Checklists for doing a hypothesis testing homework in R with an example
Hypothesis testing is used to compare population means. Based on the number of levels involved, a researcher can use independent sample t-test, chi square test, and one way ANOVA. R programming is used for all the hypothesis tests. R knowledge is therefore a paramount requirement when working on a hypothesis testing assignment. In this blog, we have explained everything you need have to make your hypothesis testing homework look captivating. An example illustrating the use of these tests is also provided.
A hypothesis test report should have at least two graphs. These graphs can either be histograms, bar charts, and a scatterplot. Always label your graphs properly.
The tables should be properly drawn and labelled according to APA 7 or the specified writing style. One should always avoid taking screenshots of the tables from the R output.
The report from a hypothesis test should follow a well laid chronological order. You need to begin your report from data cleaning, explanatory data analysis and conclude with the inferential data analysis. Always ensure that you have explained all the graphs and tables in your report.
A report will be incomplete without answering hypothesis question. You should ensure that you have properly answered the hypothesis stated in brief.
Factors that drive charitable giving and volunteering has been subject to intense discussion in the literature. (Andreoni et al., 2001; Belfield and Beney, 2000; Brooks, 2003; Bryant et al., 2003; Einolf, 2010; Hodgkinson and Weitzman, 1990; Menchik and Weisbrod, 1987; Mesch et al., 2006; Mesch et al., 2011). Charity organization, fund raisers and other philantrophic organization cuts across education, health, animal welfare, environmental, religious, poverty relief , art and culture, human rights and other institutions. When people donate their personal funds or property to charity organization, they are involved in charitable giving or donation while when they give time to a cause is termed volunteerism. Many charities rely on charitable giving by individual, corporate organization, and governments (Yao 2015). The reliance of charity organization on donation and volunteerism begs the question of what motivates donors and volunteers to give money and time to philanthropic and charitable causes?, what are those factors that drives giving of such kind and are donating money and volunteering time complementary. It is important to answer these questions because charities have small fund and rely on unpaid volunteerism which is not compulsory on the part of volunteers. Also, charity organizations run on limited resources and thus needs to understand factors that determine the likelihood of giving money and time.
Common sense might suggests that those who donate to charity will only sacrifice their money and thus not volunteer and those who are unable to donate are those that volunteer which means donation and volunteerism are substitutes. However, Drever (2010) and Low et al (2007) show that volunteering and charitable giving are both positively associated with each other. Drever (2010) showed that 83 per cent of those who regularly participated in volunteering had given to charity in the last four weeks compared to 60 per cent of those who had not volunteered in the last 12 months. Therefore, this study will also examine if the factors that drives charitable giving and volunteering and the kind of relationship that exists between volunteerism and donation.
The literature is filled with sociological and economic perspective of conceptual framework for volunteering and donation giving. Human, cultural and social capital available for people shapes their choices of giving their time and money for philanthropic purpose (Wilson & Musick, 1997). Moreover, time available, income and wealth. Cultural capital is basic values with respect to philanthropy possessed by respondents and measured by their childhood experiences with philanthropy and their race/ethnicity. Human capital is the general experience age brings with it, education, skills, and volunteering experience. Social capital are networks and connections people possess which may be used to gain information about the volunteer and donations markets but also to ease access to this markets. Social capital also includes prior social participation and pro-social attitudes and marital status. Social and cultural skills are augmented by prior learning and previous philanthropic activity and education, age, gender and race. Opportunity cost, of respondent’s time and the extent to which cash donations are tax deductible and net wealth are all factors that have been outlined as impacting decision to volunteer and charitable giving (Bryant et.al.2003).
Now to empirical results, Bryant et.al.(2003) used the 1994 Independent Sector Survey of Giving and Volunteering conducted by the Gallup Organization to study the propensities with which people are solicited for money and time as well as the probabilities that people will volunteer time or donate money. They found that 78% of respondents were asked to donate of which 85% of them did. Human, social and cultural capital was found to explain those who were solicited to volunteer while in addition to this variables, income determined whom to be solicited to donate. Moreover, variation in probabilities to donate given that respondents were not asked to donate is largely influenced by social cultural and human capital as well as income variables.
