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What is the ordinal scale in statistics?
An ordinal scale is a method of categorising observation according to a scheme in which there is a sense of ordering between categories but the difference between categories is variable and unspecified. For example, the scale {strongly disagree, disagree, neither disagree nor agree, agree, strongly disagree}.
How is the interval scale more sophisticated than the nominal and ordinal?
In an ordinal scale it is possible to order the categories by some measure. However, it is not possible to know if the difference between the categories is the same or different.For example, clothing items may be classed as extra small (XS), small (S), medium (M), large (L) and extra large (XL). This is an ordinal scale since you know that the sizes increase in the order in which these have been listed. But you do not know if the difference between S and M is the same as the difference between L and XL (or each adjacent pair).Another example is attitude surveys where answers may be "strongly disagree", "disagree", "neither disagree not agree", "agree", "strongly agree".In an ordinal scale it is possible to order the categories by some measure. However, it is not possible to know if the difference between the categories is the same or different.For example, clothing items may be classed as extra small (XS), small (S), medium (M), large (L) and extra large (XL). This is an ordinal scale since you know that the sizes increase in the order in which these have been listed. But you do not know if the difference between S and M is the same as the difference between L and XL (or each adjacent pair).Another example is attitude surveys where answers may be "strongly disagree", "disagree", "neither disagree not agree", "agree", "strongly agree".In an ordinal scale it is possible to order the categories by some measure. However, it is not possible to know if the difference between the categories is the same or different.For example, clothing items may be classed as extra small (XS), small (S), medium (M), large (L) and extra large (XL). This is an ordinal scale since you know that the sizes increase in the order in which these have been listed. But you do not know if the difference between S and M is the same as the difference between L and XL (or each adjacent pair).Another example is attitude surveys where answers may be "strongly disagree", "disagree", "neither disagree not agree", "agree", "strongly agree".In an ordinal scale it is possible to order the categories by some measure. However, it is not possible to know if the difference between the categories is the same or different.For example, clothing items may be classed as extra small (XS), small (S), medium (M), large (L) and extra large (XL). This is an ordinal scale since you know that the sizes increase in the order in which these have been listed. But you do not know if the difference between S and M is the same as the difference between L and XL (or each adjacent pair).Another example is attitude surveys where answers may be "strongly disagree", "disagree", "neither disagree not agree", "agree", "strongly agree".
How does an ordinal categorical variable works.?
An ordinal categorical variable is often used in questions for which the responses can be put into some kind of natural order but where the difference between categories is not the same. One example may be where the respondent is asked to class statements as "disagree strongly", "disagree", "neither disagree nor agree", "agree", and "agree strongly". There is a natural progression in the response but the difference between "disagree strongly" and "neither ... " [2 steps] may not be the same as that between "disagree" and "agree" [also 2 steps].The results of any analyses which attaches numerical value to the answers for processing is sensitive to the coding system used. The results with the answers coded as {1, 2, 3, 4, 5} will be quite different to those coded {1, 4, 10, 20, 25}.
What is ordinal and nominal scale?
A nominal scale is one in which the data are categoric, for example, pet animal, town, colour of eyes. There is no order in the categories. A dog is not "more" or less than a "cat". An ordinal scale in which there is an implied ordering but this is based on an arbitrary scale. The difference between a pair of adjacent categories may or may not be related to the difference between another pair. Typical survey questionnaires with answers categorised as: "strongly disagree, disagree, neither, agree, strongly agree".
What is an ideal measure of central tendency?
It depends primarily on the nature of the data. If the data are qualitative data then the only option is the mode. Sometimes data can be ordered but the interval between adjacent categories is not always the same. An example of such data might be answers to a questionnaire where the answers are "strongly disagree", "disagree", "agree" and "strongly agree". The difference between strongly disagree and disagree may not be comparable to the difference between disagree and agree. In such cases, the median is readily available but the mean depends on arbitrarily assigned weights (for the categories). You can have interval data, in which the values of the variable are known and the differences between the values are also quantified. In such cases both the mean and median may be used. The median is generally preferred for skewed data since it is not greatly affected by outliers. For more symmetric data sets there is little to choose between the median and the mean since they will be close together. However, by the Central Limit Theorem, the mean result from repeated trials will tend towards the population mean. The sample mean is a maximum likelihood unbiased estimate of the population mean. Also, the means are often one of the parameters of parametric statistical distributions. The distribution of the mean of repeated trials has been extensively studied and there are many efficient tests for testing hypotheses concerning the mean.
