【會員專屬好文】地震有季節性嗎？作者：約翰．史蒂芬．德拉普

本文選自美國NCGR占星研究協會NCGR占星調查研究年鑑 – 2018-19年冬季號 第41-48頁 ***特別感謝 Astrid Lian 翻譯好文與會員共享*** 正文 預測結果 原文 正文 地震有季節性嗎？對92年期間全球規模7以上地震分布之分析 摘要 本文假設數據的分類和呈現方式，會對這些數據得出的結論產生重大影響。 序言 突然間，沒有警告，沒有憐憫，只有混亂、破壞和死亡。一場我們稱之為地震的大規模震盪襲來，幸運的人立即身亡，而受困的倖存者在痛苦、黑暗和絕望中度過數日，直到他們因負傷及乾渴慢慢死去。救援人員在瓦礫堆中瘋狂地搜索，希望逐漸消失，空氣瀰漫著死亡的惡臭。 在人類忍受許多所謂的「神的行為」中，地震是目前為止最殘酷的一種。如果上帝的旨意「行在地上，如同行在天上」，我們是否可以察看天空，得知即將發生的事？地震可以預測嗎？地震有季節性嗎？關於美國地質調查局（United States Geological Survey / USGS）的一份聲明指出： 「不存在所謂的『地震天氣』。據統計，在寒冷的天氣、炎熱的天氣、多雨的天氣等，地震的分布大致相同。已知有關主要風暴系統（颱風、颶風等）的極大低壓變化，會引發地殼斷層的滑動（慢地震／slow earthquakes），也可能在引發一些破壞性地震上發揮作用。然而，這些數字很小，沒有統計學上的意義。」（Malcolm Johnston博士提供）[1] 。 而2010年1月不幸的海地地震，正是向我提出調查這一現象的挑戰。多年來，我一直觀察熱帶氣旋和其他惡劣天氣，在我看來地震和颶風常常同時出現在新聞頭條上。從那時的觀察過程中，我相信自己的學習有些收獲，現在將與大家分享其中的一個結果。 研究計劃 本文假設，以曆法月份來組織和記錄科學數據的傳統方式，可能會掩蓋這些數據原本存在的自然模式。 我的做法是，從美國地質調查局的地震項目中下載了1205次規模7.0以上的地震，這些地震發生在1925年至2016年、共橫跨了92年期間；然後，按照三種處理方法來組織這些數據：首先，我以傳統方法、即按曆法月份進行分類後，把數據全加總起來，這是科學機構的通用方法。再來，我根據黃道星座（Signs of the Zodiac）、大約每個月的21日到下個月21日，整理相同的數據。最後，作為對照組，我把黃道拆開來、從每個月的5日到下個月5日左右，將數據進行分類。我接著採用基本的統計程式，用圖形說明所獲得的分布，再透過卡方適合度（Chi-square Goodness of Fit）[2]和二項分布（Binomial Distribution）[3]檢定對其進行分析。變量和檢定的具體細節列於附錄中。 顯著水準(p)（Significance Level） 研究人員選擇顯著水準(p)作為衡量統計檢定成功／失敗（即存在「證據」）的臨界值（Critical Value），是假定「虛無假設」（null hypothesis）為真時獲得樣本結果的可能性；即他／她願意接受正確拒絕「虛無假設」的機率水準，那麼他／她的研究假說可能就是正確的。另外，顯著水準是受眾群體和其他研究人員在審查檢定時考量的因素，可依此決定這項資訊是否可信、有效或有用。 顯著水準以機率(p)表示，為小數形式從0.0（無機會）到1.0（肯定有機會）不等，這是一個事件因正常抽樣變化或僅僅是「隨機」（random chance）發生的可能性。 顯著水準不是固定不變的，視情況而定。最常見的是： (p) = 0.10，即10%或十分之一的機會（中等顯著）(p) = 0.05，即5%或二十分之一的機會（最普遍接受的水準）(p) = 0.01，即1%或百分之一的機會（非常高度的顯著水準） 物理科學量化檢定的顯著水準通常相當嚴格：(p)為0.05或(p) 0.01。社會科學質性檢定（如占星學）的水準比較寬鬆，認為0.10的(p)便具有中等意義[4]。 由於我們的實驗是對質性／分類變量（qualitative/ categorical variables）的次數分布進行比較，我選擇小於或等於(p)=0.10的臨界值，這是一個中等顯著水準，以證明占星學對這份地震活動樣本的影響。 處理方法一：按曆法月份 圖一以圖例形式顯示了1925年至2016年期間所發生的1205次規模7.0以上地震（EQ）之曆法月份分布。卡方適合度檢定得出的機率為(p)=0.30，表示類似的模式可能在100個隨機樣本中出現30次；或者，換句話說，這種模式是隨機的結果為30%，遠遠超過普遍接受的顯著水準。請注意，黑色的分布線大致沿著灰色的預期平均線，只有9月和11月兩處明顯偏離。 表格1是通過二項分布檢定法所得到的（單側；one-tailed）機率[5]總結。如表格所示，9月的地震低於預期，其顯著水準為(p)=0.04，11月的地震高於預期，其顯著水準為(p)=0.01，兩者都認為是高度顯著。 然而，我們必須記住，這種地震分布模式之於整體卡方值為隨機抽樣變化發生的可能性是30%，因此，在相同的1205次地震資料進行第二系列12個二項式檢定的結果，確實增加了12個類別（星座，譯註：應為月份）檢定中，結果至少有一個類別(p)小於0.05的機會。這就是所謂的「邦佛洛尼」（Bonferroni）效應。打個比方，這就像對著一個距離很近的大靶子開了12槍，你射中「靶心」（Bulls@Eyes）的機會就會增加。 以這種傳統方式來看，似乎支持了美國地質調查局（「不存在所謂的地震天氣」）堅持的「虛無假設」立場。 曆法月份分類：左為【圖1】卡方適合度檢定分布；右為【表格1】二項分布檢定法的機率總結 ＊ ＊ ＊ ＊ ＊ ＊ ＊ 處理方法二：按黃道星座 當相同的1,205次地震按黃道星座分類時，出現了一個非常不同且獨特的模式。這種分布顯示了對稱性和內聚性。 卡方檢定（The Chi-square test）返回的機率為(p)=0.10，這是一個中等但仍然顯著的結果，表示類似的模式在100個隨機樣本中只出現10次，或者說，這個結果只有10%隨機發生的可能性，與月份分類明顯不同。還注意到，黑色的分布線在12個星座中只有5個星座沿著灰色的預期平均線，這一圈的其餘部分有5個星座顯而易見地偏離，與月份分布截然不同。 此外，在對12個類別（星座）逐一進行二項分布檢定時，黃道星座明顯偏離預期平均值的結果有五個，而月份分布中只有兩個。表格2的二項式總結包含了五個中等到高度顯著的結果，而考量到這種地震分布模式的整體卡方值(p)0.10較低，這些結果獲得了某種可信度，而月份分布卻沒有。 再用一次剛剛的比喻，這個「黃道靶子」更小，更遠，而我們一樣開12槍卻命中了5次靶心。 我認為，當這個樣本按黃道星座分類時，其結果的可信度確實挑戰了美國地質調查局的立場，即「這些數字很小，沒有統計學上的意義」。 黃道星座分類：左為【圖2】卡方適合度檢定分布；右為【表格2】二項分布檢定法的機率總結 ＊ ＊ ＊ ＊ ＊ ＊ ＊ 處理方法三：分割黃道 最後，我們得到圖三，以圖形展示當我們在對照組抵消黃道的假設影響時會發生什麼。 請記住，我們觀察到月份分類都包含了一個星座的2/3和下一個星座的1/3，可能會使結果偏向於擁有較大比例天數的星座。 如果我們把黃道在月份分類比例大於2/3-1/3的影響削弱，會得到一個非常不同的結果。當透過「分割」一半黃道的影響，創建另一12個類別的對照組，並將地震的分布均勻地分配到這些中和類別裡，卡方檢定返回一個非常高的機率值，(p)=0.56，意味著100個隨機樣本中會產生56個像這樣的模式，或者說，這種分布有56%的可能性是隨機的結果。 最後，由於這種分布為隨機的機率如此之高（0.56），所得到的兩個顯著的二項式結果（表格3）幾乎毫無意義，完全是隨機抽樣變化的結果。還是用那個比喻：一個伸手就摸得到的特大靶子。 