It is common in literature to measure charitable giving and volunteering by dollar amount and hours spent respectively. However, Yao (2015) adopted another method of measurement by using frequency and occurrence of charitable giving and volunteering. In addition he considers the effect of 12 demographical attributes -- current household income, relative income group when 16 years old, marital status interacting with sex, race, religion, residential area size, number of children, education, political party affiliation, employment, and self-rank of social position – on charitable giving and volunteerism. He also undertook to determine whether donation and volunteerism are complementary or substitutes. He found that there is significant correlation between frequency of donation and frequency of volunteerism. Current income, marital status, age, religion, and self-rank of social position were found to have significant effects on the frequency of charitable giving . Race, residential area size, education, political party affiliation, and employment were all found to be insignificant in terms of charitable giving. Current income, age, and sex were also found to be contributing factors to frequency of volunteerism. Current income, income when 16, sex, and political party affiliation and employed dummy significantly contributed to the occurrence of volunteering. He also found that The logarithm of current household income, age, marital status, religion, number of children, political party affiliation, and self-rank of social position have significant effects on the complementarity between charitable giving and volunteering.
Martinez and McMullin (2004) used factor analysis to extract factors that determines the decisions to volunteer in non-governmental organizations. Five factors were extracted which are efficacy factor, competing commitments which are related to demands volunteer job have on individual time, family and finances, social networks which involves knowing or meeting others involved in volunteer activities, lifestyle changes and personal growth. They found that active member of NGOs placed greater importance on efficacy and social network while non active place greater emphasis on competing commitment than active members. Moreover, they use logistic regression to examine factors that predict volunteerism and they found that only Efficacy, competing commitments and income yield significant effect on volunteerism. While efficacy has positive effect, competing commitments and income have negative effect on volunteerism.
In a restricted study, Mesch et.al. (2006) studied effect of Race, Gender and Marital Status on volunteerism in Indiana using data for Indiana household. Relying on the hypotheses the more social capital one has, the more likely he is to engage in philanthropic behaviors. Because marital status is viewed as a social capital, they hypothesized that married people will be philanthropic than non-married people. Moreover, they proposed that female are more likely to exhibit altruistic behavior than men and White are more likely to give to charity than other races. Utilizing independent samples t-test and probit regression, they found that single females give to charity than males; married generally gives more to charity than singles and Whites gives significantly more than Black and other races. Their regression result shows that race is not significant in predicting whether a respondent is a donor or how much he gives. While being a single female and married is associated with an increase in probability of giving. Specifically, the found that single women are 9% to 10% more likely to be donors than single men. Married men are 6% more likely to be donors than single men, and married women are 11% to 12% more likely to be donors than single men. Age has a small, but significant, impact on the probability of being a donor. Income has a small positive effect for each additional $1,000 in earnings on the probability of being a donor at all. Their study is robust because they used a multi-method multi-group research designs with eight different research methodologies and did not found that the type of research design affects the result.
In another restricted studies, Pirper and Schnepf (2008) examined gender differences in charitable giving for Great Britain household, they premised on the fact that literature was replete with evidence that women are more likely to donate to charitable cause than men and men are more generous in terms of amount given. Therefore, they use micro level data to examine this claim using Quantile regression and found that in line with literature, women donated to charity more than men and are more generous than men in the amount given.
To summarize, the effect of various factors -- from the broader human, capital and social capital to specific demographic variables like gender, income, marital status, residential area size, number of children, education, political party affiliation, employment, and self-rank of social position – on various dimension of charitable giving and volunteerism like the amount, number of times, frequency and occurrence of volunteerism and However, there have not been agreement on what factors are significant or not but many evidences support factors like marital status and gender.
