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# Descriptive Statistics

Search Community Search Community. Describe the advantages and benefits of using descriptive research methods. Describe the disadvantages and limitations of using descriptive research methods. Descriptive Method from hamidehkarimy. Descriptive Modules Home Teach Research. Page Options Share Email Link.

Share Facebook Twitter LinkedIn. Pinning this post will make it stay at the top of its channel and widgets. Instead, if you just want to get more knowledge about an object, without thinking of any special use of this knowledge, you can well select your methods on the basis of the input side, starting from theory and available new data. When selecting the method of analysis it is advisable to consider whether you can base your work on a theoretical model that is already known.

Sometimes a model, even a preliminary one, could help your work decisively, on the condition that you can handle it with a suitable method of analysis.

Three usual approaches which are discussed in more detail on the page Models in the Research Process are: If you choose an existing model as a starting point, its format will somewhat restrict your freedom in selecting the method of analysis.

For example, written models are most easily handled with the methods of case study or comparison, while mathematical models consisting of variables require quantitative methods for analysis. Whichever aspects of the objects you have chosen to collect and analyze, your logical method and tools of analysis must be able to handle them.

Once you have chosen the population about which you want to get information - or in which your findings will be applied - and have perhaps opted on the principle of sampling , you will have an idea about the number of cases or specimens that have to be studied.

In this respect there are two main approaches which require completely different methods of analysis: If just one or a few objects are studied it can be feasible to study the specimens as holistic entities with their inherent sets of characteristics, all of which are essential. Suitable methods for this are, among others, Case Study and Comparative Study. If there are hundreds or thousands of cases it will be possible to focus on just a few, important attributes of the objects.

Often you will want to measure these attributes, thus transforming them into variables. Possible methods include Classification, and the quantitative methods for the analysis of variables. Time perspective of the selected model and data also regulate the selection of analysis methods.

The principal alternatives are: Synchronic, or cross-sectional view includes no temporal dimension. It can be relevant when the object of study is more or less static, or when you just want to take a "snapshot" of the object and discover its internal or contextual structure, sometimes called a static invariance. Typical methods in synchronic study are explained on the pages about Case Study , Comparative Study and Classification.

Diachronic view, which means regarding the object of study as a process. In humanistic studies time span usually agrees with the life of man, but in natural sciences it can be anything from microseconds e. For a "longitudinal" analysis of dynamic invariances , that is, processes, change and development, you must select one of the diachronic or historical methods.

Logical Structures of Descriptive Analysis Among the options that were enumerated above, the most salient clues for selecting the method of analysis can be obtained by looking at the extent of data and at the time perspective. Once you have decided on these, you can find in the cells of the following table the most often used methods of analysis for each approach. The third taxonomy that was mentioned above, concerning the existence of earlier theory, is of minor importance and you can take it into account later when fine-tuning the method.

Synchronic study no time perspective: Diachronic study of change or evolution: Intensive study of a few cases which are often studied holistically, noting all their characteristics: Analyzing Development or evolution of people, social structures, products or fashions. Extensive study of a large number of cases, of which usually only a few properties are registered and studied: Remember, too, that once the analysis is finished, and before reporting its results, you should assess their validity.

Tools for Analysis The goal of analysis is to arrange the collected material so that the answer to the initial problem of the project reveals itself. In some distributions there is more than one modal value. For instance, in a bimodal distribution there are two values that occur most frequently.

Notice that for the same set of 8 scores we got three different values -- If the distribution is truly normal i. Dispersion refers to the spread of the values around the central tendency.

There are two common measures of dispersion, the range and the standard deviation. The range is simply the highest value minus the lowest value. The Standard Deviation is a more accurate and detailed estimate of dispersion because an outlier can greatly exaggerate the range as was true in this example where the single outlier value of 36 stands apart from the rest of the values.

The Standard Deviation shows the relation that set of scores has to the mean of the sample. Again lets take the set of scores:. We know from above that the mean is So, the differences from the mean are:.

Notice that values that are below the mean have negative discrepancies and values above it have positive ones. Next, we square each discrepancy:.

Now, we take these "squares" and sum them to get the Sum of Squares SS value. Here, the sum is Next, we divide this sum by the number of scores minus 1. Here, the result is This value is known as the variance. To get the standard deviation, we take the square root of the variance remember that we squared the deviations earlier.

This would be SQRT Although this computation may seem convoluted, it's actually quite simple. To see this, consider the formula for the standard deviation:. In the top part of the ratio, the numerator, we see that each score has the the mean subtracted from it, the difference is squared, and the squares are summed.

In the bottom part, we take the number of scores minus 1. The ratio is the variance and the square root is the standard deviation. In English, we can describe the standard deviation as:.

Although we can calculate these univariate statistics by hand, it gets quite tedious when you have more than a few values and variables. Every statistics program is capable of calculating them easily for you. The standard deviation allows us to reach some conclusions about specific scores in our distribution. Assuming that the distribution of scores is normal or bell-shaped or close to it!

For instance, since the mean in our example is

## Main Topics

Descriptive statistics are used to describe the basic features of the data in a study. They provide simple summaries about the sample and the measures. Together with simple graphics analysis, they form the basis of virtually every quantitative analysis of data.

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Descriptive or Summary Statistics. In many studies this is a first step, prior to more complex inferential analysis. The two main types of descriptive statistics encountered in research papers are measures of central tendency, (averages) and measures of dispersion.