Statistics are used everyday in life, and are very important in the everyday world. One important use of statistics is to summarize a collection of data in a clear and understandable way.
For example, if a psychologist gave a personality test measuring shyness to all 2500 students attending a small college, How might these measurements be summarized? There are two basic methods: numerical and graphical. Using the numerical approach one might compute statistics such as mean and standard deviation. These statistics convey information about the average degree of shyness and the degree to which people differ in shyness. Using the graphical approach you could create a stem and leaf display and a box plot. These plots contain detailed information about the distribution of shyness scores.
Graphical methods are better than numerical methods for identifying patterns in the data. Numerical approaches are more accurate and objective. Since the numerical and graphical approaches complement each other, you should use both. Inferential statistics Inferential statistics are used to draw inferences about a population from a sample. An example is, if ten people who performed a task after twenty-four hours without sleep scored 12 points lower than ten people who performed after a normal night’s sleep. Is the difference real or could it be due to chance? How much larger could the real difference be than the 12 points? These are the types of questions answered by inferential statistics.
There are two main methods used in inferential statistics: estimation and hypothesis testing. In estimation, the sample is used to estimate a parameter and a confidence interval about the estimate is constructed. In the most common use of hypothesis testing, a “straw man” null hypothesis is put forward and it is determined whether the data are strong enough to reject it. For the sleep deprivation study, the null hypothesis would be that sleep deprivation has no effect on performance.
The word “statistics” is used in several different senses. In the broadest sense, “statistics” refers to a range of techniques and procedures for analyzing data, interpreting data, displaying data, and making decisions based on data. This is what courses in “statistics” generally cover. In a second use, a “statistic” is defined as a numerical quantity (such as the mean) calculated in a sample.
Such statistics are used to estimate parameters. The term “statistics” sometimes refers to calculated quantities regardless of whether or not they are from a sample. For example, one might ask about a baseball player’s statistics and be referring to his or her batting average, runs batted in, number of home runs, etc. Although the different meanings of “statistics” can be confusing, a careful consideration of the context in which the word is used should make its intended meaning clear. Parameters A parameter is a numerical quantity measuring some aspect of a population of scores.
For example, the mean is a measure of central tendency. Greek letters are used to designate parameters. . Parameters are rarely known and are usually estimated by statistics computed in samples. To the right of each Greek symbol is the symbol for the associated statistic used to estimate it from a sample.
Measurement Scales Measurement is the assignment of numbers to objects or events in a systematic fashion. Four levels of measurement scales are commonly distinguished: nominal ordinal, interval, and ratio. There is a relationship between the level of measurement and the appropriateness of various statistical procedures. For example, it would be silly to compute the mean of nominal measurements.
Frequency polygon A frequency polygon is constructed from a frequency table. The intervals are shown on the X-axis and the number of scores in each interval is represented by the height of a point located above the middle of the interval. The points are connected so that together with the X-axis they form a polygon. Arithmetic Mean The arithmetic mean is what is commonly called the average: When the word “mean” is used without a modifier, it can be assumed that it refers to the arithmetic mean. The mean is the sum of all the scores divided by the number of scores.
The formula in summation notation is: mean where is the population mean and N is the number.
