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DATA ANALYSIS FOR RESEARCH PROJECTS

DATA ANALYSIS FOR RESEARCH PROJECTS. TYPES OF DATA. Quantitative data measurements use scale with equal intervals examples include mass (g), length (cm), volume (mL), temperature ( o C or K) Qualitative data non-standard scales with unequal intervals or

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DATA ANALYSIS FOR RESEARCH PROJECTS

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  1. DATA ANALYSIS FOR RESEARCH PROJECTS

  2. TYPES OF DATA • Quantitative data measurements use scale with equal intervals examples include mass (g), length (cm), volume (mL), temperature (oC or K) • Qualitative data non-standard scales with unequal intervals or discrete categories examples include gender, choice, color scales

  3. Quantitative Scales of Measure

  4. Qualitative Scales of Measure

  5. Sample Data An experiment was conducted to measure the tensile strength of each of twelve pieces of two types of steel. The data from this experiment are given in the table to the right. Is there a significant difference in tensile strength between the two types of steel?

  6. Is there a better way to compare the data from these groups? • What have you used before to compare data from two different groups?

  7. It is difficult to decide (consistently) whether differences between experimental groups are significant • We need a rigorous procedure that includes a clear operational definition of dissimilarity.

  8. Statistics & Statistical Analysis • Statistical hypothesis-testing methods give us the ability to say with confidence that differences between groups are real and not just due to random chance, sampling errors, or other mistakes in data collection.

  9. Sample data for consideration… • For the following sets of data, discuss: • What was the IV and DV tested? • How should the data be processed to determine if the IV affects the DV? • How will you decide if the IV has a significant effect on the DV?

  10. Sample Data Set 1Effect of Temperature on the pressure of a sample of gas above water

  11. Graphing data • Correlation coefficient gives a measure of how strong the relationship is between the graphed variables. • Multiple trials can and should all be analyzed at the same time.

  12. Sample Data Set 2 Effect of Stress on the Height of Bean Plants after 30 Days

  13. Comparing levels of IV • If graphing the data is not appropriate, the different groups of the IV can be compared. • These types of statistics are called “Descriptive Statistics” since they: • describe the data sets • summarize groups of measurements

  14. Descriptive Statistics: Measure of Central Tendency attempt to provide one value that is most typical of the entire set of data What are some examples of measures of central tendency? Variation describes the spread within the data set * two sets of data with the same mean may have quite different spread within the data

  15. Appropriate Measures of Central Tendency and Variations for Types of Data

  16. What is “standard deviation”??? • The standard deviation is a statistic that tells you how tightly all the various examples are clustered around the mean in a set of data. This relates the variation in a set of data. • When the data points are pretty precise (close to the mean, little variation), the bell-shaped curve is steep, and the standard deviation is small. • When there is greater variation in the data, the bell curve is relatively flat. that tells you you have a relatively large standard deviation.

  17. SMALLEST VALUE FIRST QUARTILE THIRD QUARTILE LARGEST VALUE MEDIAN Displaying variation:Box-and-Whisker Plot • First Quartile (Q1) – smaller than 75% of ranked values • Median (Q2) – smaller than 50% and larger than 50% • Third Quartile (Q3) – smaller than 25% of ranked values

  18. Illustrating Distributions for qualitative data: Histograms • Symmetrical – mean equals median • Left-skewed – mean < median • Right-skewed – mean > median

  19. Statistical Hypothesis Testing • “A trend is apparent in the graph of the data, is this trend significant?” • “So the means of the groups are different, is the difference significant?” • Statistical hypothesis testing is needed to determine the significance in the results of your data analysis. • The results of these tests provide “Inferential Statistics.” We make inferential decisions based on the data we collect from a sample population.

  20. Sample Data Effect of Stress on the Height of Bean Plants after 30 Days

  21. Equal Sample Size t = = mean of Group 1 = mean of Group 2 = variance of Group 1 = variance of Group 2 = number of items or measurements Example for comparing means:t Test for Quantitative Data

  22. Statistical calculations • Use the TI-84 or TI-83 calculator OR • Use Microsoft Excel Data Analysis • Calculate the t-test for the stressed plants data on the next slide, using the graphing calculator

  23. Level of Significance Establish a level of significance In this class, use 0.05. this means the probability of error in rejecting the null hypothesis is 5/100 OR we can be 95% confident that the null hypothesis may be rejected

  24. Results from the calculator • t: value for the t-test • x1: mean from List 1 • x2: mean from List 2 • Sx1: standard deviation for List 1 • Sx2: standard deviation for List 2 • df: degrees of freedom • n1: number of values in List 1 • n2: number of values in List 2

  25. t-Test Results from Excel

  26. Statistical Hypotheses(different from your research hypothesis) Null Hypothesis suggests any observed difference between two sample means occurred by chance and is NOT significant state that there is no relationship between variables: i.e. two means are equal OR they are not statistically different Claim / Alternative Hypothesis derived from literature, research hypothesis suggests outcome of experiment if I.V. affects D.V.

