Statistics

A population is the entire group to which we want to generalize our results.  A sample is a subset of the population that we actually study.

A numerical summary of a population is called a parameter, while the same numerical summary of a sample is called a statistic.

Sampling error is the sample-to-sample variability in a statistic. (Note that the term “error” here does not mean that anyone has made a mistake.  “Error” here just refers to variability.) In general we do not know the population parameters that we are interested in.  Instead, we have to draw conclusions about them based on sample statistics … usually from a single sample. In principle, any relationship that we observe in a sample could reflect nothing more than sampling error.  In other words, this sampling error hypothesis is a possible explanation for any relationship that we observe in a sample.  It could just be a random thing that happened for this particular sample, but it is not true in the population in general.

Central limit theorem states that 

• the random sampling distribution of means will always tend to be normal, irrespective of the shape of the population distribution from which the samples were drawn.

• the mean of the random sampling distribution of means is equal to the mean of the original population.

Statistical Relationships

There are two basic kinds of statistical relationships

• relationship  between two group means - null hypothesis testing
• relationships between two quantitative variables - correlation and regression

Correlational Techniques - two basic kinds of co-relational techniques:

• Correlation
• Regression

Correlation simply expresses the strength and direction of the relationship between two variables in terms of a correlation coefficient. For interval or ratio scale data, Pearson product-moment correlation ( r ) and for ordinal scale data, Spearman rank-order correlation ( p/rho ) are used. Both these correlational techniques are linear and so if there is a very strong nonlinear relationship between tow variables, these two coefficient will underestimate the true strength of the relationship. Visual inspection of scattergrams is therefore invaluable.




Types of Data:

Potassium Replacement

The total body potassium of an adult is about 3500 mmol (50 mmol/kg body weight), decreasing with age.

To calculate the amount of potassium supplement, one should have an estimate of the potassium deficit.

On average, a reduction of serum potassium by 0.3 mmol/l suggests a total body deficit of 100 mmol. Based on this formula, a patient with a serum potassium of 2.6 mmol/l needs at least 300 mmol of potassium for the correction of the deficit.

In calculating the total body potassium deficit one has to consider factors that can independently affect serum potassium. A patient with a serum potassium of 2.6 mmol/l has less total body deficit at blood pH of 7.5 than 7.3. The reason is that alkaline serum pH (that is, 7.5) can independently lower the serum potassium by intracellular shift.