- Final Project
Quantitative Research Plan
The Final Project you have been working on throughout this course is due on Day 7 of this week.
To prepare for submitting the Final Project:
- Review the Final Project Description document located in the Learning Resources to ensure you have completed each section of the Final Project.
- Craft a 20-page quantitative research plan.
RSCH 8201: Quantitative Reasoning and Analysis
Final Project: Developing a Quantitative Research Plan
For the final project, students will develop a quantitative research plan. As such, students have two choices:
· Continue to develop the abbreviated quantitative plan completed in RSCH 8100, or
· Develop a new plan
This is not meant to be a full research plan in that students will not be constructing data collection instruments or generating data to use. The final project is meant to develop understanding about the relationships between research questions and hypotheses, research design, and statistical tests. For this project, students will consider more the design and methodology of the quantitative research they propose.
The Final Project should include the following:
A. Opening statement
B. Background of the study
a. Summary of the literature framing history of the project, using 5 articles related to the problem
b. Gaps and/or deficiencies in prior research
c. Importance of present study
i. Why the study should be pursued
ii. For whom is it important
C. Problem statement
D. Purpose of the statement
a. Research design (experimental, quasi-experimental, or non-experimental)
b. Theory tested or described
c. Intent (describe, compare, relate)
d. Variables (independent, dependent, controlling, intervening)
E. Research question(s) and hypotheses
a. Research question(s)
b. Null and alternative hypotheses for each research question, including how each of the variables will be operationalized
F. Nature of the study
i. Paradigm (quantitative)
1. Experimental, quasi-experimental, or pre/non-experimental
2. Specific design (e.g., pre-post test control group, time-series, etc. See Campbell & Stanley 1963.)
iii. Rationale for the design
2. Size, if known, or approximate/estimated size
1. Type of sampling
2. How the sample will be drawn
3. Sample size and why chosen in relation to population size
iii. Instrumentation and materials
1. Identify instrument
2. Establish reliability
3. Establish validity
iv. Data analysis plan: indicate what analytical tools will be applied to each set of data collected.
i. Potential design and/or methodological weaknesses of the study
ii. Explain how the weaknesses will be addressed
iii. Threats to validity and how they will be potentially addressed in the study
d. Ethical Concerns
i. Describe your proposed procedure for providing informed consent and any ethical concerns you may need to address.
G. Significance of the study
a. Practical contributions of the study
b. For whom the study is important
c. Implications for social change
Congratulations on making it to the final week of RSCH 8200 (Quantitative Reasoning and Analysis)! This course, along with RSCH 8100 (Research Theory, Design, and Methods) and RSCH 8300 (Qualitative Reasoning and Analysis) will serve as one of the foundations upon which you will build more advanced knowledge later. These three courses were designed to expose doctoral students to the key concepts in quantitative and qualitative design and analysis methods. The courses meet the 48 competencies that were judged important by the Walden University Doctoral Task Force and approved by the University Curriculum and Academic Policy Committee in 2008.
To continue to build the required skills for completing the doctoral dissertation, students will be required to complete at least one of the three advanced courses that will become available that aligns with the proposed dissertation methodology: RSCH 8250 (Advanced Quantitative Reasoning and Analysis), RSCH 8350 (Advanced Qualitative Reasoning and Analysis), and RSCH 8450 (Advanced Mixed Methods Reasoning and Analysis). The purpose of this document is to provide you with an overview of multivariate statistics and an overview of some of the topics that will be covered in the advanced quantitative reasoning and analysis course.
In RSCH 8200, you learned about the principles of research design and explored the main designs: experimental, quasi-experimental, and non-experimental (correlation). You also applied principles of descriptive and inferential statistics in your weekly assignments to gain mastery of univariate statistical techniques. Univariate techniques establish the relationship between two variables—one dependent and one independent variable. For example, the 2-sample independent t-test describes the relationship between an independent variable of interest (e.g., gender) and its impact on some dependent variable (e.g., financial acumen). The one-way analysis of variance, also a univariate test, allows researchers to perform a univariate test but in cases where there is more than one level of the independent variable (e.g., an experimental design may have involved three doses of a drug—the independent variable—and the effect of the doses on some medical condition, such as headache pain—the dependent variable).
