Assignment 2 Worksheet-Statistical Tests-F23

BIOL 1000 – Fall 2023 Assignment 2: Using Statistical Tests for Data Analysis Assignment 2 Worksheet Questions Complete all of the questions highlighted in yellow on this Worksheet, then transfer your answers to the questions provided in the Assignment Submission Dropbox by the deadline of Monday October 30, 2023 (by 11:59 p.m.). Name: Student ID: Answer all of the highlighted questions on this Worksheet in the space provided. There are 25 questions. Keep your answers brief and concise. PART A: Questions on EXPERIMENTAL DESIGN Question 1: Give one suitable question for this study based on the information provided in the study scenario. Question 2: State a research hypothesis that can be tested in a study of hummingbird feeding behaviour. Express the research hypothesis in your own words . Question 3: State the prediction that follows from the research hypothesis suggesting a design for a study to test the hypothesis. Use an " If …. then …" statement. Express your answer in your own words and keep answer brief (less than 50 words). Question 4: When deciding on the most appropriate statistical test to be used for data analysis, what is the main distinction between using the Chi-square Test or using the Student’s t Test. Answer this question in your own words. (Be concise using less than 50 words). PART B: Chi-square Analysis There are two problems requiring the use of the Chi-square Test: − Problem 1 - analyzes data from a field study on the flower colour preferences of the Rufous Hummingbird population near Kelowna, B.C. (August 2022) − Problem 2 - analyzes data from a field study on the flower colour preferences of the Calliope Hummingbird population near Kelowna, B.C. (August 2022) 1

BIOL 1000 – Fall 2023 Assignment 2: Using Statistical Tests for Data Analysis Question 5: State the Null Hypothesis (Ho) for a Chi-square Test for Problems 1 and 2. Question 6: State the Alternative Hypothesis (H A ) for a Chi-square Test for Problems 1 and 2. PROBLEM 1 – A Study of Feeding Behaviour by Rufous Hummingbirds Results: The data from the Kelowna Study of the number of flower visits by Rufous hummingbirds to a variety of flower colours were collected and summarized in Table 1 below. These data will be analyzed using the Chi-square Test in Problem 1 on this Worksheet. The Chi-square Test analysis is summarized in Table 2 . Table 1. Average number of visits by Rufous hummingbirds to flowers of various colours over a one-hour observation period at the Kelowna B.C. field study site in August 2022. Average of 10 observation periods. Table 2. Chi-Square analysis of behaviour of Rufous hummingbirds at the Kelowna B.C. field study site. CATEGORIES (description of Flower Colour) OBSERVED NUMBER OF VISITS / HOUR (from Table 1) EXPECTED NUMBER OF VISITS / HOUR (= based on Ho) CHI-SQUARE VALUE (Obs.-Exp.) 2 Expected Purple Flowers Blue Flowers Yellow Flowers Orange Flowers Red Flowers TOTAL For your data analysis, refer to Week 4-Lecture 8 and the other posted resources to find the steps that are to be followed to calculate the Chi-Square Value for each flower colour and the total Chi- square value as well as to determine the degrees of freedom (df) for the data in Table 2. 2 Colour of Flower Blue Orange Purple Red Yellow Number of times that Rufous Hummingbirds visited flowers over a 1 hour period of study 64 78 48 89 71

BIOL 1000 – Fall 2023 Assignment 2: Using Statistical Tests for Data Analysis Problem 2 – A Study of Feeding Behaviour by Calliope Hummingbirds Results: The data from the study of the number of flower visits by Calliope hummingbirds to a variety of flower colours were collected and summarized in Table 3 below; these data will be analyzed using the Chi-square Test in Problem 2 on this Worksheet. The Chi-square Test analysis is summarized in Table 4. Table 3. Average number of visits by Calliope hummingbirds to flowers of various colours over a one-hour observation period at the Kelowna B.C. field study site in August 2022. Average of 10 observation periods. Colour of Flower Blue Orange Purple Red Green White Yellow Number of times hummingbirds visited flowers over a 1 hour period of study 71 89 73 96 68 81 82 Table 4. Chi-Square analysis of behaviour of Calliope hummingbirds at the Kelowna B.C. field study site. CATEGORIES (description of Flower Colour) OBSERVED NUMBER OF VISITS (from Table 1) EXPECTED NUMBER OF VISITS (= based on Ho) CHI-SQUARE VALUE (Obs.-Exp.) 2 Expected Blue Flowers Orange Flowers Purple Flowers Red Flowers Green Flowers White Flowers Yellow Flowers TOTAL For your data analysis, refer to Week 4-Lecture 8 and the other posted resources to find the steps that must be followed to calculate the Chi-Square Value for each flower colour and the total Chi- square value as well as to determine the degrees of freedom (df) for the data in Table 4. Question 11: Use the Chi-Square Analysis Table ( Table 4 in this Assignment 2 Worksheet ) and the Table of Critical Chi-square Values ( Table A from Assignment 2 folder entitled “Resources for Statistical Analyses” ) to determine the answers to the following questions. (a) The number of categories (n) (with no decimal places) involved is (b) The degrees of freedom (df) (with no decimal places) are (c) The calculated Chi-Square value (to 2 decimal places) that was obtained in Table 4 (above) is 4

