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Introduction to Statistics
What is Statistics?
Statistics, as a subject matter, is a set of scientific principles and techniques that are useful in reaching conclusions about populations and processes when the available information is both limited and variable ; that is, statistics is the science of learning from data.
Questions Statistics Can Answer
- For the average person, are large doses of vitamin C beneficial?
- How can you analyze whether a diet really works?
Four Main Phases of Statistical Analysis:
- The Research Question - Any question about a population or process. When a census of the population is impossible to obtain, statistical techniques help us answer questions about the entire population based on information obtained from a subset of the population.
o Is asthma in children linked to their mother’s stress during pregnancy? Question studied by Harvard researchers.
- Design of the study and data collection – Plan for obtaining and analyzing data to be used to answer the questions of interest.
o The Harvard Medical School researchers chose to study 387 pregnant women. They decided to measure the stress level of the women and measure the level of Immunoglobulin (IgE) - a chemical linked to allergic responses - in the umbilical cord blood of each mother’s baby, when it was born.
- Descriptive statistics – Summaries of the data – both graphical and numerical summaries.
o The relevant numerical summaries of the data are the IgE averages for both the group of babies whose mothers were not stressed and the group of babies whose mom was stressed. They found that the average IgE level of the stressed mother babies was higher than the average IgE level of the non-stressed mom babies.
- Conclusions and Inferences – Inferences about a population or process based on the data.
o The Harvard researchers concluded that "This research adds to a growing body of evidence that links maternal stress, such as that precipitated by financial problems or relationship issues, to changes in children's developing immune systems, even during pregnancy.”
KEY POINT 1: Statistics concerns properties of populations. We can not use statistics to make predictions about particular individuals.
KEY POINT 2: The larger the sample size, the more information you have. The more information you have, the more willing people are to trust your results. Researchers spend a great deal of time determining what their sample size should be in order to obtain a certain degree of accuracy or to be able to detect differences that they deem important. Basically, no one wants to spend a lot of money on a study only to find out that their sample size was too small show them what they wanted to see.
KEY POINT 3: Determining the population and variables isn’t always easy. We frequently have to go about answering a question in an indirect manner. One very important method used to identify the population is to look at the subjects in the sample. The subjects in the sample were selected from the population, and so the population is made up of similar individuals.
Example: In 2002, I did a study to answer the following question: Is the fastest speed ever driven by the average male STAT 302 student greater than the fastest speed ever driven by the average female TAT 302 student? To gather data for my study, I took a simple random sample of 242 TAMU students, all of whom were enrolled in a STAT 302 course, and asked each the fastest speed they’d every driven. From this data, I determined that the average fastest speed ever driven by the males in the sample was 115 mph and the average fastest speed every driven by the women in the sample was 100 mph.
Using statistical techniques you’ll learn in this course, I can infer with reasonable confidence that the fastest mph ever driven by the average male STAT 302 student is a number between 111 and 119 mph and the fastest mph ever driven by the average female STAT 302 student is a number between 98 and 102 mph. Consequently, we can conclude that TAMU men, on average, have driven faster than TAMU women.