分割黃道分類：左為【圖3】卡方適合度檢定分布；右為【表格3】二項分布檢定法的機率總結 ＊ ＊ ＊ ＊ ＊ ＊ ＊ 小結 綜上所述，我們考慮了三種分布，按其顯著水準的順序排列： 黃道星座(p) = 0.10 （有五個顯著的類別）曆法月份(p) = 0.30 （有兩個顯著的類別）分割黃道的檢驗(p) = 0.56 （有兩個顯著的類別） 顯然，黃道星座的分布是最不可能偶然發生的，而且12個類別（星座）中顯示出五個顯著的（單側）二項式機率（即五次靶心），本研究的證據支持這樣的假設：按黃道星座的分類，呈現了這種自然現象最清晰的畫面，我們可以據此進行調查。 然而，我相信這項研究最重要的發現是，實際的地震在分類和重新分類下對每種分布的「影響」，第一是整個黃道的分布，然後是曆法月份（2/3-1/3黃道）的分布，最後是分割成一半的黃道，以便盡可能地減少其影響，同時保持地震資料在其自然時間序列中發生的完整性。 而地震模式的機率從黃道星座劃分的10%低點，跳到無黃道星座之對照組56%的高點（跟擲硬幣的機率差不多），成為黃道星座對地震活動具影響力的證據。 【圖5】地震模式於黃道與無黃道分布之機率；中和黃道後，分布降低至「虛無假設」之水準 ＊ ＊ ＊ ＊ ＊ ＊ ＊ 那麼，這是否意味著我們可以用太陽星座學來預測地震？不，當然不是。但它確實意味著我們在研究因果時，可以知道要去何時何地找關係。例如，我們的樣本在這92年中，速度較快的行星已經繞行了許多圈；冥王星和海王星還沒繞完，而天王星只繞了一圈。冥王星在那些星座花費了最多的時間，也顯示出最大的意義，所以這些慢速者也許應該成為我們研究的基礎。 哦，還有一件事：似乎確實有一個地震的季節。在這項研究中，巨蟹座和處女座的重大地震次數為83次，但在獅子座期間這數字躍升了50%，達123次，所以在獅子座期間遇上重大地震的機率大幅提高。 因此，如果你有業務往來於全球地震活躍的地區，可能你的行程會想跳過雙子座和獅子座期間，改在巨蟹座或處女座的月份出差！這就是我現在的全部內容，謝謝你的關注。 結語：地震預測 我確實相信，地震，或者說，地震發生的時間，可以有一定的預測性，因為過去我在這方面有些成功的經驗。截至本文交稿給NCGR的日期，即2018年6月27日，而自2018年1、2月這上一個交食週期以來，還沒有發生規模7以上的地震。就在地平線上，我看到一些極端的天文事件將在今年夏天發生：一連串與近地點／遠地點週期重合的食相，以及火星，在南赤緯極端地出界，正對齊了月交點，並將與在金牛座和摩羯座的土星／天王星形成半六分相／四分相。因此，根據這些訊息，我要做一個有憑據地推測，即規模7以上的地震，至少有一次，可能還有另一次，將在下列任何日期的前後一或兩天發生： 2018年7月13日 2018年7月19日 2018年7月27日 2018年8月1日 2018年8月10日 2018年8月20日 二項分布計算器[6] 6個(n) 正中1個(K) 的機率是p=0.179，所以，看起來我有大約18%的機率預測成功。時間會證明一切。 ＊ ＊ ＊ ＊ ＊ ＊ ＊ 附錄 為了避免無聊的重複，我只納入變量的具體細節，以及按黃道星座劃分地震分布的統計檢定。 地震（EQ）頻率：M7 + (1925-2016) 92年 x 365.25= 33,603天為母體1205次eq ÷ 33,603天 = 每天(p) 0.03585次M7+EQ M8+ (1901-2016) (用於增補)116年 x 365.25 = 42,369天93年eq ÷ 42,369天 = 每天(p) 0.00219次M8+EQ 黃道變量／分割黃道的檢驗365.25 ÷ 12星座 = 每個星座30.4天92年 x 30.4 = 每個星座2800.25天(p) 0.03585 x 每個星座2800.25天 = 預期100.4天 曆法月份變量／30天的月份92年 x 30 = 每月2760天(p) 0.03585 x 每月2760天 = 預期99.0天 31天的月份92年 x 31 = 每月2852天(p) 0.03585 x 每月2852天 = 預期102.3天 2月份92年 x 28.25 = 每月2599天(p) 0.03585 x 每月2599天 = 預期93.3天 卡方適合度（CHI-SQUARE GOODNESS OF FIT） 自由度（Degrees of Freedom）（如下方表格6） 自由度(df) 是一個數學概念，也是一個參數，它應用於幾個不同的統計檢定公式中，以確定(p)、即用於決定是否拒絕一個虛無假設的臨界值。最常見需要(df)的檢定是：獨立同分布（Independence distribution）的卡方適合度和卡方檢定，司徒頓t分布（Student’s ‘t’ distribution）及變異數分析的F分布（ ANOVA’s ‘F’ distribution）。 【表格6】卡方臨界值／自由度 (df)的概念既難解釋又難理解，但大致說來(df)是對分布樣本量的調整，是一種「微調」，以補償統計檢定對該分布臨界值(p)估計不足的趨勢。註：(n)代表樣本量，(k)代表類別。 自由度的個數對於每一個適合度檢定都是不同的。對於量化的分布來說，(df)一般公式是樣本量減去1：df = (n1)。對於質性的分布，它是類別數量減去1：df = (k-1) 在按12個星座分布的情況下，每個星座都是一個單獨的類別，卡方適合度檢定是這樣決定的：(df) = (k-1) = (12-1) = 11。 在接下來的兩列中包括了一個典型統計學教科書中的卡方臨界值表。正如這裡所見的表格7[7]。 標示處是我們所研究之地震／黃道分布的卡方檢定參數： (df) = 11 卡方值 = 17.12(p) = .10. 表格8放在下方表格7之後，顯示二項分布（單側）的機率。 【表格7】卡方臨界值／自由度 【表格8】二項分布（單側）的機率 ＊ ＊ ＊ ＊ ＊ ＊ ＊ 參考資料／資源 [1] https://www.usgs.gov/faqs/ there-earthquake-weather?qtnews_science_products=0#qtnews_science_products [2] Microsoft Excel電子試算表之卡方檢定 [3] http://www.socscistatistics.com/tests/binomial/Default2.aspx 例如，2800(n)中正好或大於123(k)的（單側）機率為p=0.012783 [4] https://www.socscistatistics.com/tests/Default.aspx 作為例子，本網站大多數檢定的臨界值選項為：(p).01; (p).05; 和 (p).10 [5] http://www.socscistatistics.com/tests/binomial/Default2.aspx [6] 同上 [7] Voelker, Orton and Adams, Cliffs Quick Review Statistics, Wiley Publications, New York, 2001 [8] http://www.socscistatistics.com/tests/binomial/Default2.aspx 本文選自美國NCGR占星研究協會NCGR占星調查研究年鑑 – 2018-19年冬季號 第41-48頁 預測結果 「地震有季節性嗎？」於2018年8月26日之追加內容 「結語：地震預測」的結果 我在2018年6月一篇關於地震分布的文章（2018年6月27日提交給NCGR）中，包含了一個「有憑據地推測」，即在即將到來的7、8月的交食週期中，至少會發生一次規模7以上的地震，並公布了一系列我推定地震活動最可能發生的日期。 從「結語：地震預測」 「……我看到一些極端的天文事件將在今年夏天發生：一連串與近地點／遠地點週期重合的食相，以及火星，在南赤緯極端地出界，正對齊了月交點，並將與在金牛座和摩羯座的土星／天王星形成半六分相／四分相。