  27. Null Hypothesis What would be the null hypothesis for this set of data? The mean height of stressed plants is not significantly different from the mean height of unstressed plants.

  28. Confidence Levels • Probability that findings are repeatable • Infers that results of sample are the same as results of the whole population • If we reject the null hypothesis at 95% confidence level: • 95% certainty that difference between groups is NOT due to chance • 95% certainty that results will be the same with further testing

  29. Confidence levels • Probablity of error: Error that occurs if null hypothesis is rejected when it is true and should not be rejected • Identified by Greek lowercase alpha, a • Researchers usually select a< 0.05 • If confidence level is 95%, then probability of error (a) is 5%, or 0.05

  30. Statistical Tests:Test Values and Critical Values • Test value – the result of a statistical test on your data. • Critical value – this is a reference value for each statistical test. • Your calculated statistical test value must exceed this value for you to reject the null hypothesis • You can find the critical value for each statistical test in publications and university websites. (links available on my website) • If you use Microsoft Excel for your statistics, the critical value will be given with the results.

  31. Significance of t value Determine the degrees of freedom df = (number in experimental group – 1) + (number in control group – 1) df = (10 – 1) + (10 – 1) = 18 Determine significance of calculated t by looking at table for critical t values Calculated t < critical t  not significant Calculated t > critical t  is significant At df = 18, t = 2.101; Calculated t of 1.24 < 2.101 and is not significant at 0.05 level.

  32. Rejecting Null Hypothesis If test value is not significant  null hypothesis is NOT REJECTED If test value is significant  null hypothesis is REJECTED

  33. Do Statistical Findings Support the Research Hypothesis? Null hypothesis was rejected = Research hypothesis was supported (unless research hypothesis IS a null hypothesis) Null hypothesis was not rejected = Research hypothesis was not supported

  34. Summary:Steps of Hypothesis Testing • State the null hypothesis and alternative hypothesis (claim) • Choose the confidence level (95%) and sample size • Collect the data and calculate the appropriate statistics • Make the proper statistical inference

  35. Populations of Study – Be careful what you claim! Sample specific portion of the population that is selected for the study ( 100 bean seedlings used in the study) Sampled Population population from which the sample was drawn (all the bean seedlings in the nursery from which the experimenter obtained their bean seedlings) Target Population ALL units (persons, things, experimental outcomes) of the specific group whose characteristics are being studied (all the bean seedlings of the same species)

  36. Communicating StatisticsEffect of Stress on the Mean Height of Bean Plants after 30 Days

  37. Types of Tests • For Quantitative Data: • Linear Regression • One-Way Analysis of Variance (ANOVA) • t Test • For Qualitative Data: • Chi-Squared Test • Z Test

  38. Linear Regression • Determines a linear relationship between two variables based on a correlation coefficient H0: The mass of M&M’s is not related to the surface area of M&M’s.

  39. ANOVA Test • Compares the means of more than two groups H0: There is no significant difference between the masses of plain M&M’s, almond M&M’s and peanut M&M’s.

  40. t-Test • Compares the means of two independent groups H0: There is no significant difference between the volume of plain M&M’s and peanut M&M’s. • Two-tail test determines if populations are not equal / the same (more difficult to support) • One-tail test determines if one mean is greater than the other (easier to support)

  41. Chi-Squared Test • Determines if a proportion within a sample is larger than expected; can be used for more than two groups H0: There are equal numbers of each color of M&M in a package.

  42. Z-Test • Compares proportions between two groups H0: There are equal proportions of red M&M’s in plain and peanut packages

  43. Selecting a Statistical Test Things to consider: • Number of groups of data • Type of data: Quantitative or Qualitative • Type of variable – numerical or categorical • The relationship in the null hypothesis being tested

  44. Statistical Tests Review • Comparison of two variables for correlation  correlation coefficient test • Comparing means of more than two groups/levels  ANOVA test • Comparing two means  t-test • Comparison of proportions within a population  X2 (chi-squared) test • Comparison of proportions between populations  Z test

  45. Key Questions for your Research: • What kind of data will you need to collect to test your hypothesis? (Qualitative or Quantitative) • What kind of scale will you use? • How do you plan on analyzing this data? • Comparison of groups? What will you compare? • Look for a trend? What will you graph? • How many different levels will you need data for? • How many trials? • What relevant qualitative data will you look for that may also help you interpret results?

  46. Data for ANOVA assignment Absorbance of Betacyanin Pigment from Beets Treated with Acetone

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