The Effects of Attendance on Student LearningTable 1 describes a data set taken from a survey of students sampled over three semesters – spring and fall 1993 and spring 1994 – taking a Principles of Economics course at a medium-sized public college in North Carolina, United States. These data were analyzed using a linear regression model that explored the relationship between lecture attendance and student learning. The results are reported in Table 2.Table 1: Data for testing the theory that lecture attendance affects gradeVariable Description Meangrade Student course grade (%) 72.234skip12 1 if 1 or 2 absences; 0 otherwise 0.277skip34 1 if 3 or 4 absences; 0 otherwise 0.
159skip56 1 if 5 or 6 absences; 0 otherwise 0.162skip78 1 if 7 or 8 absences; 0 otherwise 0.061skip9+ 1if 9 or more absences; 0 otherwise 0.104SATmath Pre university standardised maths test 515.647SATverbal Pre university standardised verbal reasoning test 466.
96GPA mean Grade Point Average to date x 100 269.538colprep 1 is high school program was college prep; 0 otherwise 0.538HSecon 1 if had high economics, 0 otherwise 0.454calculus 1 if have take college calculus, 0 otherwise 0.532econ 1 if previously had a college economics course, 0 otherwise 0.419hoursstudy Hours of economics studied per week 2.4hourswork Hours worked per week in a job 7.
818credithours Hours of courses taken for credit that semester 13.081extracurr 1 if 1 or more extracurricular activities, 0 otherwise 0.72fratsor 1 if fraternity or sorority member, 0 otherwise 0.214parents 0 if either parent had a high school education or less; 1 if either went to university; 2 if either gained a university degree; 3 if either studied at graduate level 1.621white 1 if white; 0 otherwise 0.951male 1 if male; 0 if female 0.
621local 1 if from North Carolina; 0 otherwise 0.899Table 2: Results of OLS regression of student course grade on lecture attendance and other explanatory variablesVariable Coefficient t-statisticIntercept 33.919 3.94skip12 0.
465 0.38skip34 -1.538 1.
11skip56 -3.228 2.29skip78 -3.
475 1.83skip9+ -3.521 2.12SATmath 0.011 1.97SATverbal 0.014 2.
35GPA 0.078 9.13colprep -0.097 0.11HSecon 2.766 3.35calculus 3.
352 3.75econ -1.027 1.19hoursstudy 0.093 0.
41hourswork -0.049 1.28credithours -0.021 0.27extracurr -0.595 0.6fratsor -1.
886 1.8parents 0.695 1.83white 4.524 2.33male 0.736 0.8local -0.
737 0.54Adjusted R2 0.435Number of Obs. 346Introduction:Quantitative research methods and data analysis are very present nowadays in the form of polls, market research surveys, crime statistics etc??¦Indeed, statistical analysis is central to quantitative methods, and is a very useful tool of inference, enabling researchers to understand patterns of correlation and causality.
Nevertheless, these same methods raise doubts and suspicion as scholars claim that they can be easily distorted and used to manipulate results and make them incline towards a particular conclusion to serve one??™s interests (Rowntree, 1981; Bryman & Cramer, 2001). However, there are techniques that enable researchers to spot misrepresentation or error in published reports based on statistical data collection and analysis; in addition, using these techniques helps researchers to obtain statistically valid results.From the formulation of the theory to the collection of data and finally, its analysis, these techniques require compliance with certain criteria such as random sampling or the knowledge of the underlying that enable researchers to use numbers to draw conclusions that can then be used and/or generalised to other studies or at the very least, to conclude correctly when generalisation is not possible. In this particular study, the basic assumption is that attending lectures benefits university students. To support this theory, quantitative and categorical data were collected from a survey of students sampled over three semesters in a college in the USA. Students??™ course grades against lecture attendance and other explanatory variables were used including means of hours of absence, SAT test results, but also dummy variables such as race or gender. 346 observations were taken and a regression was conducted.
