For quantitative studies, once you have prepared your data it is now time to analyze it. How you analyze data is heavily influenced by your research questions. Most studies involve the use of descriptive and or inferential statistics to answer the research questions. This post will explain briefly discussed various forms of descriptive statistics.
Descriptive statistics describe trends or characteristics in the data. There are in general, three forms of descriptive statistics. One form deals specifically with trends and includes the mean, median, and mode. The second form deals with the spread of the scores and includes the variance, standard deviation, and range. The third form deals with comparing scores and includes z scores and percentile rank
Trend Descriptive Stats
Common examples of descriptive statistics that describe trends in the data are mean, median, mode. For example, if we gather the weight of 20 people. The mean weight of the people gives us an idea of about how much each person weighs. The mean is easier to use and remember than 20 individual data points.
The median is the value that is exactly in the middle of a range of several data points. For example, if we have several values arrange from less to greatest such as 1, 4, 7. The number 4 is the median as it is the value exactly in the middle. The mode is the most common number in a list of several values arranged from least to greatest. For example, if we have the values 1, 3, 4, 5, 5, 7. The number 5 is the mode since it appears twice while all the other numbers appear only once.
Spread Scores Descriptive Stats
Calculating spread scores is somewhat more complicated than trend stats. Variance is the average amount of deviation from the mean. It is an average of the amount of error in the data. If the mean of a data set is 5 and the variance is 1 this means that the average departure from the mean of 5 is 1 point.
One problem with variance is that its results are squared. This means that the values of the variance are measured differently than whatever the mean is. To deal with this problem, statisticians square root the results of variance to get the standard deviation. The standard deviation is the average amount that the values in a sample are different from the mean. This value is used in many different statistical analysis.
The range measures the dispersion of the data by subtracting the highest value from the lowest. For example, if the highest value in a data set is 5 and the lowest is 1 the range is 5 – 1 = 4.
Comparison Descriptive States
Comparison descriptive stats are much harder to explain and are often used to calculate more advanced statistics. Two types of comparison descriptive stats include z scores percentile rank.
Z scores tells us how far a data point is from the mean in terms of standard deviation. For example, a z score of 3.0 indicates that this particular data point is 3 standard deviations away from the mean. Z scores are useful in identify outliers and many other things.
The percentile rank is much easier to understand. Percentile rank tells you how many scores fall at or below the percentile. For example, some with a score at the 80th percentile outperformed 80% of the sample.
Descriptive stats are used at the beginning of an analysis. There are many other forms of descriptive stats such as skew, kurtosis, etc. Descriptive stats are useful for making sure your data meets various forms of normality in order to begin inferential statistical analysis. Always remember that your research questions determine what form of analysis to conduct.