The purpose of this document is to clarify what information you need to report in assignment 2 and how it can be presented. Information on how to run and interpret the analyses is covered in the lecture material and weekly activities across weeks 3 to 6.
Important points to note:
- It usually makes more sense to present tables shortly after introducing them in-text, and to describe what is summarised in them. This allows the reader to quickly connect the results with your description.
- DO NOT present statistics in a Table and then also present the same statistics in-text.
- Fitting tables into a document and making them look nice can be difficult. The APA style guide does not prescribe a given font size or line-spacing for tables, as a one-size-fits-all approach would not work. So, if you are struggling to fit a particular Table on a single page, you could consider changing things like the font size.
1. Exploratory Factor Analysis
In addition to mentioning relevant information such as Bartlett’s Test, KMO, and the various parameters of your analyses (e.g., rotation and extraction being used, factor loading cutoff), you will need to summarise the steps taken in each successive EFA as you work towards obtaining simple structure.
The following Table is one way in which you could present the steps of your various factor analyses. You could choose to summarise these steps in-text instead.
- If you choose to use the following Table, you will need to include sufficient detail for anything that is not clear within the Table itself. For example, if you’ve decided to remove an item for theoretical reasons, you will likely need to explain the rationale for this in-text.
- You won’t see a Table like this in published papers. It’s mostly to provide an efficient way of outlining your steps so your tutor can follow what you’ve done.
- The values in the Table below are for illustrative purposes. Update as required.
Table X (updated numbering as required for your assignment)
Steps taken to refine the [new scale name here]
| Step | Number of factor(s) | % of variance explained | Item(s) excluded | Reason |
| 1 | 4 | 55.67% | 3 | Cross loading on Factors 1 (loading = .42) and 2 (loading = .39) |
| 2 | 4 | 53.31% | 8 | Not loading on any factor (highest loading = .28) |
| 3 | 3 | 50.17% | 11 | Low communality (.17) and not loading on any factor (highest loading = .24) |
| Add more rows as needed |
Table 1 below gives an example of how the factor loadings for your final solution can be presented. The data is based on a factor analysis of the 7 Up 7 Down (7U7D; Youngstrom et al., 2013), a questionnaire measure of trait bipolar disorder vulnerability.
Important information to note:
- Table 1 shows all of the items written out in full, which takes up a lot of room. If the full items are all shown elsewhere in the document (e.g., in a Table in the Method or an Appendix) you could just use a label (e.g., ‘Item 1’) rather than type out the entire wording for the item. The same applies if you’re referring to an item in-text.
- When you are running your various factor analyses you may use the “supress” function in SPSS to blank out loadings below your factor loading cut-off (some people find this helps them to interpret the output more easily). However, when reporting the results, it’s best to show all of the loadings on each factor. Table 1 presents the highest loadings for each item in bold to make it clear which factor an item is loading on. This is not compulsory though.
- When doing your factor analysis you can select an option to sort the loadings by size. This will mean that all items loading on Factor 1 are listed first, then all of the items loading on Factor 2 and so on. This can be another way of helping to clearly see which items load on each factor. In Table 1 the items are presented in the same order that they were given to respondents.
Table 1
7U7D Pattern Matrix obtained via Maximum Likelihood Extraction with Promax Rotation
| Item | Factor 1: Depression-proneness | Factor 2: Mania-proneness |
| 1. Have you had periods of extreme happiness and intense energy lasting several days or more when you also felt much more anxious or tense (jittery, nervous. uptight) than usual (other than related to the menstrual cycle)? | .14 | .65 |
| 2. Have there been times of several days or more when you were so sad that it was quite painful or you felt that you couldn’t stand it? | .69 | .15 |
| 3. Have there been times lasting several days or more when you felt you must have lots of excitement, and you actually did a lot of new or different things? | -.11 | .78 |
| 4. Have you had periods of extreme happiness and intense energy (clearly more than your usual self) when, for several days or more, it took you over an hour to get to sleep at night? | -.04 | .76 |
| 5. Have there been long periods in your life when you felt sad, depressed, or irritable most of the time? | .83 | .05 |
| 6. Have you had periods of extreme happiness and high energy lasting several days or more when what you saw, heard, smelled, tasted, or touched seemed vivid or intense? | -.03 | .77 |
| 7. Have there been periods of several days or more when your thinking was so clear and quick that it was much better than most other people’s? | -.02 | .62 |
| 8. Have there been times of a couple days or more when you felt that you were a very important person or that your abilities or talents were better than most other people’s? | .03 | .57 |
| 9. Have them been times when you have hated yourself or felt that you were stupid, ugly, unlovable, or useless? | .85 | -.11 |
| 10. Have there been times of several days or more when you really got down on yourself and felt worthless? | .89 | -.04 |
| 11. Have you had periods when it seemed that the future was hopeless and things could not improve? | .86 | -.03 |
| 12. Have there been periods lasting several days or more when you were so down in the dumps that you thought you might never snap out of it? | .87 | .01 |
| 13. Have you had times when your thoughts and ideas came so fast that you couldn’t get them all out, or they came so quickly that others complained that they couldn’t keep up with your ideas? | .19 | .57 |
| 14. Have there been times when you have felt that you would be better off dead? | .75 | .04 |
| Eigenvalues | 6.92 | 2.09 |
| Extraction SSL | 6.44 | 1.74 |
| Rotation SSL | 5.93 | 4.90 |
Note. SSL = sum of squared loadings (initial SSL are equivalent to the eigenvalues).