To evaluate the statistical significance of each one of the explanatory variables, it would have been easier with the p-value but as it has not been provided, Student??™s t-test will be used because only t-statistics have been given can be used. The t-statistic tests the null hypothesis which here would be that there is no relationship between students??™ grades and the explanatory variables, which would translate as the coefficient being equal to 0 (Field, 2000). The t-statistic depends on the degrees of freedom and the number of observations. With 346 observations, the total variance has 345 degrees of freedom (Field, 2000, Rowntree, 1981,UCLA, 2009 ). Using a t-table, for the relationship to be statistically significant at an ?-level of 0.05 (i.e.
an ?-level 5% or 95% of confidence), the critical value for 345 degrees of freedom is 1.96. This means that all t-statistics that are smaller than this critical value of 1.96 indicate a non statistically significant relationship at a 95% confidence level, between the corresponding explanatory variable and the independent variable.The results of the regression indicate that failure to attend lectures impacts grades for a certain number of absences.
Table 2 above shows that for students who are absent up to 4 times the impact is not significant because the t-statistic ranges from 0.38 to 1.11, so it is quite smaller that the critical value.
However, from 5 to 6 absences upwards, the t-statistic varies between 2.29 (which is the value for 5 to 6 absence, the most significant result) and 1.83, the lowest value that corresponds to 7 to 8 absences. 7 or 8 absences also have significant impact at 90% confidence level (because if the standard table of significance indicates a critical value of 1.6 approximately for 345 degrees of freedom). These results suggest that the students would benefit from being present at lectures, but also seems to indicate that few absences have little impact on results.Other explanatory variables with t-value of more than 1.
96 are SATmath with a t-value of 1.97, SATverbal, with a t-value of 2.35, GPA, with 9.13, Hsecon with 3.35, calculus with 3.75 , and being white, with 2.
33. The results also indicate that the fact that parents had access to higher education or that a student is fraternity or a sorority member are statistically significant at 90% confidence level, which could lead the researcher to conclude that students with parents who accessed higher education are more likely to be successful that others and so do fraternity and sorority members. having said that, it is important to note that the vast majority of the students whose data was recorded have parents who accessed higher education and very few of them are fraternity or sorority members. The R? , which is the squared multiple regression correlation coefficient, measures the proportion of variability explained by, or due to the regression and is a number between zero and one.
As additional variables are added to a regression equation, R? increases even when the new variables have no real predictive capability. To assess goodness of fit of the model, the adjusted R? which has been given, can be used. Unlike the R?, the adjusted-R? avoids this difficulty and does not increase unless the new variables have additional predictive capability (Field, 2000). The value of the adjusted R? is 0.435. So we can infer from that value that the model (and its variables) explains 43.
5% of the students??™ grades that were recorded. This implies that 56.5% of the results that were recorded are explained by variables that were omitted or could not be captured by this model.Another conclusion that can be drawn is that the results of this study cannot be generalised if it conducted as it is, and this conclusion is supported by other factors.
For example, the sample that is taken is large enough to yield valid results (Field, 2000, but it poses problems. The study is conducted based on performances recorded only for a ???Principles of Economics course??™ undoubtedly one of many courses that the students take so it would be crucial to know if the trends observed for this course also apply to other courses. Other courses might have other constraints in terms of attendance of prerequisite knowledge for example.Secondly, the sample may not have been randomly selected (which is crucial to avoid sample bias)(Rowntree, 1981) which would imply that one population is more likely to have been selected than another one. For example, here there are a majority of white and male students and we do not know if that reflects the general trend for the whole population of the college. In addition the majority of the students have parents who accessed higher education so it is not clear whether this reflects the general trend. Under these conditions, it is difficult to generalise the results because for the reasons indicated above, the model does not seem very robust and consequently, its external validity is weak.
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(1981) Statistics without tear :, A primer for non-mathematicians, Harmondsworth, Middlesex : Penguin, 1981.Trochim W. K., (2006) Exernal Validity, Available at : http://www.socialresearchmethods.net/kb/external.php [accessed on 21/03/09]