因此，根據這些訊息，我要做一個有憑據地推測，即規模7以上的地震，至少有一次，可能還有另一次，將在下列任何日期的前後一或兩天發生：7/13；7/19；7/27；8/1；8/10；8/20。」 (2018年夏季的交食週期) 這個預測非常成功：先發生了一次大地震（規模8.2），然後又一次大地震（規模7.3），分別在目標日期8月20日這一天內發生。 發生規模8以上地震（M8+ EQ’s）的平均頻率是每天0.002次，規模7以上（M7+）的頻率是0.0359。若要得到這些獨立事件在一定數量的試驗中共同發生的機率，則是乘以它們各自的頻率： p(M8+EQ, M7+EQ) = 0.002 x 0.0359 = 0.0000718 這樣就確定了試驗的總數： 6個目標日期前後一或兩天= 6個目標區、每個目標區5天= 30天「獨立試驗」 表格5中列出了這種共同發生的二項式機率： (p)=0.002，或者換句話說，大約是千分之二的機會。(來自MS Excel) 另外值得注意的是，上述的大地震發生在獅子座這個黃道星座，這在正文中已經強調過了。 最後，有大量較小規模6以上的地震活動，也發生在預測的目標日期。在6個目標日期中，有5個發生了多次地震（打中），命中率為83%，其中一半的地震似乎與日食有關，另一半則與8月下旬特別強烈的行星影響有關。我希望能在未來的文章中介紹。 結論：雖然這只是個單一的檢定，但這些證據有力地支持地震活動中存在強大的占星影響。 【表格5】共同發生的二項式機率 原文 Is There a Season for Earthquakes? An Analysis of a 92-year Year Distribution of Magnitude 7+ Worldwide Earthquakes ABSTRACT The hypothesis of this paper is to suggest that the way data is categorized and presented can make a significant difference in the conclusions that can be drawn from those data. INTRODUCTION Suddenly, without warning and without mercy, chaos, destruction and death. A massive telluric upheaval that we know as an earthquake, has struck. The lucky ones die immediately. Trapped survivors linger in pain, darkness and despair for days until they slowly expire from their injuries and thirst. Rescuers frantically search the rubble as hope fades and the stench of death fills the air. Of the many so called “acts of god” endured by man, the earthquake is by far the cruelest one of them all. If Gods’ Will “be done in earth as it is in heaven” can we not search the heavens and know what is to come? Can earthquakes be predicted? Is there a season for earthquakes? A statement by the United States Geological Survey (USGS): “There is no such thing as “earthquake weather”. Statistically, there is approximately an equal distribution of earthquakes in cold weather, hot weather, rainy weather, etc. Very large low-pressure changes associated with major storm systems (typhoons, hurricanes, etc.) are known to trigger episodes of fault slip (slow earthquakes) in the Earth’s crust and may also play a role in triggering some damaging earthquakes. However, the numbers are small and are not statistically significant.” (Contributed by Dr. Malcolm Johnston) (1) It was the tragic January 2010 Haitian earthquake that challenged me to investigate this phenomenon. For years I had been observing tropical cyclones and other severe weather and it seemed to me that from time to time earthquakes and hurricanes appeared in the news headlines simultaneously. In the course of my observations, I believe I have learned a few things since then, one of which I would like to share with you now. STUDY PLAN The hypothesis of this paper is that the traditional way scientific data is organized and recorded, by calendar month, may obfuscate natural patterns existing in those data. What I have done is to download from the USGS Earthquake Catalogue the 1,205 magnitude 7.0+ earthquakes that have occurred over the 92-year time span of 1925 thru 2016. I then organized this data according to three treatments: First, I summed the data in the traditional manner of categorizing by Calendar Month, as is the usual method of scientific institutions. Next, I arranged the same data according to the Signs of the