GOD & MATH: Thinking Christianly About Math Education



Mr. Josh WilkersonAP StatisticsApril 30, 2013Data Analysis for Austin Ridge Bible Church Reason for the Survey and Survey DesignAustin Ridge Bible Church decided to give a survey to its congregation to evaluate the areas in which people struggle to grow spiritually. Our group was given the task of analyzing data from a survey previously given and designed by the Church Leaders. The survey consisted of six subsections each containing nine related questions in the three categories of attitude, actions, and abilities. To each question the answers 1, 2, 3, or 4 were provided, defined as 1=no,not really, 2=somewhat, 3=yes, and 4=definitely. The survey was given online and the congregation was invited by the senior pastor to take the survey on two adjacent Sunday mornings. Comments on Survey DesignIn general the survey was well crafted and avoided bias well. However, our team did recognize a couple places that could benefit from small adjustments, in order to reduce response bias. The first area was getting to the actual survey; because the website requires each person to set up an account before taking the survey, we concluded that less people would end up taking the survey. This would then create non-response bias. Secondly, when both the answers “yes” and “definitely” were choices we labeled the “yes” answer as the easy out answer most people would tend toward. “Definitely” seems to be a much stronger statement when compared to “yes”, leading people to stray away from choosing that option. I would be helpful to either change one of the two answers, or explain clearly the meaning of “yes” as opposed to “definitely”. Another source of bias we identified was that since the survey was given online, new members who were not integrated into the community may not feel comfortable going to take the survey. Since we were unable to determine how long each person had been at the church from the data we were given, we could not conclude whether or not new members were underrepresented. Data AnalysisIn order to begin the process of drawing conclusions we calculated the mean (average) response for each question; measured on a scale of 1 to 4. The results are as follows:We made use of all the calculated means by taking every question with a mean response of 2.9 or less, and marking it for further analysis. The upper level of 2.9 was decided on because an answer of a 1 or 2 was considered low, therefore the questions with mean responses in the ones or twos would be areas in need of consideration for improvement. All the questions that were marked for analysis were then brought together and paired by association. For example, we noticed that question 2 in the actions category of Worship Jesus (I have recently made adjustments in my life to grow closer to Christ and obey him more fully) appeared to be dependent on question 1 in the abilities category of Worship Jesus (I know practically how to seek and understand the will of God for my life.). To test the questions dependence upon one another we used a χ2 test for independence (because we have one population with many variables) conducted in five steps, the first three will appear as follows:At first glance it appears as though the two questions are dependent on one another, because the observed values are different from the expected values. However, this may be due to sampling variability. To decide we will conduct a χ2 Independence Test (α = .05).H0: Question one and question two have no associationHa: There is an association between question one and question twoConditions:The data comes from a random sample of church members? Yes, this condition may be checked for all tests.Sample was less than 10% of the population? Yes, the congregation at Austin Ridge is more than 400 members.The sample size is large? Yes, all expected values are ≥ 5.Steps four and five consist of calculations and conclusions, which were specific to each test. We have provided steps four and five for each test in the following:Test 1: Live Sacrificially Abilities question 2 (AB-2) (I am aware of the needs in my community and how I can be part of the solution) vs. Live sacrificially abilities question 3 (AB-3) (I know how to steward my resources so that I have available time and money to serve or bless others)4. Observed: Expected: AB-2 AB-2HighLowTotalHigh8.18.917Low10.912.123Total192140 AB-3 AB-3 χ2= 6.31 P=.011 df=15. Since the p-value (.011) is less than alpha (.05) we may reject the null hypothesis, and conclude that there is an association between the answers for Live Sacrificially abilities questions 2 and 3.HighLowTotalHigh12517Low71623Total192140Test 2: Led by Scripture actions question 1 (AC-1) (On average, the number of days I read my Bible each week is …) vs. Live Generously abilities question 3 (AB-3) (I know how to steward my resources so that I have available time and money to serve or bless others).4.Observed:Expected:Ac-1Ab-3HighLowTotalHigh24630Low61420Total302050Ac-1Ab-3HighLowTotalHigh181230Low12820Total302050χ2=12.5 P-value=4.07 x 10-4 df=1Since the p-value (4.07 x 10-4) is lower than alpha (.05) we may reject the null hypothesis and conclude that there is an association