Statistically what does mean mean

This refers to any facts, observations, and information that come from investigations, and is the foundation upon which new knowledge is built. To paraphrase Author Co-nan Doyle "A theory remains a theory until it is backed up by data. Items are grouped according to some common property, after which the number of members per group are recorded e. In research, the target population includes all of those entities from which the researcher wishes to draw conclusions.

However, it is impractical to try to conduct research on an entire population and for this reason only a small portion of the population is studied, i. The inclusion and exclusion criteria will help define and narrow down the target population in human research.

Sampling refers to the process of selecting research subjects from the population of interest in such a way that they are representative of the whole population. Inferential statistics seek to make predictions about a population based on the results observed in a sample of that population. When determining sample size, most researchers would want to keep this number as low as possible for reasons of practicality, material costs, time, and availability of facilities and patients.

However, the lower limit will also depend on the estimated variation between subjects. Where there is great variation, a larger sample number will be needed. Statistical analysis always takes into consideration the sample size.

As Joseph Stalin put it, "A single death is a tragedy; a million deaths is a statistic. Their non-participation could result in an element of bias, and can only be ignored if their reasons for refusal will not affect the interpretation of the findings.

In the former, not every member of the population has a chance of being selected, while in the latter, they all do have an equal chance. It is NOT representative of the population. At each draw, every member of the population has the same chance of being selected as any other person. Tables of random digits are available to ensure true randomness. Strata may be chosen to reflect only one or more aspects of that population e. A starting point is then picked randomly and the person whose name falls in that position is taken as the first to be sampled.

A number of clusters are then randomly sampled. Generalizing the results obtained from a sample to the broad population must take into account sample variation. Even if the sample selected is completely random, there is still a degree of variance within the population that will require your results from within a sample to include a margin of error.

The greater the sample size, the more representative it tends to be of a population as a whole. Thus the margin of error falls and the confidence level rises.

It can come in many forms and can stem from many sources such as the researcher, the participants, study design or sample. The most common bias is due to the selection of subjects. For example, if subjects self-select into a sample group, then the results are no longer externally valid, as the type of person who wants to be in a study is not necessarily similar to the population that one is seeking to draw inferences about.

Examples of bias could be: Cognitive bias, which refers to human factors, such as decisions being made on perceptions rather than evidence; Sample bias, where the sample is skewed so that certain specimens or persons are unrepresented, or have been specifically selected in order to prove a hypothesis.

Memory Point - remember all the P's. Design relates to the manner in which the data will be obtained and analyzed. For this reason, consultation with a statistician is crucial during the preparation phases of any research.

Prior to embarking on the study one must already have determined the target population, sampling methods, sample size, data collection methods, and statistical tests that will be used to analyze the findings. Many studies fail or produce invalid results because this crucial step was neglected during the planning stages.

As William James commented "We must be careful not to confuse data with the abstractions we use to analyse them". Light et al were more blunt in stating "You can't fix by analysis what you bungled by design". In descriptive statistics, it often helpful to divide data into equal-sized subsets. For example, dividing a list of individuals sorted by height into two parts - the tallest and the shortest, results in two quantiles, with the median height value as the dividing line.

Quartiles separate data set into four equal-sized groups, deciles into 10 groups etc. Smaller samples are then taken and inferential statistics are used to make generalizations about the whole group from which the sample was drawn e.

Consider the issue of percentages versus percentage points - they are not the same thing. If a new law allows 10 homeowners to refinance, now only 30 mortgages are troubled. There was only one Indian student in the class who also happened to be a smoker. In the words of Henry Clay, one must still bear in mind that "Statistics are no substitute for judgement". I n all research, a certain amount of variability will occur when humans are measuring objects or observing phenomena.

This will depend on the accuracy of the measuring tool, and the manner in which it is used by the operator on each successive occasion. Thus, error does not mean a mistake, but rather it describes the variability in measurement in the study.

The amount of error must be recognized, delineated, and taken into account in order to give true meaning to the data. When humans are involved, the amount of error can be defined as inter-operator differences between different operators , or intra-operator differences when performed by the same operator at different times.

To overcome this, a certain number of objects are measured many times and by different people to detect the variation. This will then set the limits as to how accurate the results will be.

It can be tested by conducting inter-observer or intra-observer studies to determine error rates. Low inter-observer variation or error indicates high reliability. Results can have low accuracy but high precision and vice versa, which impact on the validity and reliability.

An example to illustrate this would be aiming an arrow at the centre of a target. If all arrows are close together and in the centre of the target you have high accuracy and precision Figure 1a.

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Statistical mean is a certain kind of mathematical average that's very useful in computer science, and in machine learning in particular. Simply speaking, the statistical mean is an arithmetic mean process, in that it adds up all numbers in a data set, and then divides the total by the number of data points. That's simple and straightforward, and so the arithmetic mean or statistical mean has been widely used throughout the modern era and into the age of computer programming. Here, we can differentiate the statistical mean from two other types of means that make up a group of three statistical methods called the Pythagorean means.

The other two means are called harmonic and geometric means. All three of these can be useful in machine learning and new kinds of artificial intelligence algorithm engineering.

In general, the statistical mean is helpful in all sorts of machine learning classification and decision-support tasks. Think of it this way — the program plots all the data points, and then uses the statistical mean to arrive at an average, which it uses to help the computer learn through its machine learning processes. The somewhat more complex harmonic mean and geometric mean can also be used in machine learning for specific things. For instance, the harmonic mean is often used to derive an "F-score" which helps evaluate data retrieval in a particular system.

Going back to the statistical mean, suppose you have five data points, and the total is Your statistical mean would be five, but you're not quite sure what each of those five numbers is. You could have three ones, a two and a twenty — or you could have a perfectly symmetrical five fives. You have a data set like the first example mentioned above, where the statistical mean skews a bit.

You might have a data set with the following five numbers — two, three, six, seven and