Results and Discussion Sections You have worked hard on this research project, and you are over halfway done! In the last project assignment, based on the data collected from your participants, you co

However, do NOT simply copy them and change only a few word s. You need to use your own words when writing your papers/ assignments. Otherwise, it is considered as plagiarism.  Points will be deducted if your paper does not adhere to the required format /style. Submit Your Proposal  Save your file regularly. When you are done, upload your saved word document ( must be .doc or .docx ) to the Results and Discussion Sections under the Assignments tab on Canvas. This assignment must be completed and submitted individually as indicated in the course syllabus. Let the instructor know if you have any questions or concerns about this assignment. Again, see the Findings PDF on Canvas for the data analysis results. Go over pages 5 -16 of this file to see how to interpret the statistical results; some examples are also p rovided in this file. Also, remember to go over the sample papers on Canvas . Use the sample papers and examples in this file as a guide when writing your Results, Discussion, and research paper. PSYC 3304 & 3104 , Results & Discussion Sections Page 5 of 16 See the copyright statement in the course syllabus. Pearson Co rrelations (Apply to All Students)  Use the Findings PDF file to examine whether your hypotheses were supported.  Look for the information you need to report your results based on what variab les you chose for your project .  In this e xample , I chose self -esteem , resilience , and gender . H1: The resea rcher hypothesized that there would be a positive correlation between self -esteem and resilience ; resilience would increase as self -esteem increases. o My first hypothesis tests the relationship between self -esteem and resilience . o Pages 1 -2 of the Findings PDF shows the descriptive statistics and correlations am ong the variables. I will look for the informatio n I need based on the variables I chose , self -esteem and resilience , which are highlighted below. In the Correlations matrix, you can see that each comparison has been done twice. The two highlighted cells have the same numbers. This is because SPSS correlated Self -Esteem with Resilience , and then Resilience with Self - Esteem , which are the same compari son. Therefore, when interpreting the Correlations matrix, you can draw a diagonal line across the table and focus on either the top half or the bottom half of the table. PSYC 3304 & 3104 , Results & Discussion Sections Page 6 of 16 See the copyright statement in the course syllabus. Here, I will choose the top half to focus on (but if you use the bottom half is fine as well): 1. How would I report these numbers using APA style?  r(943 ) = -.60, p < .001 2. What does this mean? (Here is a brief review for the Introductory Statistics course you took)  r stands for correlation.  943 : this is the degrees of freedom (df). In correlation, df = N – 2, which is the sample size used to compute this correlation minus the number of variables you have for that correlation. In the highlighted cell, it shows that N = 945 , and you have 2 variable s (resilience and self -esteem) for this correlation. Therefore, 945 – 2 = 943 .  -.60: This is the correlation between self -esteem and resilience . There is a negative sign, which means that there is a negative correlation between the two variables. In other words, resilience decreased as self - esteem increase d, or self -esteem decreased as resilience increased. This finding does not support my first hypothesis (stated on page 3). Note that we typically round the correlation coefficients to 2 decimal places.  The row “Sig. (2 -tailed)” shows you the p values . o A p value is the probability that the results you see are due to chance (and not due to relationship between the variables, gender differences, treatment effect, or whatever you are testing ). That’s why we would like the p value to be small (meaning unlikely due to chance ). Typically, f or the findings to be considered significant, p needs to be smaller or equal to .05 (5% of chan ce). Review pages 395 (C hapter 15) of the GF textbook . o It shows “.000” in the table; this p value is smaller than .05, which means the correlation between these two variables is significant. o Keep in mind that “.000” does not mean that p = .000 (do NOT ever report p = .000 because p value would never be exactl y 0). It shows “.000” because the p value is very small (smaller than .001). o If you double -click on the p value in the cell using SPSS , you can actually see the exact p value. In this example (shown in the screenshot to the right) , the p value is 3 x 10 -94, meaning there are 93 zeros in front of 3 before reaching the decimal point. As you can see, that’s a very small p value. o Therefore, if you see “.000” for the p value, put p < .001 in your paper. 3. How do I write up this finding for my hypothesis testing?  Restate the hypothesis.  Mention what test was used (i.e., Pearson correlation) .  Include the statistics. For P earson correlations, report M and SD for the variables, and r, df, and p for the correlation.  