Fluent Essays

QUESTION 1 1. Ten students took part in this study, the teacher was interested in knowing if the age of the participant was related to the amount of gaming usage.  In the next slide, you will find a table that ranks the student’s respective age and his or her gaming usage. Complete the appropriate test and write up the results according to the handbook. QUESTION 2 A researcher gave 9 participants two different test that measure self-esteem to see if there is a relationship between the tests.  Are they significantly similar? Complete the appropriate test and write up the results according to the handbook. QUESTION 3 A state administrator was assigned two counties to evaluate their ACT performance.  He wanted to know if there was a difference between ACT scores in the districts even though they use the same curriculum.  Complete the appropriate test and write up the results according to the handbook. QUESTION 4 A business leader wanted to which employee preparation program prepared her employees for success.  All employees completed an assessment to determine knowledge and performance.  Was there a difference in their success based on their preparation?  Complete the appropriate test and write up the results according to the handbook. QUESTION 5 In a store, items were either placed in proximity to similar items, or with items that may be used together. 68 females and 42 males participated in the study. 49 females purchased similarly placed items, and 10 males purchased similarly placed items.    Does product placement have an effect on consumer purchasing? QUESTION 6 A teacher wanted to know an intervention in her stats class made a difference in student scores.  She gave the students a pre-test before the intervention, and a post-test after the intervention. Complete the appropriate test and write up the results according to the handbook. Inferential Statistics Final Review Session Review for final Can you read, write, and analyze statistics? 2 Pop Quiz: What test would you select… Examining differences between pre-post scores of the same students. Examining similarities between student’s math & science scores. Analyzing if there is a relationship between males and females passing/failing driving tests. Determining if there is a difference between 5 schools monthly # of discipline infractions. Examining if there is a similarity between elementary and middle school students ranked incentives for test performance. After an ANOVA reveals a significant difference in groups. 3 Pop Quiz: Answers Examining differences between pre-post scores of the same students. Examining similarities between student’s math & science scores. Analyzing if there is a relationship between males and females passing/failing driving tests. Determining if there is a difference between 5 schools monthly # of discipline infractions. Examining if there is a similarity between elementary and middle school students ranked incentives for test performance. After an ANOVA reveals a significant difference in groups. Paired Sample t-test The students would be matched in each row, and scores reported in columns. Regression test The students would be matched in each row, and the scores placed in the columns. Chi-Square Test Male/female and pass/fail observations in a 2X2. ANOVA Each school would be a separate column, and the number of infractions placed in the rows. Spearman’s r s In one column place the rank for the incentives for elementary, and in the second column place the ranks for incentives for middle school. Independent Sample t-test Run separate t-tests for each combination. 4 If each test was significant (p<.05)… Examining differences between pre-post scores of the same students. Examining similarities between student’s math & science scores. Analyzing if there is a relationship between males and females passing/failing driving tests. Determining if there is a difference between 5 schools monthly # of discipline infractions. Examining if there is a similarity between elementary and middle school students ranked incentives for test performance. After an ANOVA reveals a significant difference in groups. Paired Sample t-test There was a significant difference between student’s pre-post test results. Look at the means… Regression test There was a significant relationship between student’s math and science scores. Chi-Square Test Gender is related to passing or failing driving tests. Look at which gender passed at a higher rate. ANOVA There is a significant difference between number of discipline infractions at the different schools. Run a post-hoc test to determine diff. Spearman’s r s There is a similarity between incentive preference. Age did not affect preference. Independent Sample t-test There was a significant difference between group A and group B. Wait! What do the results really mean? 5 Review basic concepts: What is the difference between descriptive and inferential statistics? Calculate and define: Mean, Median, Mode, Range Define and describe distributions: normal, bimodal Parametric vs. nonparametric testing Quantitative research vs. qualitative research Research questions and hypothesis testing Research questions guide our decisions and determine our statistical tests (see last week’s lesson for a deeper discussion) 6 Inferential Statistics When p < .05… When p > .05… Identify when to use, calculate, report (according to handbook), and interpret: Spearman’s rs Chi-Square Paired Samples t-test Independent Samples t-test ANOVA (and post-hoc testing) Regression/Pearson Product Moment r Correlations and cause/effect relationships < means we reject the null hypothesis, assume results more extreme occur fewer than 5 times in 100 Means we do not reject the null, we can’t rule out random chance Spearman’s rs-ranked data, correlations Chi-square- observed data, counts Paired sample-logically paired data, pre/post opposite of Pearson/regression Independent- differences in data ANOVA- differences in 3 or more, indep. T-test for post hoc, Tukey’s HSD, or other appropriate test Regression or Pearson 7 Final Thoughts… Thank you for your participation and effort in this class. Final is due by midnight (EST). Final practice test Select the correct test, apply the test, and communicate the answer according to the handbook. 