Oak Meadow Autonomy Survey
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1 Oak Meadow Autonomy Survey Patricia M. Meehan, Ph.D. August 7, 214 1
2 Contents Contents 3 List of Figures 3 List of Tables 3 1 Introduction 4 2 Data 4 3 Determining the Number of Factors 5 4 Proposed Model 6 5 Factor Scores 7 6 Deliverables 7 7 Appendix: Summary Statistics 8 2
3 List of Figures 1 Inter-item correlations within the five Oak Meadow subscales Distributions of student responses to survey items 1 through Distributions of student responses to survey items 21 through List of Tables 1 Number of students surveyed by school Number of students surveyed by grade level Number of students surveyed by gender Survey questions sorted by Oak Meadow proposed subscales: DM, IT, P/R, SA, and SM Correlations among all items, excluding r Proposed Factor Proposed Factor Proposed Factor
4 1 Introduction Oak Meadow designed an online student autonomy survey to measure students self-perception on five subscales: Decision-Making, Independent Thought, Persistence-Resilience, Self-Advocacy, and Self-Motivation. The survey was tested on 662 students from nine schools as well as homeschooling on students in grades seven through twelve. The goal of this analysis is to reduce the dimension of the survey and to develop a model relating the survey questions to the five subscales. Based on this model, we will compute factor scores for each student surveyed to create reference distributions for each autonomy sub-scale. Future survey participants can be compared against these reference distributions to determine their percentiles on each subscale. The Oak Meadow Student Autonomy Survey is comprised of: State or country of residence Name of school Gender Grade level Educational environment (public, private independent, charter, independent study or alternative, homeschool, international school, other) Forty autonomy items with a five-level ordered Likert response, where 1 represents strongly disagree and 5 strongly agree. 2 Data Since the results from this survey will be used to build a reference distribution for student autonomy subscales, the students surveyed should be representative of the population of middle and high school students in the United States. Selection of the students to participate was not based on random sampling, but rather convenience and the support of school administration, so the survey results may not be representative of the target population. In assessing the potential impact of the sampling bias, consider the characteristics of the selected student groups or schools and how they may relate to student autonomy. There may also be a bias due to nonresponse if students selected for the survey were unwilling or unable to participate. Students in the Unschool group (n=31), Bellows Falls Union HS (n=1), Cesar Chavez Academy (n=2), The Grammar School (n=7), and Willow Oaks (n=7) self-selected for survey participation as opposed to in-school administration by the five schools under study. To minimize bias, these students are excluded from the analysis. The data is further evaluated to identify potential invalid responses, noninformative survey questions, and data inconsistencies. Inspection of the summary statistics to identify potential errors or outliers reveals that a subset of the respondents (n = 1) listed grade levels not included in the investigation. These students are excluded from the analysis. Items with responses concentrated in a single category may not provide much information for the analysis. No survey questions are excluded on this basis. 4
5 There are two identical items in the survey (#9, 13) and the correlation 1 between these the responses to these items is only r =.59. While 89% of respondents provided answers to these two items that were within one ordinal response level of each other, the remaining cases (n=68) suggest data that is unreliable and is therefore excluded from the analysis. The correlation between items 9 and 13 is now r =.85. The final data set for analysis includes n = 536 student surveys from grades seven through twelve. 3 Determining the Number of Factors The initial model designed by Oak Meadow included five subscales to measure distinct types of student autonomy: Decision-Making (DM), Independent Thought (IT), Persistence-Resilience (P/R), Self-Advocacy (SA), and Self-Motivation (SM). As shown in Table 4 on page 1, each of these subscales is linked with a specific subset of the forty survey items. In order to evaluate the initial model, we examine the correlations within and across subscales then use confirmatory factor analysis (CFA) to determine whether the number of factors and the relationship between the items and the subscales conforms to expectations based on this initial model. This is followed by an exploratory factor analysis to identify other possible autonomy models using the available forty items then CFA analyses to test the fit of these models to the survey data. Inter-item Correlations We assess the strength of the association among items within and across subscales to identify sets of items that most clearly represent their associated subscales. These items should be strongly related to their associate subscale and weakly associated with the other subscales. Items that do not relate well with their associated subscale or are strongly associated with multiple subscales are considered for