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Just use the definition of a CDF $F_X$ for a random variable $X$: $F_X(x) = \mathbb{P}(X\le x)$ For an absolutely continuous pdf $f_X$ such as the normal distribution, we have $$F_X(x) = \int_{-\infty}^x f_X(t)dt $$. So if we want to know the probability between $a,b$ s.t. $a<b$, we have $$ \begin{align} \int_a^b f_X(t) dt &= \int_{-\infty}^b f_X(t)...


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Adding to the great answers, a statistic is some numerical characteristic of data. (Or, a result of a function that takes your data as input). So, yes, those numbers are technically statistics.


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Because sum and mean goes together by $mean = \dfrac{sum}{n}$, I suppose you can use either sum or mean together with $n$. Intuitively you'll want higher sum or mean with lower $n$. Say that there are cases where two vectors have same sum or mean and same $n$, and you are interested in which vector has larger values. Median helps here. If you say the vectors ...


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I think of summary/descriptive statistics as a tool to communicate the nature of a set of data at a glance, whether that is through tables of means and SDs, percentages, bar charts, histograms, pie charts etc. There isn't a one-size-fits-all approach: you need to examine your data types (continuous, ordinal, categorical) and distributions (e.g. normal, ...


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I second collecting more data if possible, or graphing and contextualizing the findings if you can't collect more data (with a strong call that you or someone else will need to replicate findings in a larger sample). P values have their own issues at the best of times and certainly wouldn't be very meaningful with such a small sample. My other concern is ...


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In general, dealths per capita of population is preferable to deaths per capita of confirmed cases. The reason for this is quite simple. In the latter, the denominator, number of confirmed cases depends very much on the extent, and accuracy of, testing, whereas in the former, the total population is well known. It is also worth noting that the numerator in ...


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With this dataset, it will be tricky to get reliable results. But, if you can collect more data, you can try Gaussian GLMM with an interaction term between treatment and your factor. It should contain the response variable as your measure; two fixed effects (with the interaction between them), namely treatment (Control and Infection) and your factor (M and E)...


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Percentages. If your table just shows the average age of health industry workers, that doesn't seem to tell you much. This will give you the largest tables. If you want small tables, use the means. You could also include the standard deviations (SD). For example, treat AGE as continuous. If you had a mean of 6 and a SD of two, that would say that 95% of ...


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The answer is no. Distributions can be differently higher/lower in relation to each other for different moments. Example Consider the distribution $$f(x,a) = \begin{cases} 0.075 & \text{if} & x = -a \\ 0.175 & \text{if} & x = -1 \\ 0.500 & \text{if} & x = 0 \\ 0.175 & \text{if} & x = 1 \\ 0.075 & \text{if} & x = a \\ \...


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The Dice coefficient (also known as the Sørensen–Dice coefficient and F1 score) is defined as two times the area of the intersection of A and B, divided by the sum of the areas of A and B: Dice = 2 |A∩B| / (|A|+|B|) = 2 TP / (2 TP + FP + FN) (TP=True Positives, FP=False Positives, FN=False Negatives) Dice score is a performance metric for image segmentation ...


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Confidence intervals for population proportion $p.$ As in my Comment, if the margin of error $E$ in a confidence interval (CI) for a population proportion $p$ is $1/\sqrt{n},$ where $n$ is the sample size. So the sample size required for margin of error $E$ is $n \approx 1/E^2.$ This relationship is very simple because $E$ is a function of one parameter $p.$ ...


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In ordinary (non-technical) English the word average can be used for various concepts relating to a typical value of a list of numbers: maybe the "most common" income, middle income in @Dave's line-up, or the number you get when you add all the incomes and divide by the number of incomes. If two people disagree about "the average," they ...


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The number of deaths among the number of diagnosed cases is called case fatality rate. The number of deaths scaled to the size of the population is called mortality rate. One can't say that "so far, a random Canadian would have been less likely to die from coronavirus than a random person in the US", because there is a lag between infection and ...


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The number of deaths per million essentially gives an estimate of the likelihood of death attributable to coronavirus in the overall population, normalizing the number of deaths to the population of a country (note this only counts death attributable to coronavirus, as it cannot count undiagnosed cases). Countries with larger population will naturally have ...


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From your particular description of your problem, your goal is performing some exploratory data analysis. One field of Machine Learning is called Unsupervised Learning. I believe this is what you should look into. The previous answer suggested hierarchical clustering. That is a good method for performing exploratory data analysis from a small-ish number of ...


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Machine learning is a field with many diverse techniques. Thus, whether can you apply it here depends very much of what you are trying to achieve and what technique you have in mind. Perhaps, you could describe it more precisely in your question. Having said that, the small size of the dataset (there are a bit more than 200 countries in the world) rules out ...


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Range, IQR, and really any quantile interval lengths; standard deviation/variance, kurtosis (not excess kurtosis), and all other even-power moments; and, likelihood and other chi-squared statistics (e.g. Wilk's lambda).


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Given a column of data that looks like this: 20 23 21 25 20 You need to rank the column smallest to largest and then calculate rank by noting the position in a second column: 20 1.5 20 1.5 21 2 23 3 25 4 If the data have ties (like the two 20s here in first and second place), averaged position is used. Mean rank will be the arithmetic average of the ...


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No, in this case, it does not make sense to draw error bars using SDs. Take a step back. Why do we draw error bars with SDs? As you write, it's to show where "much" of the data lies. This makes sense if your data come from a normal distribution: 68% of your data will lie within $\pm 1$ SD from the mean, so showing the mean with an error bar of $\pm ...


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There are several ways to do this. So in order to get the exact intended answer, you'd have to know the exact formula used in that book. [There are various formulas for the standard error (pooling E and NE to get a combined estimate of p, or not pooling). Some use a continuity correction, some don't. And so on.] Compare formulas with your friend. Here is ...


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You seem to have repeated measures data (also called longitudinal data) with two measurements per individual. I would start out with visualization, see for instance Plotting and presenting longitudinal data, options? and search this site. Maybe start with some kind of line plots, if you could post your data (in a readable form ..., if you cant share the data,...


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