Talk about if it’s statistically significant (based on the p value) and interpret the relationship.  Discuss whether the hypothesis was supported.  See examples on the next page (page 7) . PSYC 3304 & 3104 , Results & Discussion Sections Page 7 of 16 See the copyright statement in the course syllabus. Here is an example of how to write up this finding : It was hypothesized that there would be a positive correlation between self -esteem and resilience ; resilience would increase as self -esteem increases. To test this hypothesis, Pearson correlation was conducted. Results showed that there was a significant negative correlation between self -esteem (M = 19.49 , SD = 5.40 ) and resilience (M = 3.44 , SD = 0.78) , r(943 ) = -.60, p < .001 . In other words, resilience decreased as self - esteem increased . Therefore, the first hypothesis was not supported. Here is another example of how to write up the same finding: The researcher hypothesized that resilience would increase as self -esteem increases . However, this hypothesis was not supported as the results of Pearson correlation showed the opposite direction. T here was a significant negative correlation between these two variables, r(943 ) = -.60, p < .001 ; r esilience (M = 3.44 , SD = 0.78 ) decreased as self -esteem (M = 19.49 , SD = 5.40 ) increased . 4. How do I report my p value if it’s smaller than .05 but larger than .001? For example : the correlation between age and depression  Report close to exact p value.  In this example, age and depression : r(924 ) = -.08 , p = .0 13 5. What if my p value is larger than .05 (non -significant) ? For example: age and sleep disturbance .  Report close to exact p value.  In this example, a ge and sleep disturbance : r(925 ) = -.03 , p = .297  This finding means that there was no significant correlation between age and sleep disturbance .  However, you still need to report the results . See the example below .  Here is an example for how to write up a non -significant correlation : Researcher hypothesized that sleep disturbance would increase as age increases. However, this hypothesis was not supported. Results of Pearson correlation showed a non -significant relationship between age (M = 31. 06 , SD = 12.68 ) and sleep disturbance (M = 22.30 , SD = 5.85 ), r(925) = -.03, p = .297 . 6. Looking at the correlation matrix table, why are some Ns different? For instance, self -esteem and resilience has N of 945, whereas self -esteem and age has N of 927.  Some people did not report their age in the survey, so those data points could not be included in assessing the correlation between age and another variable. 7. For the demographic variable, if I chose age , do I use the same Correlation matrix and Descriptive Statistics table to interpret the findings?  Yes. For instance, if I chose self -esteem , resilience , and age , I will examine the correlations between ( 1) age and self -esteem as well as between ( 2) age and resilience .  The way to interpret these correlations and write them up are the same as the examples shown above.  Here is another example: It was hypothesized that resilience would increase as age increases . This hypothesis was supported as the results of Pearson correlation showed that there was a significant positive correlation between age (M = 34.06 , SD = 12.68 ) and resilience (M = 3.44 , SD = 0.78 ), r(925) = .15 , p < .001 . Older individuals showed higher resilience compared to younger individuals. PSYC 3304 & 3104 , Results & Discussion Sections Page 8 of 16 See the copyright statement in the course syllabus. Gender D ifferences (For Students who Chose Gender for Their Project) Example: I chose self -esteem , resilience , and gender . H2: It was hypothesized that females would have higher self -esteem compared to males. H3: It was hypothesized that males would have higher resilience compared to females. o My last two hypotheses test whether gender is associated with self -esteem and resilience . o Page s 3 -4 of the Findings PDF shows the gender differences. I will look for the informatio n I need based on the variables I chose , self -esteem and resilience , which are highlighted below. o For this project , 4 participants reported other for their gender. Because of the drastic difference s between the group sizes (4 versus 302 males and 4 versus 639 females), these 4 participants were excluded from the hypotheses testing. If you chose gender as your demographic variable, mention this in y our Results section. For this project, one -way analys es of variance (ANOVA s) were conducted to test the gender differences. However, for your reference: w ith 2 groups (male and female), an independent -samples t test is another common test to use. PSYC 3304 & 3104 , Results & Discussion Sections Page 9 of 16 See the copyright statement in the course syllabus. Gender differences in self -esteem (my example H2) and depression (example H3) : 8. How would I report these numbers using APA style?  Gender difference in self -esteem between male (M = 18.75 , SD = 5.14 ) and female (M = 19.83 , SD = 5.50 ): F(1, 939) = 8.19, p = .004.  