potential removal from the survey. Examination of Figure 1 on page 9 reveals that a number of items have low correlation with other items in their subscale (for example, items 4, 34, and 37 in Decision Making), while Table 5 on page 11 shows that many items have modest correlations across multiple subscales (for example, question 9 has a correlation of.5 or greater with items from Persistence/Resilience, Self-Advocacy, and Self-Motivation). In reviewing the correlation patterns, note that items 3 to 4 were written with reverse wording so it is expected that they will demonstrate a negative correlation with items 1 to 29 but this is not always the case. Confirmatory Factor Analysis of Initial Model Confirmatory factor analysis 2 revealed very high (all above.8) pairwise correlations among all the five subscales, indicating that the subscales do not discriminate well for this model. This poor discrimination may be due to a misclassification of certain items, items that relate to multiple subscales, and/or the number of subscales specified. 1 Polychoric correlations are used since responses are ordinal. 2 Implemented by the lavaan package in R. 5
6 Exploratory Factor Analysis We implement exploratory factor analysis (EFA) to provide evidence for the appropriate number of subscales to characterize the current data and to identify items for potential removal from the model. Items that are associated with more than one subscale or are weakly linked to all subscales are removed. In the exploratory analysis, we refer to the proposed new subscales as factors. These proposed new models are then tested by CFA. EFA is used to construct five models, with one to five factors. These models are evaluated by CFA, removing items with weak associations with all factors 3 or associations with multiple factors 4 and computing goodness-of-fit tests (CFI, RMSEA 5 ). Under the five-factor model, two of the factors contained only two items. This does not support a five-factor model. Under the four-factor model, fourteen items (1, 2, 3, 11, 12, 14, 15, 16, 23, 25, 26, 28, 29, 36) are associated with more than one factor and four items (4, 6, 3, 32) are not linked to any of the four factors. This model has reasonable model fit 6, but the correlation between factors one and two is somewhat high (r =.78). Under the three-factor model, ten items (1, 15, 16, 17, 18, 2, 27, 28, 29, 3) are associated with more than one factor and four items (3, 4, 6, 32) are not linked to any of the factors. This model has a reasonable model fit 7 and the correlation between factors one and two (r =.69) is lower than for the four-factor model. Further testing of this model, removing weak items and items relating to more than one factor, results in a fifteen-item survey with slightly improved model fit. 8 Further, the ordinal alpha statistic confirms that there is reasonably high internal reliability for each of these three factors (.76,.83, and.72, respectively). This provides evidence that the items within each factor are related to the same construct. 9 Under the two-factor model, five items (5, 21, 24, 31, 32) are associated with both factors and two items (4, 6) are not linked to either factor. This model has slightly poorer model fit 1. An effort to remove items with weaker associations reduced this to a one-factor model. Under the one-factor model, fourteen items (4, 5, 6, 1, 16, 32, 33, 34, 35, 36, 37, 38, 39, 4) had weak association with the factor and were excluded from the model. Interestingly, nine of the eleven negatively-worded items were excluded. The model had reasonable fit Proposed Model We propose implementing the survey with the three-factor model listed in Tables 6, 7, and 8 on page 12. While the one-factor model is a reasonable alternative, the three-factor model 3 loading values less than.3 4 loading values on at least two factors is within.2 5 The criteria used for an acceptable model fit is CFI>=.9 and RMSEA<.9. 6 CFI.93, RMSEA.95 7 CFI.91, RMSEA.1 8 CFI.96, RMSEA.8 9 A conventional cutoff is.7 or above for alpha values. 1 CFI.95, RMSEA.9, r = CFI.97, RMSEA.8 6
7 provides the opportunity to greater explore the autonomy constructs associated with the three factors. The final model selection should be informed by inspecting the groups of items and evaluating whether the items within each proposed factor characterize a meaningful autonomy scale. The groups of items should express an underlying construct based on theory or research. If the factors are not interpretable or there are items that do not seem to belong, the model can be adjusted. 5 Factor Scores Factor scores offer a means of comparing students along a particular factor. Based on the final model, factor scores can be calculated for each student to provide reference distributions for the three factors. New survey participants may be compared against this distribution by calculating their percentiles on each factor. While there are several methods for calculating factor scores, we propose using the sum scores method, which is computationally simple and easy to interpret. Factor scores for each student are calculated by summing the total item scores within each factor. These scores may also be combined to create an overall measure of student autonomy for each student. To do this, first standardize the scores within each factor 12 then sum the scores from factors one and two and subtract the score from factor 3. 6 Deliverables A CSV file with the final n = 536 dataset, including the fifteen items in the model. The final model, along with methodology for computing factor scores. Graphical summaries of the item responses by disability status. These are available in a Google Drive (link sent by ). 12 subtract the mean and divide by the standard deviation 7