Zodiac, from approximately the 21(st) of one month to approximately the 21(st) of the next month. Lastly, as a control group, I split the Zodiac by categorizing the data from approximately the 5(th) of one month to approximately the 5(th) of the next. I then applied the basic statistical procedures of graphically illustrating the obtained distributions and then analyzing the same by means of the Chi-square Goodness of Fit (2) and Binomial Distribution (3) tests. Specific details of the variables and tests are presented in an appendix. A WORD ABOUT SIGNIFICANCE LEVELS (P) The Significance Level (p) that a researcher chooses as the Critical Value upon which to measure the success/failure (i.e. the presence of ‘evidence’) of a statistical test is the probability of the obtained sample results, assuming the ‘null hypothesis” is true. It is the level of chance he/she is willing to take that he or she is correctly rejecting the ‘null hypothesis’, and that his or her research hypothesis may be correct. Also, the Significance Level is what the audience and other researchers consider when reviewing the test and may thereby decide for themselves if the information is credible, valid or useful. Significance Levels are expressed as a probability (p), in decimal form ranging from 0.0 (no chance) to 1.0 (certainly chance), which is the possibility that an event occurred by normal sampling variation or mere ‘random chance’. Significance Levels are not set in stone but are situational, the most common being: (p) = .10 which is 10% or 1 chance in 10 (moderate significance)(p) = .05 which is 5% or 1 chance in 20 (most commonly accepted level)(p) = .01 which is 1% or 1 chance in 100 (very high significance level) Significance Levels for quantitative tests in the physical sciences are often quite strict: (p) .05 or (p) .01. Levels for qualitative tests in the social sciences (like astrology) are more relaxed and a (p) of .10 is considered moderately significant.(4) Since our experiments will be comparisons of frequencies distributed by qualitative/ categorical variables, I elect to choose a Critical Value of less than or equal to (p) = .10, a moderate Significance Level, as evidence of astrological influence upon this sample of earthquake activity. TREATMENT ONE: BY CALENDAR MONTH Chart One (next column) graphically displays the distribution by Calendar Month of 1,205 M7.0+ earthquakes (EQ’s) occurring during the years 1925 thru 2016. The Chisquare Goodness of Fit test returns a probability of (p) = 0.30, indicating that a similar pattern could probably occur 30 times out of 100 random samples, or, another way, a 30% probability that this pattern is the result of random chance, much beyond the commonly accepted Significance Levels. Notice that the black distribution line roughly follows the gray expected averages line, with just two sharp departures for September and November. Table One (above) is a summary of (one-tailed) probabilities (5) obtained by means of a Binomial Distribution test. As indicated by the graph, the fewer than expected EQ’s in September has a Significance Level of (p) =.04, and the higher than expected EQ’s for November has a Significance Level of (p) =.01, both of which are each considered highly significant. However, one must keep in mind that with an