Gender difference in resilience between male (M = 3.56 , SD = 0.74 ) and female (M = 3.39 , SD = 0.79 ): F(1, 939 ) = 9.56 , p = .002 . 9. What does this mean?  F is the ratio of between -groups variability and within -group variability. o Self -esteem: 8.186 = 237 .522 29.015 o Resilience: 9.555 = 5.753 0.602 o In hypothesis testing, if there are difference s between groups, in this case between males and females, we would th ink that they are due to gender difference. o If there are differences within groups, we think of these differences as things we c an not explain (error). We don’t know why people in the same group have different scores; these are things we cannot account for in our study (e.g., individual differences, error). o Therefore, the ratio of between -groups variability and within -group s variability is basically the ratio between what we can explain and what we cannot explain , what we know versus what we don’t know , or what we can account for versus what we cannot account for .  1: this is the degrees of freedom (df) between groups. df between = number of groups – 1 = 2 groups (males and females) – 1 = 1  939 : this is df within groups. df within = (n1 – 1) + (n 2 – 1) = ( number of males – 1) + (number of females – 1) = ( 302 – 1 ) + ( 639 – 1) = 939  The row “Sig.” shows you the p values . o See the p value explanations on page 6 of this file (under Question #2) . o Self -esteem:  p = .004, which is smaller than .05. Therefore, the gender difference was statistically significant for this variable .  In other words, the average (mean ) self -esteem score for males was 18.75 , and the m ean self -esteem score for females was 19.83 . The mean d ifference between the two groups was 1.08 (19. 83 – 18.75 ), and having a p value smaller than .05 means that this 1.08 -point difference i n self -esteem was statistically significant. To be more specific, females showed a significantly higher level of self -esteem compared to males. o Resilience:  p = .002, which is smaller than .05. Therefore, the gender difference was statistically significant for this variable.  In other words, the mean resilience score for males was 3.5 6, and the m ean resilience score for females was 3.39. The mean difference between the two groups was 0.1 7 (3.5 6 – 3.39), and having a p value smaller than .05 means th at this 0.17 -point difference in resilience was statistically significant. To be more specific, males scored significantly hi gher on the resilience scale compared to females. PSYC 3304 & 3104 , Results & Discussion Sections Page 10 of 16 See the copyright statement in the course syllabus. 10. How do I write up this finding for my hypothesis testing?  Restate the hypothes es.  Mention what test s were used ( i.e., one -way analys es of variance [ANOVAs] ).  Include the statistics. For each ANOVA, repor t M and SD for the groups, and F, df, and p for the gender differences.  Talk about if it’s statistically significant (based on the p value) and interpret the relationship.  Discuss whether the hypothesis was supported.  See the example below.  Here is an example: Two one -way analyses of variance (ANOVAs) were conducted to test the last two hypotheses , which focused on gender differences. Four participants reported other for their gender. Because of the differences between the group sizes, these fou r participants were excluded from the hypotheses testing. It was hypothesized that females would have higher self -esteem compared to males. Results supported the second hypothesis in showing that female participants (M = 19.83, SD = 5.50) had significantly higher self -esteem compared to the male participants ( M = 18.75, SD = 5.14), F(1, 939) = 8.19, p = .004. The third hypothesis states that males would have higher resilience compared to females. The findings also supported the las t hypothesis as males (M = 3.56, SD = 0.74) scored higher on the resilience scale compared to females (M = 3.39, SD = 0.79), F(1, 939) = 9.56, p = .002. 11. What if my p value is larger than .05 (non -significant) ?  As you can see on page 4 of the Findings PDF, gender differences in optimism , depression , and stress were not statistically significant (i.e., their p values are larger than .05) .  If you chose one or more of those non -significant variables for your project, you still need to report the results and the close to exact p value. See the example below.  Here is an example for the non -significant gender difference in optimism : Researcher hypothesized that males would be more optimistic compared to females. However, this hypothesis was not supported. Results of a one -way ANOVA showed a non -significant difference in optimism between males (M = 10.52, SD = 4.42) and females (M = 10 .14, SD = 4.73) , F(1, 939) = 1.34, p = .248.  What does this non -significant p value (p > .05) mean? o In this example, the gender difference in optimism yielded p = . 248 , which is larger than .05. Therefore, it means that the results were likely due to chance (not due to gender difference). o In other words, the mean optimism score for males was 10.52 , and the m ean self -esteem score for females was 10.14 . The mean difference between the two groups was 0. 