You may have been wondering: What happens in cases where there is more than one independent or dependent variable? The purpose of this reading is to provide an introduction to the field of multivariate statistics and what you will cover if you decide to do a quantitative dissertation and take RSCH 8250. Included will be brief descriptions of other kinds of tests that are not covered in RSCH 8250 but may be topics that you ultimately decide to study on your own or with your dissertation mentor.
Multivariate Statistics—What are They and Why?
Multivariate statistics are analysis techniques used to understand more than one set of dependent or independent variables at the same time. Human behavior is influenced by many factors that operate simultaneously. A limitation of univariate and bivariate statistics is that they only allow consideration of the impact of one independent variable on one dependent variable. It is, in essence, an artificial simplification of the complexity of behavior. Multivariate statistical methods allow us to examine the potential influences on behavior simultaneously as well as the unique contribution of each influence on behavior. Not so long ago, statisticians performed many of the calculations by hand. The development of computer technology has allowed these same analyses to be performed much faster. The computations required for multivariate statistics are in many cases extremely complex and time consuming, and computer technology has made even some of the most complicated procedures accessible to student and professional researchers.
The approach we take is to provide students with the theoretical background to understand conceptually the underlying assumptions for the test. The primary focus is on application—students will generally complete an assignment that requires them to use PASW to calculate the statistics and report the results. This increased knowledge and proficiency should prepare you to meet the design and statistical demands required for your doctoral dissertation. It will also give you a broader range of statistics from which to choose and that are appropriate to the design now and for research you may conduct in the future. Provided in the subsequent sessions are brief descriptions of some of the common techniques, including the numbers of independent and dependent variables and one or two examples of how the technique might be applied in a research situation. For those concepts that likely will not be covered in RSCH 8250, links to full-text journal articles describing an application of the topic are provided.
If you would like more information about each of these analysis methods, there is a great online statistics book: http://statsoft.com/textbook/stathome.html. This resource provides basic information for a large number of common statistical techniques.
Advanced Analysis of Variance Designs
It is not possible to cover all types of analysis of variance (ANOVA) designs in one course. Therefore, additional designs will be presented in RSCH 8250 that extend the utility from the simple one-way ANOVA. These are factorial ANOVA, analysis of covariance (ANCOVA), and repeated measures ANOVA.
For the ANOVA designs, almost any intermediate textbook covers these topics very well, as do books that have an applied PASW focus; for example, the textbook by Green and Salkind (2008) covers these topics.
Factorial ANOVA allows the researcher to test the impact of more than one independent variable (factor) on one dependent variable. The factors are designated as main effects in the statistical model; an advantage is that the researcher can examine statistically how the main effects interact and the effect that interaction has on the dependent variable. By interact, we mean that two of the effects work together to affect the dependent variable. For example, a reading intervention may work (have an effect), but that effect may be different for girls than it is for boys. We would call this an interaction between the intervention and gender. Sometimes these are referred to as two-way (or more) factor analysis of variance (“two way” indicating two factors).
Example: An education researcher is interested in examining whether a new type of mathematics-training intervention will be successful in increasing annual achievement test scores. In addition, some literature has pointed to the fact that there may be differences in how girls and boys learn mathematics best. Therefore, the researcher proposes a quasi-experimental design in which all fifth grade students in one school will be given the mathematics intervention and all fifth grade students in a second school will be trained as usual. In the analysis, the researcher wants to know: (1) if the fifth grade students who are involved in the mathematics intervention score statistically higher than those in the non-intervention school; (2) whether girls or boys score differently on achievement tests; and, most importantly to the question, (3) whether girls who engage in the intervention perform differently than boys do. In factorial ANOVA, the interaction is typically of most interest (in fact, it is always examined first; main effects analysis follows when there is no statistically significant interaction).
ANCOVA extends the traditional one-way and factorial ANOVA designs by considering covariates. A covariate is a variable that likely has an effect on the dependent variable that we need to account for in the analysis. What we do is use the covariate to “partial out” the variance that is associated with the covariate so as to get the unique contribution of the main effect(s) on the dependent variable. In ANCOVA, additional regression calculations are used to identify the means by which the covariates contribute to the variance. We call this process partialing out the variance. By partialing out the variance associated with the covariate, we get the unique contribution of the main effect(s) on the dependent variable. In this case, there are one or more independent variables, one continuous dependent variable, and covariate variables.