between Led by Scripture actions question 1 and Live Generously abilities question 3.Test 3: Missional abilities question 1 (AB-1) (I know how to share my faith story with people who may not know Jesus) vs. Missional actions question 2 (AC-2) (I am actively seeking opportunities to develop relationships with and share my faith story with my non-believing friends).4. Observed: Expected: AB-1 AB-1HighLowTotalHigh12113Low232447Total352560HighLowTotalHigh7.585.4213Low27.4219.5847Total352560 AC-2 AC-2χ2= 7.88 P= .004 df= 15. Since the p-value (.004) is less than alpha (.05) we may reject the null hypothesis and conclude that the responses to Missional abilities question 1 and Missional actions question 2 are associated.Test 4: Live Sacrificially abilities question 2 (AB-2) (I am aware of the needs in my community and how I can be part of the solution) vs. Live Sacrificially actions question 3 (AC-3) (I am serving in my church or community regularly-I do more than just show up and enjoy the worship service).4. Observed: Expected: AB-2 AB-2HighLowTotalHigh13518Low31922Total162440HighLowTotalHigh7.210.818Low8.813.222Total162440 AC-3 AC-3χ2=14.1 P-value=1.68x10-4 df=15. Since the p-value (1.68 x 10-4) is less than alpha (.05) we may reject the null hypothesis and conclude that there is an association between the responses to the questions “I am aware of the needs in my community and how I can be part of the solution” and “I am serving in my church or community regularly-I do more than just show up and enjoy the worship service”.Test 5: Authentic Relationships abilities question1 (AB-1) (I have learned how to give and receive grace and forgiveness in relationships with all people) vs. Authentic Relationships actions question 1 (AC-1) (My close friends know what it is really going on in my life both logistically and spiritually).4. Observed:Expected: AB-1 AB-1HighLowTotalHigh15318Low192342Total342660HighLowTotalHigh28.77.742Low12.35.718Total411960 AC-1 AC-1χ2=10.3 P-value=.001 df=15. Since the p-value (.001) is less than alpha (.05) we may reject the null hypothesis and conclude that there is an association between the responses to the questions I have learned how to give and receive grace and forgiveness in relationships with all people and My close friends know what it is really going on in my life both logistically and spiritually.HighLowTotalHigh10.27.818Low23.818.242Total342660Test 6: Worship Jesus abilities question 1 (AB-1) (I know practically how to seek and understand the will of God for my life) vs. Live sacrificially actions question 2 (AC-2) (I regularly find myself seeing and working to meet the needs of others-financially, practically, or spiritually).4. Observed: Expected: AB-1 AB-1 AC-2 AC-2 χ2=5.9804 P-value=.014465 df=1HighLowTotalHigh34842Low71118Total4119605. Since the p-value (.0145) is less than alpha (.05) we may reject the null hypothesis and conclude that there is an association between the responses to the questions “I know practically how to seek and understand the will of God for my life” and “I regularly find myself seeing and working to meet the needs of others-financially, practically, or spiritually”.Test 7: Missional abilities question 1 (AB-1) (I know how to share my faith story with people who may not know Jesus) vs. Missional actions question 2 (AC-2) (I am actively seeking opportunities to develop relationships with and share my faith story with my non-believing friends). 4.Observed:Expected: AB-1 AB-1HighLowTotalHigh13215Low121325Total251540AC-2 AC-2HighLowTotalHigh9.3755.62515Low15.6259.37525Total251540 χ2=7.45 P-value=.006 df=15. Since the p-value (.006) is less than alpha (.05) we may reject the null hypothesis and conclude that there is an association between the responses to the questions “I know how to share my faith story with people who may not know Jesus” and “I am actively seeking opportunities to develop relationships with and share my faith story with my non-believing friends.”Test 8: Live Sacrificially abilities question 3 (AB-3) (I know how to steward my resources so that I have available time and money to serve or bless others) vs. Live sacrificially actions question 2 (AC-2) (I regularly find myself seeing and working to meet the needs of others-financially, practically, or spiritually).4. Observed:Expected:HighLowTotalHigh19.7312.2732Low17.2710.7328Total372360 AB-3 AB-3 HighLowTotalHigh301242Low61218Total362460 AC-2 AC-2χ2=7.86 P-value=.005 df=15. Since the p-value (.005) is less than alpha (.05) we may reject the null hypothesis and conclude that the there is an association between the responses to the questions “I know how to steward my resources so that I have available time and money to serve or bless others” and “I regularly find myself seeing and working to meet the needs of others-financially, practically, or spiritually.”Test 9: Live Sacrificially abilities question 3 (AB-3) (I know how to steward my resources so that I have available time and money to serve or bless others) vs. Live Sacrificially actions question 1 (AC-1) (I deliberately and consistently giving financially to my church).4.Observed:Expected: AB-3 AB-3HighLowTotalHigh25732Low121628Total372360HighLowTotalHigh25.216.842Low10.87.218Total362460 