Use the Health SPSS dataset to answer the following questions. Assume a .05 level of significance:
1. Is there a statistically significant difference in weight between men and women? (Conduct an independentttest.)
2. Identify the independent and dependent variables.
3. Write a null hypothesis.
4. Write an alternative non-directional (2-tail) hypothesis.
5. Interpret your results. Guidelines for interpreting independentttests can be found inWhat to Include When Writing Up IndependenttTest Results (PDF).
6. Is there a statistically significant difference in number of cigarettes smoked before and after a smoking cessation course? (Conduct a dependent t test.) The variables are labelled "Cigarettes Smoked pre" and "Cigarettes Smoked Post".
7. Identify the independent and dependent variables.
8. Write a null hypothesis.
9. Write an alternative non-directional (2-tail) hypothesis.
10. Interpret your results. Guidelines for interpreting dependentttests can be found inWhat to Include When Writing Up DependenttTest Results (PDF).
In the following two screencasts, I complete problem #3 in Chapters 5 and 6 of your Munro text.
Use the Health SPSS dataset to answer the following questions. Assume a .05 level of significance: 1. Is there a statistically significant difference in weight between men and women? (Conduct an independent t test.) 2. Identify the independent and dependent variables. 3. Write a null hypothesis. 4. Write an alternative non-directional (2-tail) hypothesis. 5. Interpret your results. Guidelines for interpreting independent t tests can be found in What to Include When Writing Up Independent t Test Results (PDF). 6. Is there a statistically significant difference in number of cigarettes smoked before and after a smoking cessation course? (Conduct a dependent t test.) The variables are labelled "Cigarettes Smoked pre" and "Cigarettes Smoked Post". 7. Identify the independent and dependent variables. 8. Write a null hypothesis. 9. Write an alternative non-directional (2-tail) hypothesis. 10. Interpret your results. Guidelines for interpreting dependent t tests can be found in What to Include When Writing Up Dependent t Test Results (PDF). In the following two screencasts, I complete problem #3 in Chapters 5 and 6 of your Munro text. Microsoft Word - Dependent t results.docx What to include when writing up Dependent t-test results 1. Remind the reader of the type of test you used and the comparison that was made. The IV and DV do not need to be specifically identified as such, but those variables need to be included. Example:
“An dependent t-test was used to compare differences in self- reported pain scores before and after medication was administered.” 2. Report significance (or non-significance) between the conditions. Example:
“There was a significant difference in the self reported pain scores before medication was administered (M = 52.88, SD = 22.42) compared with after the medication was administered (M = 41.12, SD = 9.99) conditions; t(20) = 2.68, p = .014.” The difference was significant at the p < .05="" level.="" 3.="" summarize="" your="" results="" by="" connecting="" your="" findings="" back="" to="" the="" decision="" to="" either="" reject="" or="" accept="" the="" null="" hypothesis.="" if="" there="" is="" a="" difference,="" remind="" the="" reader="" of="" the="" nature="" of="" the="" difference.="" example:=""
="" “therefore,="" the="" null="" hypothesis="" that="" stated="" that="" there="" was="" no="" statistically="" significant="" difference="" in="" self="" reported="" pain="" scores="" between="" pre-="" and="" post-medication="" was="" rejected.="" in="" other="" words,="" the="" alternative="" hypothesis="" was="" supported.="" post-test="" scores="" were="" significantly="" lower="" compared="" to="" pre-test="" scores.="" these="" results="" were="" statistically="" significant="" at="" the="" p="">< .05="" level.”="" all="" together="" now…="" “an="" dependent="" t-test="" was="" used="" to="" compare="" differences="" in="" self-reported="" pain="" scores="" before="" and="" after="" medication="" was="" administered.="" there="" was="" a="" significant="" difference="" in="" the="" self="" reported="" pain="" scores="" before="" medication="" was="" administered="" (m="52.88," sd="22.42)" compared="" with="" after="" the="" medication="" was="" administered="" (m="41.12," sd="9.99)" conditions;="" t(20)="2.68," p=".014." therefore,="" the="" null="" hypothesis="" that="" stated="" that="" there="" was="" no="" statistically="" significant="" difference="" in="" self="" reported="" pain="" scores="" between="" pre-="" and="" post-medication="" was="" rejected.="" in="" other="" words,="" the="" alternative="" hypothesis="" was="" supported.="" post-test="" scores="" were="" significantly="" lower="" compared="" to="" pre-test="" scores.="" these="" results="" were="" statistically="" significant="" at="" the="" p="">< .05="" level.”="" microsoft="" word="" -="" independent="" t="" results.docx="" what="" to="" include="" when="" writing="" up="" independent="" t-test="" results="" 1.="" remind="" the="" reader="" of="" the="" type="" of="" test="" you="" used="" and="" the="" comparison="" that="" was="" made.="" the="" iv="" and="" dv="" do="" not="" need="" to="" be="" specifically="" identified="" as="" such,="" but="" those="" variables="" need="" to="" be="" included.