Getting Started with Stats
From Stepping Up
| Letting the Numbers Talk |
| Stepping Up Guide |
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Data presentation is essential to attract interest and attention to your project. The easier way to communicate an idea is through a picture, be it a bar-graph, flow-chart, histogram, etc. In this guide, we will be giving hints on how to do this effectively.
We will also be investigating Statistics. Whenever there is data and a need for understanding the world, you need Statistics. Statistics help in handling variation in the data, reducing and summarizing data, interpreting data and drawing appropriate conclusions. Some questions that we can try to answer with statistics are: Is the global temperature increasing? Does vitamin C really prevent heart disease? Is a new engineering technique significantly better than the old one? We apply statistics to these questions to give us answers.
Sometimes, only one thing separates a science-fair project from excellence: the lack of simple statistical analysis. From the perspective of judges, good data analysis is important in science fair projects. Indeed, there is a 35 point section in the judging rubric that mentions "analysis of results using suitable graphs and statistics". Using stats can help you to determine the accuracy and clarity of your results. It can also provide "trustworthiness" to your conclusions.
On this page we wont be going through statistical methods, simply ideas that you should keep in mind when reading other sections.
One of the basic tenants of the scientific method is the idea of reproducibility: Will the same results be seen when the experiments are repeated? Scientists run the same experiments a number of times to see if the results are reproducible. However, there will always be some variation whenever experiments are repeated, due to experimental error. Statistical thinking helps determine whether differences observed between groups (e.g., control and treatment) are real or are just due to experimental error.Through the scientific method, a hypothesis proposes a model for your experiment. Then we look at the data. Is the data consistent with the model? Does it lend support to your hypothesis, or does it disprove the hypothesis? And what happens if the data is only *slightly* inconsistent with the model? What are the limits for deciding whether your hypothesis is right? Statistics allow us to establish a degree of "acceptance" or rejection". Mathematics is also useful in assessing the effects of measurement errors and other uncertainties in an experiment.
In the following guide, you will become well versed with natural variation of measurements, adequate sample sizes, graphing raw data properly for visual inspection, elimination of outliers, calculation of standard deviation and standard error of the data, and hypothesis testing. We will introduce you to Z-tests, T-tests, Chi Square, and when to use each. We will also go through normal distribution, linear regression, least-squares curve fit, and much more. The key is that statistics are used to get results and transition from the raw data to the conclusions.
Two types of statistics will be discussed:
- Descriptive Statistics are ways of using statistics to describe data, through plots and calculations such as average, standard deviation, IQR, etc.
- Inferential statistics are ways of inferring conclusions from the data. This includes the hypothesis test. This is the most powerful way that you can improve the quality of your science fair project.
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