BIOL 1000 – Fall 2023 Assignment 2: Using Statistical Tests for Data Analysis (d) The critical Chi-Square value (to 2 decimal places) that was obtained from Table A (posted in Assignment 2 Resources folder) is Question 12: What is your Conclusion from the Chi-square Test analysis after comparing your calculated Chi-square value (from Table 2 above) and the Critical Chi-square value (from Table A provided with the Assignment 2 Instructions and Worksheet)? Choose one answer. A. fail to reject the null hypothesis (Ho) B. reject the null hypothesis (Ho) Question 13: Briefly explain your answer to Question 12 (do not exceed 50 words). Question 14: State your conclusion to your statistical analysis and relate it back to your Research Hypothesis . Use the format for reporting statistical results given in Week 6-Lecture 11 on writing the text for a results section. ( Answer this question in your own words. Keep your answer brief - do not exceed 100 words). 5

BIOL 1000 – Fall 2023 Assignment 2: Using Statistical Tests for Data Analysis Question 19: State the Alternative Hypothesis (H A ) for this Student’s t Test analysis Problem 3 – A Comparative Study of Visiting Times to Red Flowers by Two Species of Hummingbirds Student’s t Test Analysis for Problem 3 – fill in each of the steps for data analysis below Results: data were collected and summarized in Table 5 below ; these data will be analyzed using the Student’s t test A survey was conducted on two hummingbird species that are found together at a field study site in Kelowna B.C. The average amount of time (in seconds) that each of 35 individual hummingbirds from each of the two species spent feeding at 10 individual red flowers over a 12-hour period in August 2022 was recorded. These data require a Student’s t Test for a statistical analysis of the feeding behaviour based on the length of time spent feeding. To save time entering these data into Excel and to avoid making any data entry errors, you can copy and paste this data table (Table 5) directly into Excel and then complete the necessary calculations to complete Table 6. 7

BIOL 1000 – Fall 2023 Assignment 2: Using Statistical Tests for Data Analysis Table 5. Average time (in seconds) spent feeding at 10 different red flowers at the Kelowna Study Site by 35 individual Rufous hummingbirds and 35 individual Calliope hummingbirds over a 12-hour period in August 2022. Sample Average time (in sec) spent feeding on individual red flowers Bird # Rufous Hummingbirds Calliope Hummingbirds 1 43 51 2 37 48 S 54 44 4 40 46 5 49 52 6 43 48 7 42 65 8 42 45 9 46 64 10 34 45 11 42 44 12 35 53 13 66 49 14 35 43 15 33 33 16 35 43 17 44 34 18 33 55 19 45 53 20 38 44 21 64 47 22 55 46 23 38 65 24 46 38 25 52 57 26 60 47 27 54 43 28 59 52 29 58 43 30 46 56 31 26 43 32 32 49 33 31 47 34 43 38 35 25 42 For your data analysis, refer to the posted resources to find the steps that must be followed to calculate the sample t statistic and determine the degrees of freedom (df) for the data in Table 5. 8

BIOL 1000 – Fall 2023 Assignment 2: Using Statistical Tests for Data Analysis Question 22: Use the summary of the Student’s t Test analysis ( provided in Table 6 above) and the Critical t Values (provided in Table B) to determine the p -value and interpret the results of this analysis. (a) The total sample size (n) (with no decimal places) for both species combined is (b) The degrees of freedom (df) (with no decimal places) are (c) The Calculated t Value (from Table 6) (with 3 decimal places) is (d) The Critical t Value (at p =0.05) from the Critical t Table (Table B in Assignment 2 Resources folder) (with 3 decimal places) is (e) The probability ( p value) from calculations in Excel (with 2 decimal places) is Question 23: What is your Conclusion from the Student’s t Test analysis after comparing your calculated t -value (from Table 6 above) and the Critical t -value (from Table B provided with the Assignment 2 Instructions and Worksheet)? Choose one answer. A. fail to reject the null hypothesis (Ho) B. reject the null hypothesis (Ho) Question 24: Briefly explain your answer to Question 23 (do not exceed 50 words) . Question 25: State your conclusion to your statistical analysis and relate it back to your Research Hypothesis . Use the format for reporting statistical results given in Week 6-Lecture 11 on writing the text for a results section. ( Answer this question in your own words. Keep your answer brief - do not exceed 100 words). 10