2. Reliability
- The note underneath Table 2 shows the Cronbach’s alpha values for the subscales. This is because the Cronbach’s alpha if item deleted statistics would be fairly meaningless without this reference point.
- Tables 1 and 2 could possibly be merged if the page orientation was changed to landscape format. Either way is fine. You’ll need to learn to apply section breaks in order to use landscape orientation (this is also a useful skill to have for managing page numbering in complex documents more generally).
Table 2
Item-Level Properties of the 7U7D obtained via Exploratory Factor Analysis
| Item | Communalities (extraction) | Item response M(SD) | Corrected item-total correlation | Cronbach’s α if item deleted |
| Item 1 (M) | .54 | 0.61 (.79) | .65 | .84 |
| Item 2 (D) | .62 | 0.79 (.90) | .75 | .93 |
| Item 3 (M) | .53 | 0.76 (.81) | .65 | .84 |
| Item 4 (M) | .55 | 0.73 (.87) | .66 | .84 |
| Item 5 (D) | .73 | 0.99 (.99) | .82 | .92 |
| Item 6 (M) | .57 | 0.49 (.77) | .68 | .84 |
| Item 7 (M) | .37 | 0.80 (.81) | .59 | .85 |
| Item 8 (M) | .34 | 0.65 (.80) | .56 | .85 |
| Item 9 (D) | .63 | 1.04 (.94) | .75 | .93 |
| Item 10 (D) | .76 | 0.93 (.92) | .83 | .92 |
| Item 11 (D) | .71 | 0.90 (.90) | .81 | .93 |
| Item 12 (D) | .76 | 0.80 (.91) | .84 | .92 |
| Item 13 (M) | .48 | 0.59 (.82) | .64 | .84 |
| Item 14 (D) | .60 | 0.68 (.89) | .75 | .93 |
Note. M = mania-proneness item, D = depression-proneness item. Mania-proneness Cronbach’s α = .86, depression-proneness Cronbach’s α = .94.
- The Cronbach’s alpha values and corrected item-total correlations do not come from the factor analysis output, but from running separate reliability analyses on the relevant items (see Week 3 content).
- Communalities come from the factor analysis output
- Mean scores and standard deviations (i.e., M(SD)) item response values come from running Explore or Descriptives
3. Descriptives
Once you have finished reporting your factor analysis, you need to move from an item-level focus to a scale-level. This means that your next step is to create whole-scale and subscale scores for your new scale. You can do this by using SPSS (Transform > Compute new variable) to add up the items that have loaded significantly on each factor. For example, to calculate participants’ mania-proneness scores (i.e., Factor 2) you would compute a variable that summed Items 1, 3, 4, 6, 7, 8, and 13 of the 7U7D. Another option is to sum and average the scores (i.e., add up those items and divide by 7). Once this is done you should report descriptive statistics for your new scale, just like you would in any research report. Since descriptive statistics for your validity indicators are useful you should include them here as well.