8 7 Appendix: Summary Statistics Hilltop Montessori 25 Match Charter Public High School 27 PVRS 313 The Compass School 35 The Putney School 136 Table 1: Number of students surveyed by school. 7th 83 8th 87 9th 123 1th 97 11th 19 12th 37 Table 2: Number of students surveyed by grade level. Female 277 Male 239 Other 2 Table 3: Number of students surveyed by gender. 8
9 DM IT Individual Questions P/R SA Correlation SM Figure 1: Inter-item correlations within the five Oak Meadow subscales. For example, within the Decision Making (DM) subscale, item 4 has low correlation with the other items in the scale while items 9, 13, 18, 23, and 27 are at least moderately correlated with each other. 9
10 Question Number Question Factor 4 I trust my own instincts when it comes to making a choice. DM 9 When faced with an important decision, I make sure I m well-informed first. DM 13 When faced with an important decision, I make sure I m well-informed first. DM 18 I don t mind making a mistake; it helps me make better choices in the future. DM 23 I weigh the possible pros and cons before making a decision. DM 24 When my friends are trying to decide what to do, I m the one to make the call. DM 27 When I make a poor decision, I recognize it and take steps to remedy it. DM 34 If someone asks what I want, I find it hard to answer. DM 37 I never know what I want when I go to a restaurant. DM 1 Don t try to influence me. I know what I like to do. IT 7 I question beliefs that others take for granted. IT 12 When I study something, I have strong opinions about it. IT 16 My friends and parents frequently don t agree with my opinions. IT 21 I often ask questions to which no one knows the answers. IT 26 I find the answers to my own questions. IT 28 Even if my friends think a movie looks lame, I ll watch it if I want to see it. IT 29 I m willing to entertain ideas with which I disagree. IT 35 If my friends don t like a book, I won t read it. IT 36 I dress like my friends. IT 5 When one strategy is not working, I try something different. P/R 1 It s useful to know when I m wrong. P/R 14 I appreciate a good challenge. P/R 19 Even when a task is difficult, I stick with it. P/R 25 I trust my own ability to handle challenges. P/R 32 If it doesn t come easily, I ll do something else. P/R 4 When something doesn t work, I stop trying. P/R 3 When I run into difficulty, I ask for help. SA 8 I m not afraid to speak up in class. SA 17 When I need help, I know what to do. SA 22 If a teacher makes a statement that I think isn t true, I speak up. SA 3 When I make a mistake, I m afraid I ll get in trouble. SA 39 I let people get away with things to avoid the conflict. SA 2 I set goals and work hard to complete them. SM 6 When my friends don t understand the work, I m the one to explain it. SM 11 I finish my school work quickly, so I can get back to my own projects. SM 15 If I don t have to read a section, but it would be useful information, I read it. SM 2 It s satisfying to complete something I did on my own. SM 31 I need a deadline to get things done. SM 33 When I don t know what I m supposed to do, I don t do anything. SM 38 I have a hard time getting started. SM Table 4: Survey questions sorted by Oak Meadow proposed subscales: DM, IT, P/R, SA, and SM. 1
11 x4 x9 x13 x18 x23 x24 x27 x34 x37 x1 x7 x12 x16 x21 x26 x28 x29 x35 x36 x5 x1 x14 x19 x25 x32 x4 x3 x8 x17 x22 x3 x39 x2 x6 x11 x15 x2 x31 x33 x38 x4 1. x x x x x x x x x x x x x x x x x x x5 1. x x x x x32 1. x x x x x x x x x6 1. x x x x x x Table 5: Correlations among all items, excluding r.3. 11
12 Question Number Question Factor 2 I set goals and work hard to complete them. SM 9 When faced with an important decision, I make sure I m well-informed first. DM 11 I finish my school work quickly, so I can get back to my own projects. SM 15 If I don t have to read a section, but it would be useful information, I read it. SM 23 I weigh the possible pros and cons before making a decision. DM Table 6: Proposed Factor 1 Question Number Question Factor 7 I question beliefs that others take for granted. IT 14 I appreciate a good challenge. P/R 22 If a teacher makes a statement that I think isn t true, I speak up. SA 25 I trust my own ability to handle challenges. P/R 26 I find the answers to my own questions. IT Table 7: Proposed Factor 2 Question Number Question Factor 33 When I don t know what I m supposed to do, I don t do anything. SM 35 If my friends don t like a book, I won t read it. IT 38 I have a hard time getting started. SM 39 I let people get away with things to avoid the conflict. SA 4 When something doesn t work, I stop trying. P/R Table 8: Proposed Factor 3 12
13 3 x1 x2 x3 x4 3 x5 x6 x7 x8 3 x9 x1 x11 x12 Count 3 x13 x14 x15 x16 3 x17 x18 x19 x Score Figure 2: Distributions of student responses to survey items 1 through 2. 13
14 x21 x22 x23 x24 Count x25 x26 x27 x28 x29 x3 x31 x32 x33 x34 x35 x36 x37 x38 x39 x Score Figure 3: Distributions of student responses to survey items 21 through 4. 14
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