AC-1 AC-1χ2=7.62 P-value=.006 df=15. Since the p-value (.006) is less than alpha (.05) we may reject the null hypothesis and conclude that there is an association between the questions “I know how to steward my resources so that I have available time and money to serve or bless others” and “I deliberately and consistently giving financially to my church.”Test 10: Prayer Dependent abilities question 2 (AB-2) (I have learned many different ways of praying—conversational, meditative, journaling, contemplative, intercessory…) vs. Missional actions question 1 (AC-1) (I pray regularly for my non-Christian friends).4.ObservedExpectedHighLowTotalHigh19625Low161935Total352560 AB-2 AB-2HighLowTotalHigh14.5810.4225Low10.4214.5835Total352560 AC-1 AC-1χ2=5.5033 P-value=.02 df=1 5. Since the p-value (.02) is less than alpha (.05) we may reject the null hypothesis and conclude that there is an association between the responses to the questions “I have learned many different ways of praying-conversational, meditative, journaling, contemplative, intercessory…” vs. “I pray regularly for my non-Christian friends.”Test 11: Authentic Relationships attitude question 1 (AT-1) (I enjoy being asked how I'm doing and am comfortable being appropriately honest) vs. Authentic Relationships actions question 1 (AC-1) (My close friends know what is really going on in my life both logistically and spiritually).4. Observed: AT-1Expected:AT-1HighLowTotalHigh36541Low131124Total491665HighLowTotalHigh30.9110.0941Low18.095.9124Total491665AC-1 AC-1 X2= 9.23 P= .0024 df=15. Since the p-value (.0024) is less than alpha (.05) we may reject the null hypothesis and concluded that there is an association between the responses to the questions “I enjoy being asked how I'm doing and am comfortable being appropriately honest” and “My close friends know what is really going on in my life both logistically and spiritually.”Test 12: Live Sacrificially abilities question 1 (AB-1) (I know my spiritual gifts and how they can be used in my church or community) vs. Missional actions question 3 (AC-3) (I am actively seeking opportunities to develop relationships with and share my faith story with my non-believing friends).4. Ab-1Ac-3HighLowTotalHigh81220Low11920Total192140Observed:Expected:Ab-1Ac-3HighLowTotalHigh9.510.520Low9.510.520Total192140χ2=.90 P-value=.34 df=15. Because our p-value (.34) is larger than the alpha (.05), we can neither reject the null hypothesis nor conclude they are dependent of one another. Test 13: Live Sacrificially abilities question 3 (AB-3) (I know how to steward my resources so that I have available time and money to serve or bless others) vs. Live Sacrificially actions question 3 (AC-3) (I am serving in my church or community regularly-I do more than just show up and enjoy the worship service).4.Observed:Expected:Ab-3Ac-3HighLowTotalHigh11718Low91322Total202040Ab-3Ac-3HighLowTotalHigh9918Low111122Total202040χ2=1.62 P-value=.20 df=15. Because our p-value (.20) is larger than the alpha (.05), we can neither reject the null hypothesis nor conclude they are dependent of one another. Test 14: Led by Scripture abilities question 1 (AB-1) (I am confident I know how to read or study the Bible and understand it clearly and practically) vs. Live Sacrificially actions question 1 (AC-1) (I am deliberately and consistently giving financially to my church).4. Observed:Expected:Ab-1Ac-1HighLowTotalHigh331548Low14822Total482270Ab-1Ac-1HighLowTotalHigh32.915.148Low15.16.922Total482270χ2=.18 P-value=.67 df=15. Because our p-value (.67) is larger than the alpha (.05), we can neither reject the null hypothesis nor conclude they are dependent of one another. Test 15: Authentic Relationships attitude question 1 (AT-1) (I enjoy being asked how I’m doing and am comfortable being appropriately honest) vs. Authentic Relationships actions question 2 (AC-2) (The real me is known and cared for at my church)4.Observed:Expected:At-1Ac-2HighLowTotalHigh18624Low7916Total251540Ac-2AC-2HighLowTotalHigh15924Low10616Total251540χ2=4 P-value=.046 df=15. Due to the fact our p-value (.046) is lower than the alpha (.05); we may reject the null hypothesis and conclude that there is an association between the questions “I enjoy being asked how I’m doing and am comfortable being appropriately honest” and “The real me is known and cared for at my church.”Test 16: Authentic Relationships attitude question 1 (AT-1) (I enjoy being asked how I’m doing and am comfortable being appropriately honest) vs. Authentic Relationships actions question 1 (AC-1) (My close friends know what is really going on in my life both logistically and spiritually)4.Observed:Expected:At-1Ac-1HighLowTotalHigh15722Low12618Total271340At-1Ac-1HighLowTotalHigh14.857.1522Low12.155.8518Total271340χ2=.01 P-value=.92 df=15. Because our p-value (.92) is larger than the alpha (.05), we can neither reject the null hypothesis nor conclude the questions are dependent of one another. Test 17: Worship Jesus abilities question 1 (AB-1) (I know practically how to seek and understand the will of God for my life) vs. Worship Jesus actions question 2 (AC-2) (I have recently made adjustments in my life to grow closer to Christ and obey him more