overall Chisquare of a 30% likelihood that this earthquake distribution pattern occurred by random sampling variation, the results from a second series of 12 Binomial tests performed on that same 1,205 EQ data set does increase the chance of obtaining a (p) less than .05 result for at least one of the 12 categories (Signs) tested. This is the so called ‘Bonferroni’ effect. To use a metaphor, that’s like taking 12 shots at a large target that is up close, increasing your chances of a ‘Bulls@Eye’. When viewed in this traditional way, the ‘null hypothesis’ position maintained by the USGS (“There is no such thing as earthquake weather”) seems to be supported. TREATMENT TWO: BY SIGNS OF THE ZODIAC A very different and distinct pattern emerges when the same 1,205 EQ’s are categorized by the Signs of the Zodiac. This distribution displays both symmetry and cohesiveness. The Chi-square test returns a probability of (p) = .10, a moderate but still significant result, suggesting that a similar pattern would emerge only 10 times out of 100 random samples, or, only a 10% likelihood of this result occurring by random chance, significantly different than the Monthly categories. Also notice the black distribution line only follows the grey expected averages line for 5 of the 12 Signs with sharp departures of 5 Signs along the rest of the wheel, distinctly different than the Monthly distribution. Furthermore, when each of the 12 categories (Signs) are tested against the Binomial distribution, the Zodiac Signs produce five significant departures from the expected average, versus only two from the Monthly distribution. The Binomial summary of Table Two contains five results ranging from moderate to highly significant and given the low overall Chi-square of (p).10 for this earthquake pattern of distribution, these results obtain a certain credibility that the Monthly distribution does not. Revisiting the previous metaphor, the ‘Zodiac target’ is smaller, farther away, and we still get five Bulls@Eyes out of 12 shots. In my opinion, when this sample is categorized by Zodiac Sign, the result does credibly challenge the USGS position that “the numbers are small and are not statistically significant”. TREATMENT THREE: BY SPLITZODIAC Lastly, we have Chart Three (next page) that graphically demonstrates what happens when we neutralize the assumed influence of the Zodiac in a control group. Keep in mind that each of the Monthly categories we have observed contain 2/3’s of one Sign and 1/3 of the next, potentially skewing a result in favor of the Sign with the larger proportion of days. If we dilute the influence of the Zodiac more than the 2/3 – 1/3 proportion of the Monthly categories, we get a very different result. When a control group of 12 categories is created by ‘splitting’ the influence of the Zodiac in half and spreading the distribution of earthquakes evenly into those neutralized categories, the Chi-square test returns a very high probability value of (p)=.56, meaning 56 out of 100 random samples would produce a pattern like this one, or, that there is a 56% likelihood that this distribution is the result of random chance. Finally, with such a high probability of random chance for this distribution (.56), the two significant Binomial results that were obtained (Table