questions to 120 people and each questions include 4 nominal categories; I want to make comparison of people's answers according to their socio-demographic characteristics such as their educational level or socioeconomic status. All of my comparison criteria consist of nominal categories and number of categories change between 3 to 6. I cannot drop or combine comparisons; categories in other words number of categories are fixed.    My question is when I compare the frequency distribution of people's answers based on their education levels (for example) through chi-squared test, I got a warning that says (for instance) 7 cells have less than count five; minimum expected count is; 43.  I got this warning for almost my all questions - demographic characteristics comparisons.    Shall I underestimate this warning and use my test results or is there a different test I should use? If I should use a different test, which one?
111247
1) I had a dataset with missing data for baseline variables and outcome variables. Through multiple imputation in SPSS (10 imputations, 50 iterations, PMM for scale variables) I imputed the missing data for the baseline variables. When I analyse the data (i.e. only the 10 imputation data sets) and use the independent sample t-test for a continuous variable results are pooled. This includes mean and p-value, but not standard deviation. Is it correct that I can take the average of the 10 standard deviations calculated for the imputed data sets to calculate the pooled standard deviation?  2) The pooled p-value from the independent t-test on 10 imputation data sets in SPSS is not the average of the 10 p-values that are calculated: am I correct? As I believe a correction is made for the fact that the p-value is based on imputed data?  3) I want to impute the missing data for the outcome variables as well. I did not include those variables in the first imputation process since one of the outcome variables is affected by the value of one of the baseline variables for which data was missing. So I figured that I would first impute the baseline variable, create a 'complete' data set for it and than impute the outcome variables using that data and the other baseline variables. Is it actually possible to impute a second time? And how would I do that? Now (after the first imputation process) I have a dataset which is 11 times as large as originally (original data set + 10 x imputed data set). Do I use all 10 imputation data sets to run the imputation process again which would result in another tenfold of that data set (so 100 fold of my original data set size)? And is it true this would lead to a larger standard deviation for scale variables?
43620
There are there groups (colA, colB, colC) representing three different measurement methods. The question is whether there is a difference between the three methods. To decide the question we perform experiments and measure the same thing with each method. The output of each method is a label not a value on a numeric scale. In addition, we do not have a control group so we do not know which method's output is the right one in the experiment. I solved the question in the way below  but I became uncertain whether it is a correct solution. I might have oversimplified the problem. Consequently, the chi-square approach used tests something else not what we want.  Data:             colA,    colB,    colC experiment1 label1,  label1,  label2 experiment2 label3,  label1,  label3 experiment3 label4,  label4,  label2 experiment4 label5,  label4,  label5 ...    My first approach, probably oversimplified:   As we do not know which label is correct and which not, we regard at first all the outputs of method A correct and compare them to the other two columns and count the same labels in the same experiments in the other columns, then we regard all the outputs of method B correct and then method C. So we get the label count below:   I. colA regarded as correct colA(4) colB(2) colC(2)  II. colB regarded as correct colA(2), colB(4), colC(0)  III. colC regarded as correct colA(2), colB(0), colC(4)   Then we compute a chi-square test for each, here II. and III. are the same. (There are more than 5 expected values in each column it is just the example to highlight the problem.) This way we get three p values for each test, from which we select the highest one to be on the safe side and decide whether the deviations between columns are likely to be caused by chance only.    My second approach would probably be:   The data same data transformed in a different format:                          label1, label2, label3, label4, label5 methodA (earlier colA)       1,      0,      1,      1,      1, methodB (earlier colB)       2,      0,      0,      2,      0, methodC (earlier colC)       0,      2,      1,      0,      1,   Here the expected values for each label would be greater than 5 with the real data. However, we do not want to test whether the distribution among the labels are caused by chance only but whether there is a difference between the methodA, methodB and methodC. Can Chi-Square be used here? What other tests would you propose to use to see whether there is a difference between the three methods?  What would be your solution?
15873
Suppose there is a very big (infinite?) population of normally distributed values with unknown mean and variance.  Suppose also that we have a sample, S, of n values from the entire population. We can calculate mean and standard deviation for this sample (we use n-1 for stdev calculation).  The first and most important question is how is stdev(S) related to the standard deviation of the entire population?  An illustration for this issue is the second question:  Suppose we have an additional number, x, and we would like to test whether it is an vis-a-vis the general population. My intuitive approach is to calculate Z as follows:  $Z = \frac{x - mean(S)}{stdev(S)}$  and then test it against standard distribution if n>30 or against t-distribution if n&lt;30.  However, this approach doesn't account for n, the size of the sample. What is the right way to solve this question provided there is only single sample S?
56859
What is the difference?For what kind of purpose do we use the weighted average method?Why don't we instead always use the normal average method?and also,how to get the weighted average of some numbers?Also,do we have first to get the mean(normal average) of numbers in order to get their weighted average?  Thank you so much.
38198
Problem The average height of an American was reported to be 70. Many believe that college students are shorter than average. A random sample of students produced the following data:    $n=140$, $mean = 65.39$, $s = 4.64$    Find the test statistics  Steps Taken to Solve I decided that this type of problem was a 1 sample T-test. These are my steps to the Hypothesis Test.     Null Hypothesis = No difference, so $M = M_o = 0$ Alternative Hypothesis = $M &lt; 50$     $t = \frac{50 - 0}{\frac{4.64}{\sqrt{140}}} = 166.7467$     Is this approach correct so far?