METHODOLOGY AND DESIGN
We make use of secondary data collected by the Inter-University Consortium for Political and Social Research on giving and volunteering in the United States in 2001. The data set consists of 4,178 observations and over 500 variables which span over demographics and information about volunteerism and donation.
After surveying the literature, we observe there are various ways volunteerism and charity giving have been measured. For the purpose of this work, I used six different measurement of volunteerism and charity donation. They are frequency, occurrence and time/amount spent.
Frequency of volunteerism and Donation
Frequency of volunteerism is generated by adding together all questions that asked if the respondents have volunteered in the past year in specific area. These questions are coded in 0 and 1 for yes and no respectively. There are 14 of these questions from religion, culture and so on. The possible values of the data ranges from 0 for subject who do not volunteer in any of the areas and 14 for respondents who volunteered in all. The summary statistics shows that the minimum is 0 and the maximum is 6 which means there is no error. We took similar step to create frequency of donation from questions that asked if the respondents have donated in any of 15 areas spanning from religion, political parties and others. This means that the possible values are from 0 for subjects who do not donate to any of the areas to 15 for respondents who donate to all. The summary statistics shows that the minimum is 0 and the maximum is 15 which means there is no error in the data.
Occurrence of volunteer and donation
Occurrence of volunteerism was provided in the data set (V8) while frequency of donation was created from the frequency data above, we recoded it into a binary variable which takes value of 0 for frequency value of 0 and 1 for frequency value that is greater than 0. Value of 0 means no occurrence of volunteerism or donation i.e. respondents have never donated or volunteered while the value of 1 means that the respondents have volunteered or donated to at least one area. The descriptive statistics shows that 26.3% of the respondents have volunteered in the past 12 months while 73.5% have not. Similarly, 91.8% have donated to at least one cause while 8.2% have not.
Volunteer hours and Total Donation
The exact amount donated and hours volunteered was also considered. The amount donated were part of the data set (TOTGIVET) while hours volunteered was calculated by summing hours volunteered for each organization that is provided in the data. Average volunteer hours are 25.11 while the average total giving is $2617.06.
The explanatory variables considered are enumerated below
|Volunteer over the Internet in past year||Measures whether the respondents have willingly through the internet volunteered himself||This variable like will be useful in examining complementarity between volunteering and donation. if both are complement, this should be associated with variables that measured donation.|
|asked to volunteer||If the respondent have been asked to volunteer in the past.||Respondents that have been asked have knowledge about volunteerism and should volunteer more.
|asked to donate||If the respondent have been asked to donate in the past.||Respondents that have been asked is more likely to donate than respondent not asked
|internet donation||Measures whether the respondents have willingly through the internet donated
||This variable like will be useful in examining complementarity between volunteering and donation. if both are complement, this should be positively associated with variables that measured volunteering.|
|confidence level||How much confidence respondents have in charity organizations. Measured as a binary 0 for no confidence, 1 for Yes
||Decision to volunteer or donate may largely depend on the confidence the respondents have in charity organization to be effective. If there is more confidence, there is high probability of donating and volunteering|
|trust||Whether respondent trust others or believe people can be trusted. Measured as a binary, 0 for no and 1 for Yes||if respondents trust others he wont have probem donating as he is optimistic that the right thing will be done with is donation.|
|volunteered in youth||Whether the respondents have volunteered as a youth. Measured as a binary, 0 for no and 1 for Yes||people that have volunteered before are more likely to volunteer again depending on their experience|
|fundraiser in youth||Whether the respondents have being involved as a fundraiser as a youth. Measured as a binary, 0 for no and 1 for Yes||same as above
|parents volunteered||Whether the respondent’s parent have volunteered. Measured as a binary, 0 for no and 1 for Yes
|| we learn a lot from our parents and they are our role model. if the parent have been actively involved in volunteerism or donation before, the kid if likely to grow up the same.