Three) are virtually meaningless, completely the result of random sampling variation. Again, with the metaphor: a huge target well within arms’ length reach. CONCLUSION In summary, we have three distributions to consider, in the order of their Significance Levels: (p) = .10 Signs of the Zodiac (with five significant categories)(p) = .30 Calendar Months (with two significant categories)(p) = .56 Split Zodiac Control (with two significant categories) Clearly, the Signs of the Zodiac distribution is the least likely to have occurred by chance and with five of the 12 categories (Signs) showing significant (one-tailed) Binomial probabilities (i.e. five Bulls@ Eyes), the evidence in this study supports the hypothesis that categorizing by Signs of the Zodiac presents the clearest picture of this natural phenomena upon which to conduct our investigations. However, I believe the most significant find in this study is the ‘effect’ on each distribution as the actual earthquakes are categorized and re-categorized, first as an all Zodiac distribution, then as a Calendar Month (2/3-1/3 Zodiac) distribution, and lastly by splitting the Zodiac in half in order to minimize its influence as much as is possible while maintaining the integrity of the earthquake data occurring in their natural sequence of time. The probability then jumps from a low 10% for the earthquake pattern by Zodiac Signs to a high of 56% for the non-Zodiac Signs control group (about the same probability as a coin flip), suggesting evidence for the influence of the Signs of the Zodiac on earthquake activity. So, does this mean that we can forecast earthquakes with Sun Sign Astrology? No, of course not. What it does mean is that we can know when and where to look in our research of cause and effect. For example, in the 92 years of our sample the faster planets have been around the wheel many times. Pluto and Neptune have not, however, and Uranus only once. Pluto has spent the most time in those Signs showing the greatest significance, so perhaps these slow movers should be the basis of our research. Oh, and there is one other thing: There does seem to be a season for earthquakes. In this study, the number of significant earthquakes during Cancer and Virgo were 83 but the number jumps 50% to 123 quakes during Leo so the odds of experiencing a significant earthquake during Leo go up considerably. So, if you have business in a seismologically active part of the world, you might want to skip the trip during Gemini and Leo and go in the months of Cancer or Virgo instead! That’s all I have for now. Thank you for your kind attention. EPILOGUE: AN EARTHQUAKE PREDICTION I do believe that earthquakes, or rather, the timing of them, can be predicted with some specificity, as I have had some success with this in the past. As of the date of submission of this paper to NCGR Publications, June 27, 2018, there have been no M7+ earthquakes since the last eclipse cycle of Jan/ Feb 2018. Just on the horizon, I see a number of extreme astronomical events due to occur this summer: A series of eclipses that coincide with the perigee/apogee cycles, and Mars, out of bounds in an extreme southern declination, is aligned with the Lunar Nodes and will be semi-sextile/ square to the forming Saturn/ Uranus trine in Taurus and