Example 1: Using the example above, the researchers are interested in knowing whether family income—a proxy measure for socioeconomic status (SES), which means we are assuming that income is a reasonable approximation of SES—plays any role in mathematics achievement. Perhaps the researcher has found evidence that students who are from families representing higher SES tend to perform better. In the analysis, the same questions are addressed, but by including income, we are statistically controlling for the potential effects of income on the dependent variable (mathematics achievement). Thus, the results should show us how the main effect variables (gender and intervention) and the interaction (gender*intervention) affect mathematics achievement after accounting for any independent effect of the covariate of income on the dependent variable.
Example 2: A common analysis using ANCOVA is to test the impact of an intervention in which there is a pretest and posttest given to determine change over time. In this case, the pretest serves as the covariate, and the dependent variable is the posttest score. When using the pretest as a covariate, you are, in effect, statistically controlling for pretest differences; that is, you are statistically equating everyone at the outset so that true differences in posttest scores can be discovered.
Repeated Measures ANOVA
Repeated measures (sometimes referred to as within groups) ANOVA examines the impact of time on a particular dependent variable. In a repeated measures design, the dependent variable is assessed at multiple points in time, and the analysis focuses on change in the dependent variable over time. Thus, there are one or more independent variables, a time independent variable, and one dependent variable. Typically, the impact of the intervention is assessed by examining the interaction of the main effects of time and the independent variable(s).
Example: A sports psychologist is interested in understanding the impact of exercise on psychological well-being. She sets up an experiment in which participants are randomly assigned to one of three conditions. Participants in the first condition will be required to come to the lab to exercise 3 days per week using a special exercise routine that focuses on relaxation and meditation. The second group will engage in weekly exercise that includes cardiovascular training (treadmill and/or elliptical machine). Those in the comparison group will be asked to continue their typical daily routine and not to increase or decrease exercise. The study will run for three months, and the researcher will take blood pressure readings and administer a life satisfaction scale. For the data analysis, the researcher will use a repeated measures ANOVA in which the main effects are treatment (with three levels, one representing each treatment condition), time, and the interaction (time*treatment), which leads to the most important question: Does the intervention improve life satisfaction differently in the three conditions?
In the case of simple linear regression, one independent variable is assessed to determine the extent to which it predicts the value of one dependent variable (another way of saying this is to determine the extent to which the independent variable explains variance in one dependent variable). In multiple linear regression, multiple independent variables are included to determine the unique effects of those variables (together or separately) on one continuous dependent variable. There are many benefits of a multiple regression analysis, including the ability to assess the unique effects of each independent variable (predictor) on one dependent variable (the outcome), to study the overall effect of some or all of the variables acting together, and to enter variables in groups in a hierarchical fashion (which can be a powerful way to test theoretical models and to develop the most parsimonious answer to a research question).
Example: A management researcher is interested in developing a new model of financial performance. He believes that a financial success variable (the dependent variable, created from key financial performance indicators) can be predicted by measures of business culture (these might include variables such as company satisfaction, number of documented absences, trust in management, and perception of openness to innovation. The researcher collects data on these variables through a survey administered to all employees (except for the CEO and senior executive team). Using multiple regression, the dependent variable (financial performance) is regressed on the four independent variables listed above. The results will show how each independent variable uniquely explains variance (variability) in the dependent variable. It will also tell the researcher how much of the variability in financial performance is explained by knowing the values of the four independent variables.
Logistic regression has all of the same advantages as linear multiple regression. The important difference is that, in logistic regression, one or more independent variables are used to predict a categorical dependent variable.
Example: In public health research, we are typically interested in knowing the predictors of health outcomes. Suppose a researcher was interested in understanding more about treatment seeking. Using the health belief model as a conceptual framework, she hypothesizes that a number of factors impact treatment seeking for prostate cancer. One thousand men aged 45 years or older are randomly sampled to participate in a prostate cancer screening study. As part of the baseline, the men are asked if they have been screened for prostate cancer. They are also asked a number of questions regarding income, access to transportation, residency (urban, suburban, or rural), and their belief in their own likelihood of acquiring prostate cancer. The researcher will analyze the data using logistic regression with the outcome (dependent) variable being the screening variable (Yes or No) and the other variables—income, access, residency, and susceptibility—entered as independent (predictor) variables. As in multiple regression, the researcher will be able to explain the overall explained variance of the predictors in the outcome. Also, she will compute odds ratios that will convey the likelihood that the men with lower income, with no access, who live in rural areas, and who have lower perceived susceptibility will seek treatment compared to other men in the sample.
