Statistical tools help in analyzing data and drawing conclusions from them. These tools play a crucial role in analyzing various investment opportunities. The analysis helps in forecasting of returns and understanding the risk. We will be discussing various statistical concepts in this reading.
Statistics refers to both data as well methods to collect and analyze data. Descriptive statistics describes the data by summarizing it effectively. Calculating mean, median, mode, standard deviation, etc. are examples of descriptive statistics. Inferential statistics involves in making forecasts, estimates, or judgments about a larger group from the observed smaller group. The inference about the larger group is made using the probability theory.
We will discuss descriptive statistics in this reading and inferential statistics in the later readings.
A population is defined as all members of a specified group. For example, if 70,000 candidates apply for the June CFA level I exam then that 70,000 number is the population. The population of presidents of the USA has 44 members as 44 members have served as the president of the USA. Any descriptive measure of a population characteristic is called a parameter. A population can have many parameters, but the important parameters related to investments are a mean value, the range of returns, and the variance of returns.
A sample is a subset of a population. Any descriptive measure of a sample is called a sample statistic. The sample is used when the population size is too big. Suppose you have to calculate the average height of the residents of China, then it would be very expensive to measure the heights of more than 1 billion people. In such cases, a sample is taken from the population and then average is taken and then the inference is made about the whole population.
Measurement Scales
We need to distinguish between different measurement scales to choose the appropriate statistical methods for summarizing and analyzing data. The four major scales for data measurement are nominal, ordinal, interval, and ratio.
Nominal scales categorize data but do not rank them. They don't provide much information about the data and represent the weakest level of measurement. Assigning names or number that do not reveal any rank can be termed as nominal scales. Assigning number 1 to government bonds and number 2 to corporate bonds is an example of nominal scale. This scale categorizes the bonds according to their issuer but does not rank them.
Ordinal scales categorize the data with respect to some characteristic and provide a rank for the data. Thus, these scales are stronger than the nominal scales. These can be both numeric and non-numeric. Ranking the bonds per their riskiness by the credit rating agencies like Moody's and S&P are an example of ordinal scales. These scales, however, do not tell the exact difference between the differently ranked data. For example, we cannot say that the difference between the A-rated bond and AA rated bonds is equal to the difference between AA rated and AAA rated bonds.
Interval scales provide both the ranking as well as the assurance that the differences between scale values are equal. For example, the temperature difference between 400C and 410C is equal to the temperature difference between 410C and 420C.
Ratio scales represent the strongest level of measurement. This scale has a true zero as the origin apart from all the characteristics of an interval scale. We can meaningfully take ratios as well add and subtract amounts within the scale. Rates of return and the money are measures in ratio scales. Temperature does not have a true zero because 00C does not mean the absence of temperature. It is just the freezing point of water. So, it is not a ratio scale but an interval scale. We cannot take ratio for the temperature. We cannot say that 400C is twice as hot as 200C. But in the case of money, we can say that $400 is twice of $200 because it has a true zero.
Next LOS: Parameter, sample statistic, and frequency distribution