Table 3
Descriptive Statistics for the 7U7D and Validity Indicators
| M (SD) | Actual range | Potential range | Cronbach’s α | |
| 7U7D | ||||
| Mania-proneness | 3.82 (3.68) | 0-18 | 0-21 | .86 |
| Depression- proneness | 6.13 (5.50) | 0-21 | 0-21 | .94 |
| Validity indicators | ||||
| BAS-D | 10.64 (2.49) | 4-16 | 4-16 | .81 |
| BAS-FS | 11.41 (2.40) | 4-16 | 4-16 | .74 |
| BAS-RR | 15.98 (2.61) | 5-20 | 5-20 | .78 |
| Trait BIS | 12.11 (2.45) | 4-16 | 4-16 | .75 |
| N = 760 |
Note. Standard deviations are presented in parentheses following the relevant mean.
Important points to note:
- You might be wondering why no data for a “7U7D total” score here, as in many cases subscales would be summed to provide a total scale score. In this case, the assumption is that depression-proneness and mania-proneness are theoretically distinct. If they were added together and we then ran correlations using 7U7D total, we could be obscuring a lot of important data about how depression-proneness and mania-proneness relate differently to other constructs. When designing a new scale, it is up to you to think about whether your subscales can and should be meaningfully combined or not.
- The actual range is the minimum and maximum values that you observed in your data set. The potential range is the minimum and maximum values that it is possible to obtain on the measure. These values can be found by multiplying the number of items by the lowest scale anchor (minimum possible response) and by the highest scale anchor (maximum possible response), and averaging this score if necessary.
- For example, if you have 10 items on a 1 (Strongly Disagree) to 7 (Strongly Agree) scale, the potential range is 10-70 if you are summing the items, or 1-7 if you’re using an average.
- The benefit of using an average rather than summed range is that it can make the results more easily interpretable. For example, 17 items measured on a 7-point scale (1 = Strongly Disagree, 7 = Strongly agree) has a potential summed range of 17-119, with the average potential range being 1-7. If the overall average score was 68 it can be hard to figure out what this means within the range of 17 to 119. However, if the average score of 4 (68 / 17 = 4) is used, it’s easier to more quickly conceptualise what that means within the context of the Strongly Disagree/Strongly Agree response format.
- You should always be aware of the potential range, as without knowing this you cannot spot out-of-range values (errors) in your data set.
- Another purpose of looking at the actual and potential ranges is to get a sense of how people were responding (you could also look at skewness and kurtosis results, and also histograms in the Explore analysis). For example, if everyone was scoring quite low on a particular measure, that might tell us something about the sample we have, or perhaps the items are biased in such a way that most people feel that they need to give a certain type of response. These issues could influence how accurate our findings are, and could be something worth mentioning in the Discussion.
- For example, if you have 10 items on a 1 (Strongly Disagree) to 7 (Strongly Agree) scale, the potential range is 10-70 if you are summing the items, or 1-7 if you’re using an average.
- Cronbach’s alphas for each measure need to calculated separately (see Week 3 workbook activity for a guide on this).
- The importance of showing the alphas for the validating measures is that if a measure is unreliable it could undermine the accuracy of any conclusions you draw about the validity of the new scale.
4. Validity Correlations
Now that you have presented descriptives, it is time to present your validity correlations. Since it would also be useful to the reader to know how your new scale or subscales are correlated, you might as well present this information at the same time.
Important points to note:
- The results in these tables are based on bivariate correlations between scale scores that have been created in SPSS AFTER completing the factor analysis. The matrix of factor correlations that are given in the factor analysis output is a bit different to that obtained by running bivariate correlations. This is because it runs correlations that are weighted by the factor loadings. The best approach is to run your own separate correlations (see Week 4 or Week 6 activities).
- If we had a meaningful “7U7D total” variable, then usually we would probably use that as a focus when testing our validation hypotheses, with the subscale data simply providing an extra level of richness. However, as noted previously, depression-proneness and mania-proneness are being considered as fairly different constructs that are not strongly correlated enough for a “7U7D total” variable to be meaningful.
Table 4
Correlations between the 7U7D and BIS/BAS Scales
| 1. | 2. | |
| 1. Mania-proneness | – | |
| 2. Depression-proneness | .54*** | – |
| 3. BAS-D | .11** | -.12** |
| 4. BAS-FS | .13*** | -.10* |
| 5. BAS-RR | -.11** | -.19*** |
| 6. Trait BIS | -.09 | .21*** |
| N = 760 |
Note: * p < .05, ** p < .01, *** p < .001
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