Descriptive Statistics
Descriptive Statistics
1.1 Descriptive vs. Inferential
There are two main branches of statistics: descriptive and inferential. Descriptive statistics is used to say something about a set of information that has been collected only. Inferential statistics is used to make predictions or comparisons about a larger group (a population) using information gathered about a small part of that population. Thus, inferential statistics involves generalizing beyond the data, something that descriptive statistics does not do.
Other distinctions are sometimes made between data types.
• Discrete data are whole numbers, and are usually a count of objects. (For instance, one study might count how many pets different families own; it wouldn’t make sense to have half a goldfish, would it?)
• Measured data, in contrast to discrete data, are continuous, and thus may take on any real value. (For example, the amount of time a group of children spent watching TV would be measured data, since they could watch any number of hours, even though their watching habits will probably be some multiple of 30 minutes.)
• Numerical data are numbers.
• Categorical data have labels (i.e. words). (For example, a list of the products bought by different families at a grocery store would be categorical data, since it would go something like {milk, eggs, toilet paper, . . . }.)
Scales of Measurement
Statistical information, including numbers and sets of numbers, has specific qualities that are of interest to researchers. These qualities, including magnitude, equal intervals, and absolute zero, determine what scale of measurement is being used and therefore what statistical procedures are best. Magnitude refers to the ability to know if one score is greater than, equal to, or less than another score. Equal intervals means that the possible scores are each an equal distance from each other. And finally, absolute zero refers to a point where none of the scale exists or
1.1 Descriptive vs. Inferential
There are two main branches of statistics: descriptive and inferential. Descriptive statistics is used to say something about a set of information that has been collected only. Inferential statistics is used to make predictions or comparisons about a larger group (a population) using information gathered about a small part of that population. Thus, inferential statistics involves generalizing beyond the data, something that descriptive statistics does not do.
Other distinctions are sometimes made between data types.
• Discrete data are whole numbers, and are usually a count of objects. (For instance, one study might count how many pets different families own; it wouldn’t make sense to have half a goldfish, would it?)
• Measured data, in contrast to discrete data, are continuous, and thus may take on any real value. (For example, the amount of time a group of children spent watching TV would be measured data, since they could watch any number of hours, even though their watching habits will probably be some multiple of 30 minutes.)
• Numerical data are numbers.
• Categorical data have labels (i.e. words). (For example, a list of the products bought by different families at a grocery store would be categorical data, since it would go something like {milk, eggs, toilet paper, . . . }.)
Scales of Measurement
Statistical information, including numbers and sets of numbers, has specific qualities that are of interest to researchers. These qualities, including magnitude, equal intervals, and absolute zero, determine what scale of measurement is being used and therefore what statistical procedures are best. Magnitude refers to the ability to know if one score is greater than, equal to, or less than another score. Equal intervals means that the possible scores are each an equal distance from each other. And finally, absolute zero refers to a point where none of the scale exists or