Topics Covered in More Advanced Courses (or Independently)
If you are interested in these topics, you may want to work independently with a faculty member to help gain proficiency. However, some brief introductions are provided.
Multivariate Analysis of Variance (MANOVA)
MANOVA is a powerful multivariate test that allows researchers to understand the effect of one or more independent variables on multiple dependent variables. Many times, instead of doing several individual ANOVA tests using different dependent variables, researchers will combine them all in one test (which helps control Type I error rate, as you learned in RSCH 8200). MANOVA can be employed using ANOVA tests described above. There are factorial MANOVA, MANCOVA (MANOVA that includes covariates), and repeated measures MANOVA.
Example: A policy researcher is interested in understanding the extent to which people of different ages attend to current events information. Having this information could be useful in developing campaign strategies. The researcher randomly selects 3000 people of voting age from the population in a large Midwestern metropolitan area. Approximately 2000 agree to participate. Each completes a short survey that asks the participants to rate their perceived knowledge in three current events areas (e.g., health care reform, economic recovery, and the war in Afghanistan). The analysis involves a MANOVA that has six levels of the independent variable (age group: 18–25 years, 26–34 years, 35–45 years, 46–55 years, 56–64 years, and 65 years or older) and three dependent variables (perceived knowledge of the three current events). Note that this looks like an ANOVA with the exception that there are three DV (ANOVA has only one DV).
Discriminant Function Analysis (DFA)
DFA is used to answer the question: What are the best predictors (independent variables) of membership in a particular group (dependent variables)? DFA is used as a follow-up test to MANOVA (where the independent variables and dependent variables essentially switch roles). In the follow-up, the research is looking to see which of the dependent variables from the MANOVA predict membership in the MANOVA independent variables. However, DFA has an independent life of its own as a technique for predicting correct classification. The classification scheme developed can be then used for other kinds of analyses.
Example: Colleges and universities are always trying to find the right predictors of success. A researcher decides to use archival data from the previous 10 years to see if she can determine what combination of predictors predicts success in college. She has determined that there are three groups: those who dropped out, those who are still enrolled but have not graduated, and those who graduated. There are a number of variables that will be examined: high school grade point average (GPA), entrance SAT or ACT score, first-term GPA, and history of community service in high school. The DFA will be set up such that four independent variables (high school GPA, SAT or ACT score, first-term GPA, and community service history) will be analyzed to determine the best set of predictors for retention (the dependent variable).
Path Analysis (PA)
PA allows expansion of the power of multiple and logistic regression and involves two or more independent variables and one dependent variable. The advantages are that the researcher can test direct effects (e.g., in a model in which Variables A and B predict Variable C, which in turn predicts Variable D (see below), and that one can test directly the relationship between Variables A and C, and between Variables C and D, but the indirect relationship between Variables A and D can also be assessed (how A affects D as it operates through C). This technique provides additional power for testing models in ways that are beyond the scope of regression (although PA is accomplished essentially by running several regression models simultaneously). When using PA, the researcher should have some theoretical support for ordering the variables in a specific way.
Example: The transtheoretical model of behavior change posits that people weigh the pros and cons (benefits and costs from the health belief model) when deciding to take action on changing a bad behavior. A researcher believes that self-efficacy for stopping smoking mediates the relationship between the perceived benefits (pros) of quitting and the perceived risks (cons) of quitting and the stage of readiness to quit smoking. Five stages describe the behavior change process: precontemplation, contemplation, preparation, taking action (quitting smoking), and maintaining non-smoking behavior. To analyze this model, the researcher sets up a model similar to that below and examines all direct effects: the relationships between pros (A) and cons (B) of quitting and self-efficacy (C), between self-efficacy and stage of readiness to quit smoking (D), and between pros (A) and stage of readiness (D) and cons (B) and stage of readiness (D). However, because the researcher has path analysis available, he can also test the indirect relationships; for example, how pros (A) impacts stage of change (D) as it acts through self-efficacy (C). In a sense, this is testing a meditational model.