Capricorn. So, on the basis of that information, I will take an educated guess that at least one, and probably another, M7+ earthquake will occur on any of the following dates, +/- a day or two: July 13, 2018 July 19, 2018 July 27, 2018 August 1, 2018 August 10, 2018 August 20, 2018 BINOMIAL DISTRIBUTION CALCULATOR (6) The probability of exactly 1 (K) out of 6 (n) is p = .179 So, it looks like I have about an 18% chance of a successful prediction. Time will tell. August 26, 2018 Addendum to “Is There a Season for Earthquakes?”THE RESULTS OF THE “EPILOGUE EARTHQUAKE PREDICTION” In a June 2018 article (submitted to NCGR on June 27, 2018) on the distribution of earthquakes, I included an “educated guess” that at least one M7+ earthquake would strike during an upcoming July/August Eclipse Cycle and posted a series of dates that I ascertained earthquake activity was most likely to occur. From the “Epilogue: An Earthquake Prediction” “…. I see a number of extreme astronomical events due to occur this summer: A series of eclipses that coincide with the perigee/apogee cycles, and Mars, out of bounds in an extreme southern declination, is aligned with the Lunar Nodes and will be semi-sextile/square to the forming Saturn/Uranus trine in Taurus and Capricorn. So, on the basis of that information, I will take an educated guess that at least one, and probably another, M7+ earthquake will occur on any of the following dates, 7/13; 7/19; 7/27; 8/1; 8/10; 8/20; +/- a day or two”. (Summer Eclipse Cycle 2018) This forecast was very successful: First one large earthquake (a M8.2 EQ) and then another (a M7.3 EQ) occurred each within one day of Target Date 8/20. The average frequency for M8+ EQ’s is .002 per day and that of M7+ is .0359. The probability of these independent events jointly occurring within a certain number of trials is obtained by multiplying their respective frequencies: p(M8+EQ, M7+EQ) = .002 x .0359 = .0000718 A total number of trials is determined in this way: 6 Target Dates +/-2 days = 6 Targets Zones of 5 days each = 30 ‘Independent Trials’. The Binomial probability of this joint occurrence is here in Table 5: (p)= .002, or in other words, about 2 chances in 1,000. (from MS Excel) Also worthy of note is that these large quakes occurred in the Zodiac Sign of Leo which has been emphasized in the main article. Finally, there was an exceptional amount of smaller M6+EQ activity that also occurred on the forecast Target Dates. There were multiple EQ’s (Hits) on 5 of the 6 Target Dates for a Hit Rate of 83%, and half of those quakes seemed to have been associated with the Eclipses, the other half with exceptionally strong planetary influences in late August. I hope to present in a future article. Conclusion: While this is just a single test, the evidence strongly supports the presence of potent astrological influences on earthquake activity. Appendix In order to avoid a boring redundancy, I will include just the specific details of the variables and statistical tests for the Earthquake Distribution by Signs of the Zodiac. EQ Frequency: M7+ (1925-2016) 92yrs x 365.25= 33,603 days in Population Space 1205 eq ÷ 33,603 days = (p) 0.03585 M 7+ EQ per day M8+ (1901-2016) (for addendum) 116yrs x 365.25 = 42,369 days 93 eq ÷ 42,369 days = (p) 0.00219 M8+ EQ per day