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# Critical values for Pearson's correlation coefficient r

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In this paper, I present an introduction to quantitative research methods in social sciences. The paper is intended for non-Economics undergraduate students, development researchers and practitioners who although unfamiliar with statistical techniques, are interested in quantitative methods to study social phenomena. The paper discusses conventiona...

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Context 1
... larger the sample size, the higher the reliability of the correlation coefficients even if the value of the Pearson's correlation coefficients, r, is small in size. This is illustrated using the critical values of the Person's r in Table 3. The first column from left to right shows the degrees of freedom, df, resulting from subtracting the number of variables involved in the correlation (i.e. ...
Context 2
... the example presented in Figure 3 that shows a Pearson's r (146)= -0.178, you could determine its level of statistical significance by following a few steps: first, decide whether you need a one-tailed or two-tailed test. Second, calculate the degrees of freedom and locate them in Table 3. As 148 households were interviewed for that study, df = 146 (148-2). ...

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... Through LR and NR, new models were created to predict SPI, aSPI, RDI, and eRDI (dependent variables) using AMO, NAO, ONI, and PDO (independent variables). To find out whether the predictive models were valid (significantly different from 0), hypothesis tests were applied (Ramsey 1989;Niño 2012) between the PC and SC of the models and the critical correlation coefficients of Pearson (CPC) and Spearman (CSC). The goal is to associate and calculate accurate predictive models of SPI, aSPI, RDI, and eRDI through the variation in AMO, NAO, ONI, and PDO for the state of Sinaloa. ...
... Following de Souza and Reis (2022), to find out which coefficients are significantly different from 0, a hypothesis test was applied (null hypothesis: PC vs CPC ≠ 0; SC vs CSC ≠ 0 and alternative hypothesis: PC vs CPC = 0; SC vs. CSC = 0). The CPC and CSC values and degrees of freedom are CPC =|0.276|; n = 49 and CSC =|0.282|; n = 49, which were obtained from Ramsey (1989) and Niño (2012). ...
... Since PC and SC outperformed CPC and CSC (Figs. 4a-f and 5a-f), respectively, it is established that all the models are significantly different from 0 (Ramsey 1989;Niño 2012); that is, they are good predictive models ). In addition, according to Cohen (1988), who was cited by Niño (2012), PC = 0.370 (R 2 = 0.140), a strong correlation in any study. ...
Article
The goal is to calculate predictive models capable of making reliable associations between meteorological drought indices (MDr) (standardized precipitation index (SPI), agricultural standardized precipitation index (aSPI), reconnaissance drought index (RDI) and effective reconnaissance drought index (eRDI)), and climate indices (CI) (Atlantic multidecadal oscillation (AMO), North Atlantic oscillation (NAO), oceanic El Niño index (ONI), and Pacific decadal oscillation (PDO)) from 7 weather stations in Sinaloa for the period 1969–2018. From the National Water Commission (CONAGUA) and the National Meteorological Service (SMN), free online data on precipitation and temperature (maximum and minimum) were obtained. For the calculation of MDr, Drought Indices Calculator (DrinC) software was used. CI were obtained from the National Oceanic and Atmospheric Administration (NOAA 2022) online database. To evaluate association, Pearson and Spearman correlations (initial correlations) were applied. For the models, linear and nonlinear regressions were used. To establish whether the correlations (initial and model correlations) were significantly different from 0, a hypothesis test was applied (between the correlation coefficients and the critical correlation coefficients). The CI with the greatest association with MDr are ONI and PDO. Only two stations (La Concha and Rosario) registered significant predictive capacity, expressed in 12 models. At La Concha and Rosario stations, the best indices, scales, and time steps to predict MDr are RDI–3 (Jul–Sept) and aSPI–3 (Jul–Sept), respectively. Although the models had R2 values of 0.231 ≤ R2 ≤ 0.384, all the correlations (0.481 ≤ correlations ≤ 0.620) are significantly different from 0. This study provides, for the first time for Sinaloa, models that accurately predict MDr through four CI. Application of these models can prevent overexploitation and contamination of water resources in this purely agricultural state, considered the breadbasket of Mexico.
... This is because the minimum value of the correlation coefficient for the variables of construct B was 0.299, while for construct C, it was 0.397. On the other hand, the critical value for Pearson's correlation coefficient r with a significance level of 0.5% was only 0.273 [48]. The reliability test did find that the alpha value for construct B was 0.935, while it was 0.6 for construct C. Cronbach's alpha with a value of 0.935 is considered as excellent, while Cronbach's alpha of 0.6 is satisfactory [49]. ...