24143
An investigator wishes to produce a combined analysis of several datasets.  In some datasets there are paired observations for treatment A and B.  In others there are unpaired A and/or B data.  I am looking for a reference for an adaptation of the t-test, or for a likelihood ratio test, for such partially paired data.  I am willing to (for now) to assume normality with equal variance and that the population means for A are the same for each study (and likewise for B).
39781
So I have a question with my teacher's solution below and I'm confused about one of the steps in their solution. I would appreciate some clarification.  Two brands of coffee were compared. Two independent random samples of 50 people each were asked to taste either Brand A or Brand B coffee, and indicate whether they liked it or not. Eighty four percent of the people who tasted Brand A liked it; the analogous sample proportion for Brand B was ninety percent.   (A) At α = 0.01, is there a significant difference in the proportions of individuals who like the two coffees? Use the p-value approach.   So I circled in blue a step where I'm confused about in the teacher's solution. I don't understand why P(Z&lt;-0.89) = 0.2061.   On the z-score table -0.89 is equal to 0.1867 so shouldn't it be that value instead? where did 0.2061 come from? Is it possible that the teacher made an error or am I not understanding something?
65583
The phrase p-hacking (also: , "snooping" or "fishing") refers to various kinds of statistical malpractice in which results become artificially statistically significant. There are many ways to procure a "more significant" result, including but by no means limited to:   only analysing an "interesting" subset of the data, in which a pattern was found; failing to adjust properly for multiple testing, particularly post-hoc testing and failing to report tests carried out that were not significant; trying different tests of the same hypothesis, e.g. both a parametric and a non-parametric test (), but only reporting the most significant;   experimenting with inclusion/exclusion of data points, until the desired result is obtained. One opportunity comes when "data-cleaning outliers", but also when applying an ambiguous definition (e.g. in an econometric study of "developed countries", different definitions yield different sets of countries), or qualitative inclusion criteria (e.g. in a meta-analysis, it may be a finely balanced argument whether a particular study's methodology is sufficient robust to include); the previous example is related to optional stopping, i.e., analyzing a dataset and deciding on whether to collect more data or not depending on the data collected so far ("this is almost significant, let's measure three more students!") without accounting for this in the analysis; experimentation during model-fitting, particularly covariates to include, but also  regarding data transformations/functional form.   So we know p-hacking can be done. It is often listed as one of the  and was mentioned in the ASA report on statistical significance, , so we also know it's a Bad Thing. Although some dubious motivations and (particularly in the competition for academic publication) counterproductive incentives are obvious, I suspect it's hard to figure out quite why it's done, whether deliberate malpractice or simple ignorance. Someone reporting p-values from a stepwise regression (because they find stepwise procedures "produce good models", but aren't aware the purported p-values are invalidated) is in the latter camp, but the effect is still p-hacking under the last of my bullet points above.  There's certainly evidence that p-hacking is "out there", e.g.  looks for tell-tale signs of it infecting the scientific literature, but what is the current state of our evidence base about it? I'm aware that the approach taken by Head et al was not without controversy, so the current state of the literature, or general thinking in the academic community, would be interesting. For instance do we have any idea about:   Just how prevalent is it, and to what extent can we differentiate its occurrence from publication bias? (Is this distinction even meaningful?) Is the effect particularly acute at the $p \approx 0.05$ boundary? Are similar effects seen at $p \approx 0.01$, for instance, or do we see whole ranges of p-values affected? Do patterns in p-hacking vary between academic fields? Do we have any idea which of the mechanisms of p-hacking (some of which are listed in the bullet points above) are most common? Have some forms proven harder to detect than others because they are "better disguised"?   References  Head, M. L., Holman, L., Lanfear, R., Kahn, A. T., &amp; Jennions, M. D. (2015). . PLoS Biol, 13(3), e1002106.
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I have the mean and standard deviation of a large sample (30k obs) and the mean and std of a subsample (2k obs). The means are percentage figures (i.e. between 0 and 100% and hence not a normal variate). Also the means are not independent, since one is based on a subsample from the other.    Despite seemingly a harmless question, I could not find an appropriate testing procedure. Any ideas on how to test whether the mean of the subsample is different to the mean of the entire sample are much appreciated.
8674
How are they all versions of the same basic statistical method?
82733
I recently conducted a online survey and are now having trouble deciding for the right analysis method. For example: I wanted to see if there is a correlation between Factor A and Factor B. However in my survey I did not ask the participants to directly rate Factor A and Factor B, but rather asked multiple subquestions for these two factors which were rated from 5(Strongly Agree) to 1 (Strongly Disagree). I created a sum score for item A and a sum score for item B by summing up the values of each subquestion and calculated the mean of the sumscores to measure them. So my question ist: Which method would be best to use here? I want to test if e.g. people with a higher score in Factor A would be more likely to decide for Factor B. I actually planned using Spearman or ANOVA depending on the number of independent variables, but I am not sure if that would really be the correct way to measure the correlation.
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I've been asked to review the literature for all studies that estimate the mean and median Blood Lead Level (BLL) in a certain country, and then perform a meta-analysis to come up with one overall value for the mean and median level.   Is such a thing typically done? I'm not interested in any "effect size," just a univariate measure.   I'd like to create a forest plot and do some of the standard tests of heterogeneity across studies. Is there a package and function in R that will allow me to do a meta-analysis of mean and median BLLs?  Just to clarify, this would be a separate meta-analysis for means, and a separate meta-analysis for medians.