|attend religious services frequently||Measures religiosity of the respondents||Religion preaches helping ones neighbor. A devout person may likely be more donate to charity than non religious person|
|member of religion group||Measures religiosity of the respondents
||same as above
|household size||number of members in the household||Larger household may mean high competition for resources (time and income) and may limit the ability to donate and volunteer|
|children in household||if there is at least a child less than 18|| people that have kids will likely volunteer and donate more, especially to kid related philanthropy.|
|Married||marital status (1=married, 0=others)
||married people have been hypothesized as having more social assets than others. This social contact can motivate to donate and volunteer.
|Education||education level of the respondents
||more educated people are more exposed and have greater social contact than less educated. Thus, the more educated the more likely to donate and volunteer|
|Employment status||whether respondent is employed (1) or not (0||employed people have no much time to volunteer but income to donate from while unemployed have less income to donate from but more time to volunteer|
|Age||Age of respondents (continuous scale||Altruism develop as age advanced. Therefore, Age may likely be important factor in explaining decisions to volunteer and donate.|
|Household Income||Income of household (continuous scale)||The higher the income, the higher the resources available. Moreover, researchers have found income to be associated with charity giving|
|Home ownership||another measurement of household income||household which owns their house have more resources that should be devoted to rent freed up
|White||Whether the respondent is White or non White (1 for White 0 otherwise)||it has been discussed in literature that race influence decision to donate and volunteer
|Gender||male or female||gender have been found to influence charity and volunteerism. Female are more altruistic and will likely volunteer and donate than male.|
|household volunteer||if respondents or one or more respondents household volunteer or donate
||Man is a social animal and we are influenced by those around us. A person with household that volunteer may likely volunteer than someone who have no volunteer household.|
In order to estimate the relationships, we use chi-square, independent samples t-test, one way anova, multiple linear regression model and multiple logistic model. chi-square is used to examine associatin between categorical dependent and independent variables. Thus, to determine association between occurrence of volunteerism and donation and the independent variables above, we employ the chi-square test which is based on the difference between observed and expected count. For continuous variables like frequency, amount and total hours spent, we use the independent t-test when the independent variable have only two levels (for example gender; only male and female while if the dependent have more than two levels, one way ANOVA is utilized.
In order to estimate the effect of the independent variables we run a multiple linear regression model for continuous variables and multiple logistic regression for occurrence of volunteerism and donation. all the independent variable were included and then Backward selection criteria is used to wield out insignificant variables.
All assumptions were met for independent t-test and ANOVA except normality of the dependent variables. However, since we have a large sample, non-normality will not bias the result. Moreover, for t-test, where assumption of homogeneity of variance is not met, we report statistics and p-value for unequal variance. For chi-square, the variable type (categorical vs categorical) assumption is met and all expected count is greater than 5. For linear regression, only outliers pose problem as there are outliers in the data set and are much that removing them may be counterproductive.
