1. STEM Fair Graphs & Statistical Analysis

2. Objectives: – Today I will be able to: Construct an appropriate graph for my STEM fair data Evaluate the statistical significance of my data using the appropriate statistical test Informal Assessment – students questions and responses to STEM Fair Discussions Formal Assessment – STEM fair data collection and analysis rubric Common Core Connection – Value Evidence – Use technology and digital media strategically and capably

3. Lesson Sequence Evaluate: Warm-Up Explain: Pass out STEM Fair Checklist Explain: Pass out STEM Fair Data Collection and Analysis Rubric Explain/ Evaluate: Review Data,Graphing and Statistics Expectations Evaluate: Exit Ticket

4. Warm - Up Convert the speed of 60 miles/ hour to meters/second. Note ( ): – 1 mile = 5280 feet – 3.28 feet = 1 meter

5. Objectives Today I will be able to: – Construct an appropriate graph for my STEM fair data – Evaluate the statistical significance of my data using the appropriate statistical test

6. Homework Study for the Lab Equipment and Safety Quiz tomorrow Work on STEM fair Data Analysis Section

7. Agenda Warm-Up Pass out STEM Fair Checklist Pass out STEM Fair Data Collection and Analysis Rubric Review Data,Graphing and Statistics Expectations Exit Ticket

8. Pass out STEM Fair Checklist and Data Collection and Analysis Rubric

9. Data

10. Data Tables Make sure the data tables include: – A title – Appropriate labels and SI units for both the dependent and independent variables – Averages of data Your graphs should be a representation of the averages of your data! Not all the data that you collect!

11. Graphs

12. What type of graph should I use to analyze my data?

13. Types of graphs Pie Chart – Used to compare parts to a whole (percentages) Bar Graph – compare values in a category or between categories. Multiple bar graphs compare relationships of closely related data sets. These graphs may be used to demonstrate relationships in non-continuous data or data intervals. DO NOT use for your STEM project

14. Types of Graphs Continued Time-Series Plot – dependent variable is numerical and the independent variable is time XY Line Graph – dependent and independent variables when both are numerical and the dependent variable is a function of the independent variable Scatter plot – Shows how two variables MAY be related to one another

15. Why do I need error bars on my graph?

16. Error bars Show variability in data Indicate error and/or uncertainty in measurement A larger size error bar means the measurement/ data collected is not as accurate Error bars should be one standard deviation in length

17. What is standard deviation?

18. Standard Deviation Determines validity of data set for each testing group If data points are close to the average, there is a small standard deviation and the data is valid If the standard deviation is large, the data points are not close to the average and the validity of the data is questioned

19. What is the coefficient of correlation (r)?

20. Coefficient of Correlation (r) used to fit a straight line (best-fit) to sample data to summarize the relationship between x and y values. Sample correlation coefficient (r) is calculated to measure the extent to which x and y are linearly related. – Example would be looking at the relationship between % salinity in water (x) and nitrate level (y). Example of results would be that a simple linear regression model explained 91.3% of total variation in nitrate level by relating it to salinity

21. Coefficient of Correlation (r) Only use if graph is a line graph or scatterplot (not for time series) Describes the direction and strength of 2 sets of variables Calculate when the line of best fit is made on a graph in excel R Values – Positive Correlation = Direct relationship for data – Negative correlation = Indirect relationship for data – r = 0, no correlation – r < 0.5, weak correlation – r > 0.8, strong correlation – r = 1 perfect correlation

22. Coefficient of Correlation examples

23. Graphing Checklist Discuss with a partner: – What type of graph is being used to analyze the data? Is this graph the correct choice? – Are error bars used? – Can my scatterplot have a line of best fit? Should a coefficient of correlation be calculated?

24. STEM Fair: Statistical Analysis

25. Summary Statistics Mean – represents population mean (calculated same as the average) Standard Deviation – shows the variability of an observation in a sample

26. Summary Statistics Cont. Confidence Interval - the width of the interval shows how precisely the value of the mean is known Shows the degree of confidence that our mean is between two values typically a 95% CI is used

27. Steps to Completing Statistical Analysis 1.Data collection & input 2.Data summary & reduction 3.Data analysis: Perform statistical test(s) and draw conclusion

28. Drill What is an independent variable? What is a dependent variable What is a control?

29. Types of graphs Pie Chart – Used to compare parts to a whole (percentages) Bar Graph – compare values in a category or between categories. Multiple bar graphs compare relationships of closely related data sets. These graphs may be used to demonstrate relationships in non-continuous data or data intervals. Sadly, Bar Graphs May be Used

30. Types of Graphs Continued Time-Series Plot – dependent variable is numerical and the independent variable is time XY Line Graph – dependent and independent variables when both are numerical and the dependent variable is a function of the independent variable Scatter plot – Shows how two variables MAY be related to one another

31. Test Assumptions Most statistical tests have assumptions that should be met such as: Data follows a normal population distribution & Large enough sample size to detect change. We are ignoring statistical test assumptions for this project.

32. Types of Statistical Tests Paired T-Test Unpaired T-Test ANOVA Chi-Square Coefficient of Correlation

33. T-Tests This test is used to compare the data from two different testing groups to determine if they are significantly different. There are two different types: PAIRED: Used when the data consist of pairs of observations on the same person or object. Example: comparing the heart rate of individuals before and after watching a scary movie. UNPAIRED: Used when the data from one group are not directly linked to the data of the other group. Example: comparing the effect of red light versus blue light on the growth of plants.

34. ANOVA This test is used to determine whether there are any significant differences between the means of three or more independent (unrelated) groups. Example: determining whether exam performance differed based on test anxiety levels amongst students. Students are divided into three independent groups (e.g., low, medium and high-stressed students). Most of you will be doing this type of test!

35. Chi-Square Test This test is used to determine if there are differences between two or more frequency distributions. Both independent and dependent variables need to be categorical data. Example: comparing the foraging height (upper, middle, and lower) of yellow warblers in different tree species (oak, maple, aspen, and hazel).

36. Analyzing the Test Results Two possible conclusions after carrying out a test – Reject Hypothesis – Fail to reject Hypothesis (we can never accept the alternative hypothesis)

37. Analyzing the Test Results (cont.) P-values – one way to report the result of an analysis is by saying whether or not the hypothesis was rejected at a specified level of significance (we will use.05) The smaller the calculated p-value, the greater the difference between the groups. Example: the difference in means from our testing groups is statistically significant at the.05

38. Discuss with a partner What type of statistical test should I use to analyze my data?

39. STEM Fair Data Collection and Analysis Due: September 27 Mr. Klotz’s Expectations: – Data Tables – Appropriate Graphs – Complete Statistical Analysis Worksheet and Place in the Folder

40. Exit Ticket What questions do you have about the Data Collection and Analysis Section?