The Standard Deviation vs. the Standard Error 

Assuming your two variables are quantitative and you are looking to investigate the association between them, you can use a Spearman's rank correlation analysis. Though I dont use SPSS, any decent statistical package will have that analysis as an option.

I'm so glad this was helpful for you!

You're very welcome!

Thank you so much!

This is such a great compliment. Very much appreciated, thank you!!

Nope. SE and SEM refer to the same thing.

I'm glad it was helpful!

Thank you. You are very welcome!

Thank you, you're very welcome!!

You would use the standard deviation that you calculated from your sample. That is the best estimate you have of the true population standard deviation.

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You're welcome!

Each treatment will have it's own mean and SEM, so in this case the SEM would be calculated with N=5. The idea of an "average SEM" comes into play when you are using an Analysis of Variance (ANOVA), where one of the assumptions is equality of variances, therefore all of the treatments should have the same estimate for the variance, and if balanced (same number of replicates for all treatments) the SEMs would also be the same.

Glad to hear it! I've been slacking lately but need to get back on it!

Exactly my same question, why is that sqrt of n down there? In other words, why taking something that is already a mean between all the observation and basically dividing this quantity again for all the observation? What that value, which comes from a single sample, which is basically the mean of a mean of distances from the mean, tell us about the population?

When you are comparing two populations, you are often comparing their means. The statistical tests used to compare means (t-test, ANOVA, etc) use the measure of uncertainty around your estimation of the mean (SE) as part of the calculation in determining if the two means are significantly different from one another (the more uncertainty there are in the estimates, the harder it would be to declare them significantly different). Because the distribution of sampling means (the distribution of the means of all possible samples taken of size n) becomes more narrow as n increase, the probability that any sample mean more truly represents the true population mean increases (therefore the SE is smaller in these calculations). This principle is called the law of large numbers. The formulas are based on mathematical properties.

Thank you!

Where ever we do not know the sd of population we can use the sample sd instead

Your mean and SD calculated from your sample are your best estimate of the population parameters, therefore you would use those to calculate your SE.

Yes!

@@biostatisticsbydesign thank u but if so then why do we need to find the CI from the Z tables? Why not take 2 SE to be the CI as 2 SE contain 95% of the means ie we are 95% sure that the true mean will lie within 2 SE.

The standard error (SE) measures how accurately a sample represents a population. It tells you how different the population mean is likely to be from a sample mean. The standard error is the average error that would be expected in using a sample mean as an estimate of the real population mean. The standard error is inversely proportional to the sample size. It tends to zero as the number of observations in the sample increases, so the sample represents the population more accurately (the "law of large numbers"). The standard deviation describes the variation between observations/individuals within a sample or population, and is an unbiased estimator, meaning that on average, the SD will not change as sample size increases. This is why we divide by the square root of N to estimate the SE.

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You're very welcome!