Table 1 presents test of association between occurrence and the independent variables and difference in means for the frequency and amount of donation and volunteerism. Column 1 reports chi-square statistics and p-value for the chi-square test. We see that internet donation is strongly associated with occurrence of volunteerism (p<0.001). Similarly, those that are asking to volunteer, donate or self-volunteering is highly associated with occurrence of volunteerism. Moreover, trust, confidence in charity, past volunteerism, parent volunteerism, attending religious and being a member of religious activities, household size, number of children in household, marital status, education, employment status, home ownership, race and having volunteer in household all are significantly associated with occurrence of volunteer activities. Surprisingly, only gender (p=0.879) is not significantly associated with occurrence of volunteer activities. Column 2 presents chi-square test result for occurrence of charity giving/donation. We see that volunteering over the internet in the past is not significantly associated with occurrence of donation (0.193) whereas asking to volunteer is significantly associated with occurrence of donation. Moreover, trust, confidence in charity, past volunteerism, parent volunteerism, attending religious and being a member of religious activities, household size, marital status, education, employment status, home ownership, race and having volunteer in household all are significantly associated with occurrence of volunteer activities. However, having children in household (p=0.862) and gender (0.954) are not significantly associated with occurrence of volunteer activities. Column 3 presents the t-test/anova result of difference in means of total donation for the independent groups. We see that no significant difference exists in mean donation of those who volunteered on the internet or not or those who donate or not. Confidence level in charity, having children in household, employment and gender does not significantly affect total amount of donation while we found significant difference in means based on asking to volunteer, asking to donate or volunteer, trust, past volunteerism, parent volunteerism, attending religious and being a member of religious activities, household’s size, marital status, education, home ownership and having volunteer in household. Column 4 presents the t-test/anova for total volunteer hours and we see that only past volunteering on internet, employment status and trust are significant while all other variables are not statistically significant. This means that hours volunteered differs only by past volunteering on internet, employment status and trust. Column 5 presents the t-test/ANOVA result for frequency of volunteerism; we see that all the independent variables are significant which means hours volunteered is significantly different by all the independent variables. The last column provides the t-test/ANOVA result for frequency of donation, we see that all independent variables except past volunteering on internet (0.198), having children in household (0.965) are have significantly different means of frequency of donation.
Table 1: Test of Associations and different in means
|occurrence of volunteerism||occurrence of Donation||Total Donation||Total Volunteer Hours||frequency of volunteerism||frequency of donation|
|Volunteer over the Internet in past year||8.322(0.004)||1.692(0.193)||-0.341(0.733)|
|asked to volunteer||252.59(<0.001)||146.182(<0.001)||5.34(<0.001)||0.357(0.721)||24.876(<0.001)||20.43(<0.001)|
|asked to donate||112.1(<0.001)||231.74(<0.001)||5.338(<0.001)||0.004(0.997)||13.134(<0.001)||25.827(<0.001)|
|volunteered in youth||112.99(<0.001)||74.85(p<0.001)||3.534(<0.001)||-0.316(0.752||13.342(<0.001)||17.238(<0.001)|
|fundraiser in youth||66.01(<0.001)||73.383(p<0.001)||1.772(0.076)||-0.872(0.384)||11.160(<0.001)||16.928(<0.001)|
|attend religious services frequently||63.47(<0.001)||85.336(p<0.001)||4.162(<0.001)||-0.211(0.833)||14.676(<0.001)||10.72(<0.001)|
|member of religion group||39.21(<0.001)||85.14(p<0.001)||4.293(<0.001)||-0.409(0.683)||9.879(<0.001)||11.265(<0.001)|
|children in household||17.03(<0.001)||0.03(0.862)||-0.85(0.3960||-0.535(0.592)||5.312(<0.001)||0.044(0.965)|
|occurrence of volunteerism||occurrence of Donation||Total Donation||Total Volunteer Hours||frequency of volunteerism||frequency of donation|
The regression result presented below estimates the effect of the independent variables on the dependent variables. Column 1 presents the odds ratio for occurrence of volunteerism. While those internet volunteerism, marital status, home ownership is true for have lower odds of occurrence of volunteerism than those these factors are not true for while those who household volunteer, employment, education, religion, parents volunteered, trust are true for have higher odds of occurrence of volunteerism than those these factors are not true for. Similarly, column 2 presents the odds ratio for occurrence of donation, we see that those who volunteer over the internet, asked to volunteer, donate, confidence level, trust, volunteered in youth, parents volunteered, attend religious services and age are true for have higher odds of occurrence of donation than those these factors are false for. The regression result in column 3 shows that membership of religion group, household size, children in n household, home ownership, household volunteer, Age, household income are all significant variables that explain total amount donated. Column 4 shows that internet volunteerism, trusts and employment status are the only significant variables that explain hours volunteered. Internet volunteerism, asked to volunteer, trust, parents volunteered, attend religious services, children in household, education, home ownership, gender, household volunteer and Age are all significant variables that explain frequency of volunteerism. Finally, all variables except Internet volunteerism, confidence level, attend religious services, marital status are significant in explaining frequency of donation.