="" example:="" “an="" independent="" t-test="" was="" used="" to="" compare="" differences="" in="" midterm="" exam="" grades="" between="" men="" and="" women.”="" 2.="" report="" significance="" (or="" non-significance)="" between="" the="" groups.="" example:="" “there="" was="" a="" significant="" difference="" in="" the="" midterm="" exam="" scores="" for="" men="" (m="60.18," sd="18.24)" compared="" to="" women="" (m="38.04," sd="9.87);" t(19)="3.41," p=".003.”" 3.="" summarize="" your="" results="" by="" connecting="" your="" findings="" back="" to="" the="" decision="" to="" either="" reject="" or="" accept="" the="" null="" hypothesis.="" if="" there="" is="" a="" difference,="" remind="" the="" reader="" of="" the="" nature="" of="" the="" difference.="" example:="" “therefore,="" the="" null="" hypothesis="" that="" stated="" that="" there="" was="" no="" statistically="" significant="" difference="" in="" midterm="" grades="" between="" men="" and="" women="" was="" rejected.="" men="" had="" a="" significantly="" higher="" midterm="" grades="" compared="" to="" women.="" this="" was="" statistically="" significant="" at="" the="" p="">< .01="" level.”="" all="" together="" now…="" “an="" independent="" t-test="" was="" used="" to="" compared="" differences="" in="" midterm="" exam="" grades="" between="" men="" and="" women.="" there="" was="" a="" significant="" difference="" in="" the="" midterm="" exam="" grades="" for="" men="" (m="60.18" sd="18.24)" compared="" to="" women="" (m="38.04," sd="9.87);" t(19)="3.41," p=".003." therefore,="" the="" null="" hypothesis="" that="" stated="" that="" there="" was="" no="" statistically="" significant="" difference="" in="" midterm="" grades="" between="" men="" and="" women="" was="" rejected.="" men="" had="" a="" significantly="" higher="" midterm="" grades="" compared="" to="" women.="" this="" was="" statistically="" significant="" at="" the="" p="">< .01="" level.”="" (="" c="" h="" a="" p="" t="" e="" r="" 2="" )organizing,="" displaying,="" and="" describing="" data="" objectives="" after="" studying="" this="" chapter,="" you="" should="" be="" able="" to:="" 1.="" discuss="" the="" nature,="" purpose,="" and="" types="" of="" statistics="" available="" for="" analyzing="" data.="" 2.="" recognize="" and="" define="" mathematical="" symbols="" commonly="" used="" in="" statistics.="" 3.="" correctly="" identify="" the="" measurement="" scale="" of="" a="" variable.="" 4.="" explain="" the="" relationship="" between="" the="" measurement="" scale="" of="" a="" variable="" and="" the="" correct="" statistic="" to="" use.="" 5.="" discuss="" the="" fundamental="" principles="" of="" data="" handling.="" 6.="" construct="" and="" interpret="" frequency="" tables,="" bar="" charts,="" histograms,="" stem-and-leaf="" plots,="" frequency="" polygons,="" and="" cumulative="" frequency="" polygons.="" 7.="" describe="" variables="" using="" appropriate="" measures="" of="" central="" tendency,="" dispersion,="" shape,="" and="" skewness.="" 8.="" explain="" the="" use="" of="" percentiles.="" the="" nature="" of="" statistics="" statistics="" is="" a="" branch="" of="" applied="" mathematics="" that="" deals="" with="" the="" collection,="" organization,="" and="" interpretation="" of="" data="" by="" using="" well-defined="" procedures.="" researchers="" use="" various="" techniques="" to="" gather="" these="" data,="" which="" become="" the="" observa-="" tions="" used="" in="" statistical="" analyses.="" thus,="" the="" raw="" materials="" of="" research="" are="" data,="" gathered="" from="" a="" sample="" that="" has="" been="" selected="" from="" a="" population.="" 19="" (="" 30="" )="" (="" section="" 1="" obtaining="" and="" understanding="" data="" )="" (="" chapter="" 2="" organizing,="" displaying,="" and="" describing="" data="" 39="" )="" applying="" statistics="" to="" these="" data="" permits="" the="" researcher="" to="" draw="" conclusions="" and="" to="" under-="" stand="" more="" about="" the="" sample="" from="" whence="" the="" data="" were="" obtained.="" statistics,="" as="" a="" field,="" uses="" its="" own="" language,="" including="" special="" symbols="" that="" represent="" for-="" mulas="" and="" other="" mathematical="" expressions="" and="" specialized="" terms="" that="" describe="" different="" types="" of="" variables.="" this="" chapter="" introduces="" and="" defines="" some="" of="" these="" specialized="" terms="" and="" symbols.="" symbols="" and="" formulas="" for="" descriptive="" statis-="" tics="" vary="" depending="" on="" whether="" one="" is="" describ-="" ing="" a="" sample="" or="" a="" population.="" a="" population="" includes="" all="" members="" of="" a="" defined="" group;="" a="" sam-="" ple="" is="" a="" subset="" of="" a="" population.="" characteristics="" of="" populations="" are="" called="" parameters;="" charac-="" teristics="" of="" samples="" are="" called="" sample="" statistics.="" to="" distinguish="" between="" them,="" different="" sets="" of="" symbols="" are="" used.="" usually,="" lowercase="" greek="" let-="" ters="" are="" used="" to="" denote="" parameters,="" and="" roman="" letters="" are="" used="" to="" denote="" statistics.="" some="" of="" the="" more="" commonly="" used="" symbols="" can="" be="" found="" in="" table="" 2-1.