Structural Equation Modeling (SEM)
PA is a very basic form of SEM. SEM expands the power of PA by allowing for testing of very complex models, with direct and indirect effects, that have more than one dependent variable and more than one independent variable (the variables can be categorical or continuous).
Example: Burkholder and Harlow (2003) used longitudinal structural equation modeling (a cross-lagged panel design) to show the temporal order of events in the cognitive processes related to sex risk behavior. In this model, a longitudinal test of the transtheoretical model of behavior change, behavioral risk for HIV (assessed at the one-year follow-up) was associated with higher perceived risk (assessed at baseline), lower self-efficacy for condom use (assessed at the 6-month follow-up), lower decisional balance (weighing of pros and cons of condom use). The cross-lagged design provides some evidence for a temporal order of cognition-predicting behavior.
Burkholder, G. J., & Harlow, L. L. (2003). An illustration of a longitudinal cross-lagged design for larger structural equation models. Structural Equation Modeling, 10(3), 465–486.
Available in the Academic Search Premier database with Accession Number 10130838.
Survival Analysis (SA)
SA is a technique used to model the time to failure of something. In engineering, it is used to understand impacts of time to failure of machinery. In public health, it is used to understand mortality information (what are the predictors of survival to a particular time?). The application can be extended beyond mortality, however. For example, someone might be interested in understanding the predictors of retention in a recovery clinic. Another example from education might be to understand the factors that impact retention in college. Survival analysis allows researchers to use a number of independent variables to predict one dependent variable outcome.
Example: Murtaugh, Burns, and Schuster (1999) conducted a survival analysis to understand factors affecting retention in college students. They found that increasing high school GPA and first-term GPA was associated with retention and that older age was associated with attrition. Taking an orientation course reduced risk for attrition.
Murtaugh, P. A., Burns, L. D., & Schuster, J. (1999). Predicting the retention of university students. Research in Higher Education, 40(3), 355–371.
Available in the Academic Search Premier database with Accession Number 2186295.
Factor Analysis (FA)/Principle Components Analysis (PCA)
PCA and FA are two different but related procedures. Rather than get into the details of why they are different (or whether from a practical standpoint they really are), it is simpler to say that both are techniques for data reduction and are a key part of developing psychological tests and scales. Both are used to take a large number of items and reduce the set to a smaller number of components that explain what is going on in the data. PCA/FA are used quite frequently to design psychological tests and scales that measure various psychological/mental and educational concepts in which a large number of items are reduced to a small subset of items that are related to each other in a meaningful way.
Example: Berberoglu and Tosunoglu (1995) used factor analysis to develop an environmental attitudes scale for Turkish university students. An item pool of nearly 175 items was reduced to 47 items that measured four underlying dimensions of environmental attitudes.
Berberoglu, G., & Tosunoglu, C. (1995). Exploratory and confirmatory factor analyses of an environmental attitude scale (EAS) for Turkish university students. Journal of Environmental Education, 26(3), 40–43.
Available in the Academic Search Premier database with Accession Number 9507114004.
Meta-analysis is not specifically a multivariate technique; however, this statistical approach is becoming much more common and can help answer very important questions regarding the progression of knowledge in a given area of research. In essence, the unit of analysis in this approach is the study, just as the individual is the unit of analysis in many research studies conducted to explore individual behavior (in essence, the study is the participant). In meta-analysis, researchers draw a sample of studies from the population of studies that have been performed in a specified domain based on rigorous and clearly defined inclusion criteria. Researchers then compute the effect sizes in each of the studies and use the sample of effect sizes to draw inferences about the relationships between these variables in the population. The effect sizes for each individual study are the dependent variables, and the independent variables are whichever variable the researcher gleans from relevant studies that are of interest to test. The clear benefit to meta-analysis is that researchers can synthesize knowledge in a particular domain and can use such a study to arrive at conclusions about the actual relationships that occur in the population (i.e., if some studies show a relationship between gender and pro-social behavior, and some do not, a meta-analysis can combine the effects of many studies to demonstrate what the “true” effect is).
Example: Barak, Hen, Boniel-Nissim, and Shapira (2008) conducted a meta-analysis of Internet-based psychotherapy effectiveness and found that there was a medium effect size similar to that for traditional therapy. Several studies were analyzed that examined traditional versus Internet-based psychotherapies and found no differences; the authors argued for online psychotherapy interventions.