Table 2: Regression Result.
|occurrence of volunteerism||occurrence of Donation||Total Donation||Total Volunteer Hours||frequency of volunteerism||frequency of donation|
|Volunteer over the Internet in past year||0.554**
|asked to volunteer||2.024 ***
|asked to donate||1.247 **
|volunteered in youth||1.245**
|fundraiser in youth|| 0.483***
|attend religious services frequently||1.495***
|member of religion group||1114.85***
|household size|| -1078.92***
|children in household||1571.09***
***, **, ** denotes significance at 1%, 5% and 10% respectively; only significant results reported
From the result so far, it can be seen that factors that are specific to donation significantly explain occurrence of volunteerism. For example, those that donate on internet have 67.9% more odds of volunteering than those who did not donate while those who were asked to donate have 24.7% more odds of volunteering than those who were not asked to volunteer on the internet. In the same vein, those who volunteer over the internet have 2.67 times odds of those who did not do of donating and those who are asked to volunteer have 62.1% more odds than those not asked to volunteer. This confirms what have been found that volunteerism and donation are complementary. (Andreoni et al., 1996; Apinunmahakul, Barham, and Devlin, 2008; Brown and Lankford, 1992; Cappellari, Ghinetti, and Turati, 2011; Menchik and Weisbrod, 1987).
We investigated three measures of volunteerism and donation – occurrence, frequency and amount – which means we have three levels where the least is occurrence (we cannot talk of how many times or total if an event do not occur at all) followed by frequency and then the amount. Since we have many significant variables, it is instructive to wield hierarchically to arrive at the most important. All variables that are significant for occurrence are considered first and pass to the next hierarchy and those from these that are significant in explaining frequency pass to the next stage. Considering volunteerism, we see that only volunteer over the internet and trust is significant in explaining occurrence, frequency and total hours of volunteerism. While volunteer over the internet have negative effect, trust have positive effect. Specifically, those that have volunteer over the internet have 44.6% lower odds of occurrence of volunteerism in the past year, 0.453 lesser frequency and 19.44 lesser hours of volunteerism than than those who have not volunteered on the internet. This makes sense because those who have already volunteered may be unwilling to volunteer for another organization especially if they have volunteered for many organizations in the past. Those who trust others have 41.6% higher odds of occurrence of volunteerism in the past year, 0.29 more frequency but 5.482 lesser hours of volunteerism than those who do not trust others. The negative effect on number of hours volunteered is surprising given positive effect on other measure. However, this may be due to other factors that compete with the time of the volunteer. Therefore, an interaction with employment for example may be appropriate. However, this is not considered here but may be undertaken by future researches. This means to increase volunteerism, the organization should target those who have not volunteered on the internet over the past year and people that trust others.
For donation, we see that Age and household income is significant in explaining occurrence, frequency and total amount of donation. Both have positive effect. An year increase in Age increases odds of occurrence of donation by 2.6%, increases frequency of donation by 0.047 and the amount donated by $63.99. This proves the assertion that altruism increases with age and it is clear where age is not explaining volunteerism. As one grow older, volunteering may be difficult but one can donate to a cause he would have volunteered for if he were in his youthful days. Income has a very small effect on donation. the effect is so small that the odds ratio is 1 but this does not mean a$1 increase in household income do not change the odds of occurrence at all but so small that the change is negligible.
To conclude, due to complemetarity found between volunteerism and donation factors that affects both should be taken with importance. Therefore, volunteer over the internet, trust, age and household income are the most important factors out of the over 20 factors considered. Surprisingly, much publicized factors like gender and marital status are not significant. This is not surprising because all of these studies used one aspect of measurement of volunteerism and donation while the measures we used are exhaustive.
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