What is the difference between descriptive and inferential statistics?

'''Descriptive Statistics''' are a group of procedures that summarize data graphically and statistically. Descriptive statistics are designed to describe a sample, and is contrasted with Inferential Statistics which is designed to draw conclusions from the sample to the larger population. [[Image:Fe40.png]] - Imagine you conduct a study to determine whether males or females are happier. After collecting data on 1000 subjects you could use "Descriptive Statistics" to identify characteristics of the sample, such as the mean happiness levels, ranges of scores, standard deviation, and so forth; and you could use "Inferential Statistics" to identify if your sample of data generalizes toward the larger population of males and females beyond those in your study.

'''Inferential Statistics''' are designed to draw conclusions about a population from a sample of data, and is contrasted with Descriptive Statistics which is designed to describe only the sample. [[Image:Fe40.png]] - Imagine you conduct a study to determine whether males or females are happier. After collecting data on 1000 subjects you could use "Descriptive Statistics" to identify characteristics of the sample, such as the mean happiness levels, ranges of scores, standard deviation, and so forth; and you could use "Inferential Statistics" to identify if your sample of data generalizes toward the larger population of males and females beyond those in your study.



'''What is the theory behind Inferential Statistics?''' If Inferential Statistics allow you to draw conclusions from a sample to the larger population, how do we know the conclusions are accurate? How researchers address that question is the heart of statistical reasoning: 
*We will never know with 100% confidence that the results of the study can generalize toward the intended population (unless and until we study the entire population) but we can determine the probability or percentage of our confidence in the accuracy of the study results by using probability distributions.
*A probability distribution describes the frequency or probabilities that an event can take. [[Image:Fe40.png]] - If you flip a coin, there are two possible outcomes – Heads and Tails. So the probability of each one occurring is 1/2 or 50%. If you asked someone how likely it is that a flipped coin would come up heads, the answer is 50%. For a more complex example, think of a distribution of IQ scores. How likely is it that someone would score a 160? By using a probability distribution of IQ scores, such as the example one below, you could calculate the frequency of people who score 160 (or who score above 160, or who score below 80, and so forth). <center>[[Image:OUTPUT0.png|400px]]</center>
*Using probability distributions, statisticians have created a process for establishing the probability that the results from a sample are accurate of the population. Statisticians have created all possible probability distributions for every possible statistical situation. The process involves comparing your sample to the appropriate probability distribution. If there is a low probability that the results of your sample are due to chance, then we accept the results of the study as accurate to the population. 
*How low does the probability have to be? In the social sciences, researchers have agreed as a field upon a '''5% or less''' probability level. In other words, if there is less than a 5-percent probability that your results were due to chance, then we deem the results as "significant". Probability is written as "p", so significance is written as "p<u><</u>.05". 



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