Analyzing categorical data #3 - Questions and Answers

Question 1 Indicate whether the following variables are categorical or numerical? If they are numerical, state whether they are discrete or continuous. (a) The price of randomly selected sweaters in a department store. (b) The first three digits of the social security number of randomly selected US residents. The eye color of randomly selected Columbia students. (c) The number of views of randomly selected YouTube videos. The speed of randomly selected cars on Broadway. Answer Quantitative data that can be described in terms of numbers, whether discrete or continuous, are referred to as numerical data. Discrete data have countable, finite or infinite integral values. All numerical values on a number line, including fractions and decimals, are accepted as continuous data. The number of pupils in a class and the number of sands on a beach are two examples of discrete data. Students' heights and weights are two examples of continuous data. In most cases, interval or ratio level of measurement is used for numerical data. Qualitative data is another name for categorical data. They exhibit qualitative traits like beauty and integrity, which is why they are sometimes referred to as attribute data. Since categorical data can either be named or ranked according to a certain preferred order, the level of measurement is nominal or ordinal. (a) The cost of a department store's randomly chosen sweaters is represented by numerical data. Each sweater is a discrete numerical variable since it can be counted as a distinct, non-negative integral number. (b) The social security numbers' first three digits constitute a categorical variable. This is so that, despite the fact that they are composed of numbers, they may be used to identify persons rather than to do any algebraic operations. A categorical variable is the eye color of the randomly selected Columbian students. This is so because people are categorized using qualitative or categorical factors like their gender, ethnicity, or hair color. (c) A discrete numerical variable is the number of views of YouTube videos that were chosen at random. The number can be counted whether it is finite or countably infinite, for this reason. A continuous numerical variable is the speed of certain autos on Broadway that are randomly chosen. This is because speed, when measured with a suitable and precise gauge, can take on any value (such as 120 mph, 120.1 mph, 120.2 mph, and so on). Question 2 What is cross tabulation? Answer Step 1 Chi square test is described as the form of a test that determines interdependence and also correlation between categorical variables. Step 2 Cross tabulation is described as the quantitative methodology of analysis of variables and relationship between them. It is important to mention that cross tabulation is also called as contingency table and it allows proper understanding of different types of variables and correlation between them. It is used in the industry of market research and the analysis is done on categorical data. Question 3 For the chi-square tests in the analysis of categorical data, the rejection region 1.is always located in the lower tail of the distribution. 2.is always equally split in the two tails of the distribution. 3.is always located in the upper tail of the distribution. 4.depends on the probability of a type II error. Answer Step 1 Chi-Square test for independence: In the test for independence, we test whether there is an association between the categorical variables. Null hypothesis: There is no association between the two categorical variables. Alternative hypothesis: There is an association between the two categorical variables. Step 2 Here, to test the association between categorical variables, the critical region is always located in the upper tail of the distribution. That is, Option 3 is correct. Question 4 What is the best measure of central tendency for 2 nominal level variables and why? Answer Step 1 Nominal scales are used, without any quantitative significance, to label variables. One might clearly call "labels" the "nominal" scales. A nominal scale represents a group attribute that doesnt