38 (10.52 – 10.14 ), and having a p value larger than .05 means that this 0.38 -point difference i n optimism was NOT statistically significant. To be more specific, there was no gender difference in optimism levels. o Keep in mind that when reporting statistical results/findings that are not significant, use non - significant instead of insignificant . The word, insignificant , implies that the study is not important, which is not the same as not finding statistical significance in the study. PSYC 3304 & 3104 , Results & Discussion Sections Page 11 of 16 See the copyright statement in the course syllabus. Differences between Smokers and Non -Smokers (For Students who Chose Smoking Status for Their Project) In the example below , I chose resilience , depression , and smoking status . H2: It was hypothesized that non -smokers would have higher resilience compared to smokers. H3: It was hypothesized that smokers would have higher depression scores compared to non -smokers. o My last two hypotheses test whether smoking status is associated with resilience and depression . o Page s 5-6 of the Findings PDF shows differences between smokers and non -smokers. I will look for the informatio n I n eed based on the variables, resilience and depression , which are highlighted below. For this project, one -way analys es of variance (ANOVA s) were conducted to test differences between smokers and non -smokers. However, for your reference: with 2 groups ( smokers and non -smokers ), an independent -samples t test is another common test to use. PSYC 3304 & 3104 , Results & Discussion Sections Page 12 of 16 See the copyright statement in the course syllabus. Differences between smokers and non -smokers in resilience (H2) and depression (H3) : 12. How would I report these numbers using APA style?  Difference in resilience between smokers (M = 3.27 , SD = 0.85 ) and non -smokers (M = 3.47 , SD = 0.76 ): F(1, 943 ) = 7.70 , p = . 006  Difference in depression between smokers (M = 11.12 , SD = 11.17 ) and non -smokers (M = 7.58 , SD = 8.17 ): F(1, 943 ) = 19.57 , p < .001 13. What does this mean?  F is the ratio of between -groups variability and within -group variability. o Resilience: 7.699 = 4.657 0.605 o Depression : 19.567 = 1470 .564 75.155 o In hypothesis testing, if there are differences between groups, in this case we would think that they are due to the differences between smokers and non -smokers . o If there are differences within groups, we think of these differences as things we c an not exp lain (error). We don’t know why people in the same group have different scores; these are things we cannot account for in our study (e.g., individual differences, error). o Therefore, the ratio of between -groups variability and within -groups variability is basically the ratio between what we can explain and what we cannot explain , what we know versus what we don’t know , or what we can account for versus what we cannot account for .  1: this is the degrees of freedom (df) between groups. df between = number of groups – 1 = 2 groups (males and females) – 1 = 1  943 : this is df within groups. df within = (n1 – 1) + (n 2 – 1) = (number of smokers – 1) + (number of non - smokers – 1) = ( 138 – 1 ) + ( 807 – 1) = 943  The row “Sig.” shows you the p values . o See the p value explanations on page 6 of this file (under Question #2) . o Resilience:  p = . 006, which is smaller than .05. Therefore, the difference between smokers and non - smokers was statistically significant for this variable.  In other words, the mean resilience score for smokers was 3.27 , and the m ean resilience score for non -smokers was 3.47 . The mean difference between the two groups was 0. 2 (3.4 7 – 3.27 ), and having a p value smaller than .05 means that this 0.2-point difference i n resilience was statistically significant. To be more specific, non -smokers showed significantly higher resilience compared to smokers. o Depression :  p < .001, which is smaller than .05. Therefore, the difference between smokers and non - smokers was statistically significant for this variable.  In other words, the mean depression score for smokers was 11.12 , and the mean depression score for non -smokers was 7.58 . The mean difference between the two groups was 3.54 (11.12 – 7.5 8), and having a p value small er than .05 means that this 3.54 -point difference in depression was statistically significant. To be more specific, smokers scored significantly higher on the depression scale compared to non -smokers. PSYC 3304 & 3104 , Results & Discussion Sections Page 13 of 16 See the copyright statement in the course syllabus. How do I write up this finding for my hypothesis testing?  Restate the hypotheses.  Mention what tests were used ( i.e ., one -way analyses of variance [ANOVAs]).  Include the statistics. For each ANOVA, report M and SD for the groups, and F, df, and p for the gender differences.  Talk about if it’s statistically significant (based on the p value) and interpret the relationship.  Discuss whether the hypothesis was supported.  See the example below.  