="" this="" chapter="" also="" introduces="" descriptive="" sta-="" tistics.="" these="" are="" the="" type="" of="" statistics="" that="" we="" use="" to="" describe="" variables="" by="" summarizing="" their="" values="" into="" more="" understandable="" terms="" without="" losing="" or="" distorting="" too="" much="" of="" the="" informa-="" tion.="" frequency="" tables,="" bar="" charts,="" histograms,="" percentages,="" and="" measures="" of="" central="" tendency="" and="" dispersion="" are="" the="" most="" common="" statistics="" used="" to="" describe="" sample="" characteristics.="" variables="" and="" their="" measurement="" data="" are="" the="" raw="" materials="" of="" research="" and="" provide="" the="" numbers="" upon="" which="" we="" perform="" statistics.="" the="" most="" common="" way="" a="" researcher="" acquires="" data="" is="" by="" designing="" a="" study="" that="" will="" allow="" the="" collection="" of="" information="" (e.g.,="" data)="" that="" will="" answer="" a="" specific="" research="" question.="" (="" table="" 2-1="" )="" mathematical="" symbols="" in="" statistics="" symbol="" meaning="" mathematical="" functions="" +="" plus="" −="" minus="" ×="" multiply="" divide="" xi="" sum="" of="" the="" numbers="" in="" the="" variable="" x;="" add="" up="" all="" the="" values="" of="" the="" variable="" x="" (="" i="" )x2="" sum="" of="" the="" squared="" x’s;="" square="" each="" value="" of="" the="" variable="" x="" and="" then="" add="" up="" all="" the="" squared="" values="" xi2="" sum="" of="" the="" x’s,="" squared;="" add="" up="" all="" the="" values="" of="" the="" variable="" x="" and="" then="" square="" the="" total="">< less="" than="" ="" less="" than="" or="" equal="" to="">Greater than Greater than or equal to =Equal to |x|The absolute value of x p(A)Probability of event A happening (marginal probability) (Continued) ( Table 2-1 ) MATHEMATICAL SYMBOLS IN STATISTICS (Continued) SymbolMeaning Mathematical Functions p(A|B)Probability of event A happening if B happens (conditional probability) p(AB)Probability of both event A and event B happening (intersection of A and B) p(AB)Probability of event A happening or event B happening (union of A and B) Statistical Symbols aAlpha: the significance level set for the study pThe p-value of the computed statistic H0The null hypothesis HAThe alternative hypothesis errorType I error in hypothesis testing errorType II error in hypothesis testing NPopulation size nSample size fFrequency pi, p95Percentile rank at the ith percentile, 95th percentile mMu, the population mean xx-bar, the sample mean s2Sigma squared, the population variance sSigma, the population standard deviation s2Sample variance sSample standard deviation CIConfidence interval dfDegrees of freedom 2Chi-square rPopulation correlation coefficient rSample correlation coefficient The researcher then attempts to answer the question by examining the data collected on the characteristics of interest in the study; in health research, this is usually about people or events. Sometimes researchers collect their own data, and sometimes they use data that may be avail- able from other studies or government sources. Once collected, the data must be organized, examined, and interpreted using well-defined procedures. Almost all quantitative studies involve data that are entered into a computer-based statisti- cal spreadsheet or database for subsequent data analysis. The logistics and time required to col- lect data, enter it into a statistical spreadsheet or database, and prepare it for data analysis are often greatly underestimated and poorly understood. Davidson (1996) recommends tak- ing control of the structure and flow of one’s data from the beginning. It is hoped that this will help eliminate faulty data leading to faulty conclusions. Appendix A contains an overview of how a good computer database can be cre- ated in SPSS (the process is similar for other programs such as SAS and STATA) and how one’s data can be initially cleaned so that it is suitable for analysis. What Is a Variable? In research, the specific characteristics or parameters of interest are commonly called variables. A variable is any characteristic that can and does assume different values for the dif- ferent people, objects, or events being studied. We measure the value of the variable for each participant in our study, and then record these measurements in a spreadsheet or database to form a data set. This set of observed mea- surements collected from study participants allows us to describe the variables. For exam- ple, demographic variables describe the basic characteristics of human populations or study samples such as age, gender, ethnicity, marital status, number of children, education level, employment status, and income. Each observa- tion within these variables is assigned a number using different rules: age is measured in years, gender is identified as male or female (can be coded “0” and “1”), income is measured in dol- lars earned per year, and so on. It is important to note that for a characteris- tic to be considered a variable, it is critical that everyone in a given sample does not have the same value for the characteristic. For example, gender, which can assume two values (male and female), is not a variable when studying a