[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-39775-en":3,"doc-seo-39775-105":29,"detail-sidebar-cat-0-en-105":90},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},39775,1099514068365,"Aurelia","https://ap-avatar.wpscdn.com/avatar/10000253d8d9f28188e?_k=1776742907772140068",8,"Research & Report","Determining Sample Size for Research Activities","The text presents an efficient method for determining required sample size so results remain representative of a defined population. It provides a chi-square–based formula and defines each parameter: confidence level value, population size, assumed population proportion for maximum variance, and degree of accuracy. A ready-to-use reference table is supplied, with an example using a population of 9000 high school teachers leading to a required sample size of 368 for merit pay opinions.","# DETERMINING SAMPLE SIZE FOR RESEARCHACTIVITIES\n\nROBERTV.KREJCIEUniversity of Minnesota,DuluthDARYLE V.MORGANTexas A.&M.University  \nTHE ever increasing demand for research has created a needfor an efficient method of determining the sample size needed tobe representative of a given population.In the article“Small Sam-ple Techniques,\"the research division of the National EducationAssociation has published a formula for determining sample size.Regrettably a table has not been available for ready,easy referencewhich could have been constructed using the following formula.  \ns=X²NP(1-P)÷d²(N-1)+X²P(1-P).  \ns=required sample size.  \nX²=the table value of chi-square for 1 degree of freedom at thedesired confidence level(3.841).  \nN=the population size.  \nP=the population proportion (assumed to be .50 since thiswould provide the maximum sample size).  \nd=the degree of accuracy expressed as a proportion (.05).  \nNo calculations are needed to use Table 1.For example,onemay wish to know the sample size required to be representative.of the opinions of 9000 high school teachers relative to merit payincreases.To obtain the required sample size enter Table 1 atN=9000.The sample size representative of the teachers in thisexample is 368.Table 1 is applicable to any defined population.  \nTABLE 1  \nTable for Determining Sample Size from a Given Population  \n\n| N   | S.   | N   | S   | N   | S   |\n| --- | --- | --- | --- | --- | --- |\n| 10   | 10   | 220   | 140   | 1200   | 291   |\n| 15   | 14   | 230   | 144   | 1300   | 297   |\n| 20   | 19   | 240   | 148   | 1400   | 302   |\n| 25   | 24   | 250   | 152   | 1500   | 306   |\n| 30   | 28   | 260   | 155   | 1600   | 310   |\n| 35   | 32   | 270   | 159   | 1700   | 313   |\n| 40   | 36   | 280   | 162   | 1800   | 317   |\n| 45   | 40   | 290   | 165   | 1900   | 320   |\n| 50   | 44   | 300   | 169   | 2000   | 322   |\n| 55   | 48   | 320   | 175   | 2200   | 327   |\n| 60   | 52   | 340   | 181   | 2400   | 331   |\n| 65   | 56   | 360   | 186   | 2600   | 335   |\n| 70   | 59   | 380   | 191   | 2800   | 338   |\n| 75   | 63   | 400   | 196   | 3000   | 341   |\n| 80   | 66   | 420   | 201   | 3500   | 346   |\n| 85   | 70   | 440   | 205   | 4000   | 351   |\n| 90   | 73   | 460   | 210   | 4500   | 354   |\n| 95   | 76   | 480   | 214   | 5000   | 357   |\n| 100   | 80   | 500   | 217   | 6000   | 361   |\n| 110   | 86   | 550   | 226   | 7000   | 364   |\n| 120   | 92   | 600   | 234   | 8000   | 367   |\n| 130   | 97   | 650   | 242   | 9000   | 368   |\n| 140   | 103   | 700   | 248   | 10000   | 370   |\n| 150   | 108   | 750   | 254   | 15000   | 375   |\n| 160   | 113   | 800   | 260   | 20000   | 377   |\n| 170   | 118   | 850   | 265   | 30000   | 379   |\n| 180   | 123   | 900   | 269   | 40000   | 380   |\n| 190   | 127   | 950   | 274   | 50000   | 381   |\n| 200   | 132   | 1000   | 278   | 75000   | 382   |\n| 210   | 136   | 1100   | 285   | 1000000   | 384   |\n\nNote.—N is population size.Sis sample size.  \nKREJCIE AND MORGAN  \n1,000,000  \n\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  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provided?\",\"answer\":\"The table is entered using the population size N to obtain the required sample size S. For a population of 9000 high school teachers, the required sample size is 368.\"}]",1783086707,10,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":27},"determining-sample-size-for-research-activities","",{"@graph":35,"@context":84},[36,52,67],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":21},"https://docshare.wps.com/document/determining-sample-size-for-research-activities/39775/",{"url":51,"name":13,"@type":53,"author":54,"headline":13,"publisher":56,"fileFormat":59,"inLanguage":23,"description":14,"dateModified":60,"datePublished":61,"encodingFormat":59,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":55},"Person",{"url":40,"name":57,"@type":58},"DocShare","Organization","application/pdf","2026-07-09","2026-07-03",true,{"@type":64,"interactionType":65,"userInteractionCount":20},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"What problem does the document address?","Question",{"text":74,"@type":75},"It addresses the need for an efficient way to determine the sample size required for a study to be representative of a given population.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"What are the main components of the sample size formula?",{"text":79,"@type":75},"The formula uses chi-square at a chosen confidence level, population size (N), assumed population proportion (P=0.50), and the accuracy level expressed as a proportion (d).",{"name":81,"@type":72,"acceptedAnswer":82},"How is the table used and what example result is provided?",{"text":83,"@type":75},"The table is entered using the population size N to obtain the required sample size S. 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