Here is an exam ple: Two one -way analyses of variance (ANOVAs) were conducted to test the last two hypotheses, which focused on differences between smokers and non -smokers . It was hypothesized that non -smokers would have higher resilience and lower depression scores compared to smokers. The last two hypotheses were supported by the data. R esults showed that non -smokers (M = 3.47, SD = 0.76 ) had significantly higher resilience compared to smokers (M = 3.27, SD = 0.85 ), F(1, 943) = 7.70, p = .006 . Furthermore, non -smokers (M = 7.58, SD = 8.17) scored significantly lower on the depression scales compared to smokers (M = 11.12, SD = 11.17) , F(1, 943) = 19.57, p < .001 . What if my p value is larger than .05?  As you can see on page 6 of the Findings PDF, all differences between smokers and non -smokers were statistically significant (i.e., all p values were ≤ .05) .  However, for the sake of practice and learning, see page 10 of this file regarding non -significant differences between 2 groups (under Question #11) . PSYC 3304 & 3104 , Results & Discussion Sections Page 14 of 16 See the copyright statement in the course syllabus. Results Pearson correlations were conducted to test the three hypotheses in this study . The researcher hypothesized that resilience would increase as self -esteem increases . However, this hypothesis was not supported as the results showed the opposite direction. There was a significant negative correlation between these two variables, r(943) = -.60, p < .001; resilience ( M = 3.44, SD = 0.78) decreased a s self -esteem ( M = 19.49, SD = 5.40) increased. The second hypothesis stated that older individuals would have higher self -esteem. Results supported this hypothesis in showing that self -esteem increased as age ( M = 34.06 , SD = 12.68 ) increased. Lastly, it was hypothesized that resilience would increase as age increases . This hypothesis was supported, as the results of showed that there was a significant positive correlation between age and resilience, r(925) = .15 , p < .001 . Older individuals showed highe r resilience compared to younger individuals. Example 1: self -esteem, resilience, and age You do not need to repeatedly report the means ( Ms) and standard deviations ( SD s) of the variables every time you mention them. In the above example, you can see that the Ms and SD s of resilience and self -esteem were reported when discussing the first hypothesis. I did not report them again, even when they were mentioned in the last two hypotheses. Similarly, the M and SD of age were reported only once in this Results section. PSYC 3304 & 3104 , Results & Discussion Sections Page 15 of 16 See the copyright statement in the course syllabus. Results The researcher hypothesized that resilience would increase as self -esteem increases . To test this hypothesis, Pearson correlation was conducted. Results showed that there was a significant negative correlation between resilience ( M = 3.44, SD = 0.78) and self -esteem ( M = 19.49, SD = 5.40), r(943) = -.60, p < .001. In other words, resilience decreased as self -esteem increased. Therefore, the first hypothesis was not supported. To examine gender differ ences in resilience and self -esteem , one -way analyses of variance (ANOVAs) were conducted to test the last two hypotheses. Four participants reported other for their gender. Because of the differences between the group sizes , these four participants were excluded from the hypotheses testing. It was hypothesized that females would have higher self -esteem compared to males. Results supported the second hypothesis in showing that female participants ( M = 19.83, SD = 5.50) had significantly higher self - esteem compared to the male participants ( M = 18.75, SD = 5.14), F(1, 939) = 8.19, p = .004. The third hypothesis states that males would have higher resilience compared to females. The findings also supported the last hypothesis as males ( M = 3.56, SD = 0.74) scored higher on the resilience scale compared to females ( M = 3.39, SD = 0.79), F(1, 939) = 9.56, p = .002. Example 2: self -esteem, resilience, and gender PSYC 3304 & 3104 , Results & Discussion Sections Page 16 of 16 See the copyright statement in the course syllabus. Results The researcher hypothesized that there would be a negative correlation between resilience and depression, which was supported by the data. Results of Pearson correlation showed that higher resilience was significantly associated with lower depression levels ( Mresilience = 3.44, SD resilien ce = 0.78 ; Mdepression = 8.10 , SD depression = 8.75), r(942) = -.50, p < .001 . Two one -way analyses of variance (ANOVAs) were conducted to test the last two hypotheses, which focused on differences between smokers and non -smokers. It was hypothesized that non -smokers would have higher resilience and lower depression scores compared t o smokers. The last two hypotheses were supported by the data. Results showed that non -smokers (M = 3.47, SD = 0.76) had significantly higher resilience compared to smokers (M = 3.27, SD = 0.85) , F(1, 943) = 7.70, p = .006. Furthermore, non -smokers (M = 7.58, SD = 8.17) scored significantly lower on the depression scales compared to smokers (M = 11.12, SD = 11.17) , F(1, 943) = 19.57, p < .001. Example 3: resilience, depression, and smoking status