Variables for Zodiac / Split Zodiac Control 365.25 ÷12 signs = 30.4 days per sign 92yrs x 30.4=2800.25 days per sign (p) .03585 x 2800.25 days per sign = 100.4 expected Variables for Calendar Months 30 Day Months 92yrs x 30 =2760 days per month (p) .03585 x 2760 days per month = 99.0 expected 31 Day Months 92yrs x 31 = 2852 days per month (p) .03585 x 2852 days per month = 102.3 expected February Months 92yrs x 28.25 = 2599 days per month (p) .03585 x 2599 days per month = 93.3 expected CHI-SQUARE GOODNESS OF FIT Degrees of Freedom (Table 6 below) Degrees of Freedom (df ) is a mathematical concept and a parameter that is applied to the formulas of several different statistical tests in order to determine (p), the critical value used to decide whether or not to reject a null hypothesis. The most common tests that require (df ) are: The Chi-square Goodness of Fit and Chisquare Test for Independence distribution, the Student’s ‘t’ distribution and ANOVA’s ‘F’ distribution. The (df ) concept is as difficult to explain as it is to understand, but the bottom line is that (df ) is an adjustment, a ‘fine tuning’, of the sample size of a distribution to compensate for the tendency of a statistical test to under-estimate that distribution’s critical value, (p). Note: (n) stands for sample size, (k) stands for categories. The number of Degrees of Freedom are determined differently for each of the applicable tests employed. For a quantitative distribution, the usual formula for (df ) is the sample size minus one: df = (n1). For qualitative distributions, it is the number of categories minus one: df = (k-1) In the case of a distribution by 12 astrological signs, each sign is a separate category, square Goodness of fit Test is determined in this way: (df ) = (k-1) = (12-1) = 11. Included in the next two columns is a Chi-square Critical Values Table from a typical statistic’s textbook. As seen here in Table 7. (7) Highlighted are the parameters of the Chi-square test of the Earthquake/Zodiac distribution we have examined: (df ) = 11 Chi-square value = 17.12(p) = .10. Table 8 follows Table 7 in the next columns to show the showing the binomial distribution (one-tailed) probabilities REFERENCES / RESOURCES (1) https://www.usgs.gov/faqs/ there-earthquake-weather?qtnews_science_products=0#qtnews_science_products (2) Microsoft Excel Spreadsheet Chi-sqr Test (3) http://www.socscistatistics.com/ tests/binomial/Default2.aspx e.g. The (one-tailed) probability of exactly, or greater than, 123(k) out of 2800(n) is p = .012783 (4) https://www.socscistatistics. com/tests/Default.aspx As an example, most of the Tests on this site have Critical Values options of: (p).01; (p).05; and (p).10 (5) http://www.socscistatistics. com/tests/binomial/Default2.aspx (6) ibid (7) Voelker, Orton and Adams, Cliffs Quick Review Statistics, Wiley Publications, New York, 2001 (8) http://www.socscistatistics. com/tests/binomial/Default2.aspx 作者簡介 約翰．史蒂芬．德拉普（John Steve DeLapp） 高中起自行創業，是擁有多家與運輸相關及汽車診斷維修業務公司的老闆。1970年代中期，通過玫瑰十字會（Rosicrucian Fellowship）的函授課程習得基礎占星學，此後持續觀察和研究世運占星，對熱帶氣旋和劇烈風暴特別感興趣。二十世紀的1990年代，他是NCGR的活躍成員，並在巴爾的摩、安納波利斯和里奇蒙分會講演，主題為猶太教／基督教經文中豐富的占星學訊息，以及丹．魯迪海爾（Dane Rudhyar）對於地理占星測定圖（Geodetic Equivalent）的理論。最近自商界退休，全身心投入至個人網站Astroweather.com，觀察預報颶風和惡劣天氣，並發表研究報告。他的電郵：sjdelapp@gmail.com中文翻譯、編輯 / Astrid