Barak, A., Hen, L., Boniel-Nissim, N., & Shapira, N. (2008). A comprehensive review and meta-analysis of the effectiveness of Internet-based psychotherapeutic interventions. Journal of Technology in Human Services, 26(2/4), 109–159.
Available in the SocINDEX with Full Text database with Accession Number 34775089.
Cluster analysis is a statistical technique that allows researchers to classify typologies. For example, in all of the people who smoke cigarettes, it may be useful to try to reduce individuals to certain groups or typologies: perhaps the smoker who smokes only socially and has little or no symptoms of anxiety. Each of these dependent variables (smoking status, social nature of tobacco use, and anxiety symptoms) can be combined to determine specific types of smokers that may make it simpler to intervene on them. Statistically, correlation or regression is used to determine how “close” individuals are in specific characteristics, and those people are grouped together to form a cluster. The process continues until the clusters that emerge represent the best fit to the data that exist. A number of different solutions are usually presented; the challenge is to determine which solution (number and description of clusters) makes the most sense theoretically.
Example: Inbakaran and Jackson (2006) used six demographic variables and four location variables relative to tourist areas and involvement in the tourism industry to better understand a host community’s attitudes toward the tourism industry and attitudes toward further tourism development. The researchers found four distinct clusters or groups of people: (1) those who were living in or had a connection to a tourist industry were mostly female, younger, single, and better educated; (2) those who did not live near a tourist area and had a low connection to the tourism industry were also mostly female, mid 30s, well educated, and married with children; (3) those who lived far from a tourist area were mostly males of retirement age and less well educated; and (4) those who did not live near a tourist area but had a high connection to the tourism industry were in their 40s, were not well educated, and represented a balance of males and females. Understanding these clusters of people can be important to community leaders who want to ensure continued economic development associated with tourism and tourism-related industry while having the knowledge necessary to reach key people who may favor or oppose such expansion and provide them with the necessary information needed to help change attitudes.
Inbakaran, R., & Jackson, M. (2006). Resident attitudes inside Victoria’s
tourism product regions: A cluster analysis. Journal of Hospitality and Tourism Management, 13(1), 59–74.
In Pearson’s correlation, the relationship between two variables is investigated. In canonical correlation, the relationships between two sets of variables are investigated. For example, a researcher may want to examine how three different measures of depression (and the subscales) are related to two separate measures of anxiety (and the subscales in the tests). In the clinical literature, depression and anxiety are often seen together or may be difficult to distinguish. Canonical correlation analysis would help to understand the variability that is shared across tests and subscales (what the tests measure that are common) and that which is unique (what might differentiate anxiety and depression).
Example: Lichtenberg, DeVore Johnson, and Arachtingi (1992) used canonical correlation to determine that there was a statistically significant relationship between certain irrational beliefs, using the Irrational Beliefs Scale, gender, age, and frequency and type of illness.
Lichtenberg, J. W., DeVore Johnson, D., & Arachtingi, B. M. (1992). Physical illness and subscription to Ellis’s irrational beliefs. Journal of Counseling and Development, 71(2), 157–162.
Available in the Academic Search Premier database with Accession Number 9302071356.
In many research areas, the variables of interest are discussed and measured at the nominal and ordinal levels. Just as the t-test is a simple version of the more complex techniques based on the general linear model (e.g., ANOVA), the chi-square test is a simple case of techniques that can address more complex questions. Log-linear analysis (LLA) provides researchers with a way to analyze multidimensional contingency tables and to identify which variables have significant relationships, as well as which cells are over- or underrepresented in the responses. LLA can be used for inferential and prediction studies (similar to ANOVA and multiple regression).
Example: Salter (2003) did a study using LLA to examine the MBTI profiles of college faculty as compared to the general population. The analysis showed that the INTJ profile was significantly overrepresented in the faculty sample.
Salter, D. (2003). Loglinear techniques for the analysis of categorical data: A demonstration with the Meyers-Briggs Type I indicator. Measurement and Evaluation in Counseling and Development, 36(2), 106–121.
Available in the Academic Search Premier database with Accession Number 10377101.
* Dr. Daniel Salter, Dr. Evelyn Johnson, and Dr. Carl Shepiris reviewed and provided comments on this document.
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