fully).4. Observed:Expected:Ab-1Ac-2HighLowTotalHigh181331Low7714Total252045Ab-1Ac-2HighLowTotalHigh17.213.831Low7.86.214Total252045χ2=.254 P-value=.614 df=15. Because our p-value (.614) is larger than the alpha (.05), we can neither reject the null hypothesis nor conclude that the questions are not independent of one another To conduct the tests our group split up into six groups and each ran the test on three sets of questions. The data was then compiled together, in order to draw conclusions. Comments on Methods Used for AnalysisWe have identified one possible source of bias in our analysis. By recording all the mean responses without confidence intervals, we did not account for sampling variability in the means used to decide which questions we were going to use in the independence tests. However, we believe that through our testing we were able to partially negate this bias by making sure our values were not due to sampling variability. Conclusions Drawn from Data AnalysisFrom our analysis of the data, the team is able to find which questions were dependent on one another. Here are the questions that showed dependency on one another.1. Live Sacrificially: I am aware of the needs in my community and how I can be part of the solution (Ab-2). vs. Live Sacrificially: I am serving in my church or community regularly-I do more than just show up and enjoy the worship service (Ac-3).2. Live Sacrificially: I am aware of the needs of my community and how I can be part of the solution. (Ab-1). vs.Live Sacrificially: I know how to steward my resources so that I have available time and money to serve or bless others (Ab-3).3. Live Sacrificially: I know how to steward my resources so that I have available time and money to serve or bless others (Ab-3). vs. Live Sacrificially: I am deliberately and consistently giving financially to my church (Ac-1).4. Live Sacrificially: I know how to steward my resources so that I have available time and money to serve or bless others (Ab-3). vs.Live Sacrificially: I regularly find myself seeing and working to meet the needs of others-financially, practically, or spiritually (Ac-2).5. Led by Scripture: (Ac-1) On average, the number of days I read my Bible each week is… vs.Live Sacrificially: (Ab-3) I know how to steward my resources so that I have available time and money to serve or bless others.6. Missional: I know how to share my faith story with people who may not know Jesus (Ab-1). vs. Missional: I am actively seeking opportunities to develop relationships with and share my faith story with my non-believing friends (Ac-2).7. Authentic Relationships: I enjoy being asked how I’m doing and am comfortable being appropriately honest (At-1). vs.Authentic Relationships: The real me is known and cared for at my church (Ac-2). 8. Authentic Relationships: I enjoy being asked how I am doing and am comfortable being appropriately honest (At-1). vs.Authentic Relationships: My close friends know what is really going on in my life both logistically and spiritually (Ac-1).9. Authentic Relationships: I have learned how to give and receive grace and forgiveness in relationships with all people (Ab-1). vs.Authentic Relationships: My close friends know what it is really going on in my life both logistically and spiritually (Ac-1). 10. Worship Jesus: I know practically how to seek and understand the will of God for my life (Ab-1). vs.Live Sacrificially: I regularly find myself seeing and working to meet the needs of others-financially, practically, or spiritually (Ac-2).11. Prayer Dependent: (Ab-2) I have learned many different ways of praying—conversational, meditative, journaling, contemplative, intercessory… vs. Missional actions: (Ac-1) I pray regularly for my non-Christian friends.These eleven pairs of questions are representative of areas Austin Ridge Bible Church needs to focus on helping their congregation improve in. Through the use of the χ2 Independence Test, we were able to prove a significant relationship between each pair of questions and the following issues should be addressed by the church to raise the overall mean responses:Question 1: The congregation should be made aware of the ways they can help improve the community which, mathematically, would lead them to show up more regularly ready to serve.Question 2-5: The congregation does not know how to steward both their time and money. If they are taught this then the church should see a raise in more people serving and giving regularly to the church.?Question 6-9: The congregation struggles with communicating their feelings and faith with other people, which leads to them being cut off from sharing the gospel and strengthening their faith through others. This needs to be emphasized so more people will evangelize for Christ.Question 10: The congregation does not understand their calling in this world. If the church emphasis ways the congregation can serve God and how, then there should be a raise in people looking to help others financially, practically, and spiritually.Question 11: The congregation does not have many ways of praying. Helping people connect to God would open up people to pray more for their non-Christian friends. ................
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