1. What effect does noise pollution have on helpfulness? A person with a cast on one arm gets out a car and drops an armload of books in front of pedestrians. Will the pedestrians help? Maybe. Sometimes there was a loud gasoline lawn mower operating nearby when the books were dropped and sometimes the mower was not operating. Of the 25 pedestrians who could have helped when the mower was operating, four did so. Of the 25 who could have helped when the mower was quiet, 20 did so. Of the 25 who could have helped when the mower was operating, four did so. The chi square test is the best choice. The results were significant, (, (X2 [1, N=50] = 20.51, p < .001). Reject the null hypothesis. Pedestrians are significantly less likely to help in the presence of a loud noise.   Observed Expected (O-E)2 (O-E)2 /E noise helped 4 12 64 5.333333 no noise helped 20 12 64 5.333333 noise did not help 21 13 64 4.923077 no noise did not help 5 13 64 4.923077 X2 20.51282 2. A leader wanted to know if there was a difference in employee attendance rates based on the shift that employees work. Here is the data: First shift Second shift Third shift 0 2 3 1 1 2 1 2 4 1 1 1 1 1 3 0 1 2 1 2 4 2 1 1 3 Perform the test, report the results, and complete any additional tests. Answer: The ANOVA is the best choice. There was a significant difference between the employee attendance based on shift, (f [2,22] = 9.60, p < .01). Post hoc independent sample t-tests were conducted. There was a significant difference between attendance between first (M = .89) and second shift (M=1.42), (t [14] = 1.87, p < .05). There was a significant difference between first (M = .89) and third shift (M= 2.56), (t [16] = 3.91, p < .01). There was a significant difference between second shift (M=1.42) and third shift (M= 2.56), (t [14] = 2.42, p < .05). Anova: Single Factor SUMMARY Groups Count Sum Average Variance First shift 9 8 0.888889 0.361111 Second shift 7 10 1.428571 0.285714 Third shift 9 23 2.555556 1.277778 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 12.9346 2 6.467302 9.597088 0.001008 3.443357 Within Groups 14.8254 22 0.673882 Total 27.76 24           First shift Second shift Mean 0.888888889 1.428571429 Variance 0.361111111 0.285714286 Observations 9 7 Pooled Variance 0.328798186 Hypothesized Mean Difference 0 df 14 t Stat -1.867600341 P(T<=t) one-tail 0.041446865 t Critical one-tail 1.761310136 P(T<=t) two-tail 0.082893729 t Critical two-tail 2.144786688     First shift Third shift Mean 0.888888889 2.555556 Variance 0.361111111 1.277778 Observations 9 9 Pooled Variance 0.819444444 Hypothesized Mean Difference 0 df 16 t Stat -3.905667329 P(T<=t) one-tail 0.000629328 t Critical one-tail 1.745883676 P(T<=t) two-tail 0.001258656 t Critical two-tail 2.119905299     Second shift Third shift Mean 1.428571429 2.555555556 Variance 0.285714286 1.277777778 Observations 7 9 Pooled Variance 0.85260771 Hypothesized Mean Difference 0 df 14 t Stat -2.421884652 P(T<=t) one-tail 0.014800274 t Critical one-tail 1.761310136 P(T<=t) two-tail 0.029600549 t Critical two-tail 2.144786688   3. A researcher wanted to know if two educator created assessments assessed the same skills. Students were given both assessments. The data are below: Assessment A Assessment B Student 1 10 11 Student 2 10 12 Student 3 10 13 Student 4 10 14 Student 5 20 19 Student 6 15 18 Student 7 25 18 Student 8 25 18 Student 9 25 18 Student 10 14 18 Student 11 14 18 Student 12 14 18 Answer: The best choice for this scenario is the regression, because the data is paired and you are looking for similarities. There was a significant relationship between the assessments, (r [10] = .70, p < .05). According to Cohen, this would be a large effect size. SUMMARY OUTPUT Regression Statistics Multiple R 0.701889326 R Square 0.492648626 Adjusted R Square 0.441913488 Standard Error 4.594106787 Observations 12 ANOVA   df SS MS F Significance F Regression 1 204.9418 204.9418 9.710205796 0.010946026 Residual 10 211.0582 21.10582 Total 11 416       4. With the same data from question #9, what if the researcher wanted to know if the students performed differently on two assessments? Answer: The paired samples t-test would determine if the scores for each student were different. There was no difference in the student’s performance on assessment A (M = 16) and assessment B ( M = 16.25), (t [11] =.19, p > .05). (Practical note- it was a huge hint here that the previous answer was highly correlated, which means that there couldn’t be a significant difference here). t-Test: Paired Two Sample for Means   Assessment A Assessment B Mean 16 16.25 Variance 37.81818182 8.204545455 Observations 12 12 Pearson Correlation 0.701889326 Hypothesized Mean Difference 0 df 11 t Stat -0.187666682 P(T<=t) one-tail 0.427277438 t Critical one-tail 1.795884819 P(T<=t) two-tail 0.854554876 t Critical two-tail 2.20098516