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During the COVID-19 era, most countries, including Malaysia, have shifted from face-to-face teaching systems to online teaching programs. The aim of this study is to identify the main challenges that higher education students face during e-learning based on their residential location throughout Peninsular Malaysia. This study further examines the readiness of higher education students to apply e-learning. Therefore, a cross-sectional survey approach is used to fulfil the outlined objectives. Accordingly, 761 public (95.3%) and private (4.7%) higher education students residing in Peninsular Malaysia are sampled in this study. The survey was administered online for 37 days, from 21 October 21 to 6 December 2021, using either WhatsApp or Facebook. The raw data is inferentially (Principal Component Analysis, K-Means Clustering, Kruskal Wallis, and spatial analysis) and descriptively (mean, standard deviation & percentage) analyzed. It has been revealed that six clusters of students in Peninsular Malaysia face various challenges while following the e-learning program. Most states in Peninsular Malaysia are dominated by students in Cluster D (Terengganu, Perlis, Penang, Selangor, WP Kuala Lumpur, and WP Putrajaya) and Cluster B categories (Melaka, Johor, Kelantan, and Kedah). Students in the Cluster D category tend to suffer from physical health disorders and social isolation, while students in the Cluster B category face problems with decreased focus in learning, mental health disorders, and social isolation. The outcomes further indicate that the more challenges students face during e-learning programs, the lower their willingness to continue with the program. The results of this study are significant in addressing the challenges of e-learning, which will help stakeholders address and strengthen student abilities.
... To verify the instrument's validity and reliability can be delivered and utilized in excellent condition, a pilot study with 50 respondents should be conducted beforehand 27,28 . The results of the analysis found that all variables (35 variables) were valid for use since the value of the correlation coefficient (r xy ) is greater than the critical value for the Pearson's Correlation coefficient r 29 The minimum value of the correlation coefficient of this study is 0.299 exceeding the critical value for the Pearson's Correlation coefficient r with a level of significance of 0.5%, which is 0.273 30 . The results of the reliability test also showed an alpha value of 0.935. ...
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The outbreak of the pandemic Covid-19 has transformed the education system in most countries worldwide. Following the lockdown measures in Malaysia, the Malaysian education system has fully transformed from conventional learning to online learning or known as e-learning as an alternative to minimize social contacts and physical communication to curb the transmission of Covid-19. In this regard, this study aims to identify the challenges faced by students in higher learning institutions throughout Malaysia during the implementation of the e-learning program. This study is based on a large sampling consisting of 2394 students from both public and private universities. The result from this study is analyzed through inferential methods such as the Spatial Analysis, the Principal Component Analysis, and the Mann–Whitney U test and through descriptive methods using the frequency analysis and the percentage analysis. Findings from this study suggest that location significantly influenced the challenges faced by students throughout the implementation of e-learning in higher learning institutions. For example, students in rural areas which can be identified as “vulnerable groups” are more likely to face both technical and connection with the internet access, tend to have a declining focus on learning and are prone to physical health problems, facing social isolation and low digital literacy compared to students in urban areas. Based on geographical analysis, students in Sabah, Perlis, and Melaka are most at risk of facing e-learning challenges. An anomaly case of students in Kuala Lumpur, however, posed another different result compared to other cities as they confront similar challenges with students in rural areas. This study provides the nuances of location and its implications for vulnerable groups that may put them at disadvantage in the e-learning program. Findings from this study will help to inform the relevant authorities and policymakers in improving the implementation of e-learning in Malaysia, especially towards the vulnerable groups so that it can be delivered more systematically and efficiently.
... The results of the validity test in this study show that all the variables in construct B are valid due to having a correlation coefficient value (r χγ ) that is greater than the critical value for Pearson's Correlation coefficient r [42]. To measure validity, this study used the critical value of the Pearson's Correlation coefficient r with a significance level of 0.5%, which is only 0.273 [43]. This is proven when the minimum value of the correlation coefficient for variables in construct B shows a value of 0.299. ...
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Amid the outbreak of the COVID-19 pandemic in the year 2020, educational platforms have been forced to change and adapt from conventional physical learning to virtual learning. Nearly all higher learning institutions worldwide are forced to follow the new educational setting through virtual platforms. Sabah is one of the poorest states in Malaysia with the poorest infrastructure, with the technology and communication facilities in the state remaining inept. With the changes in virtual platforms in all higher education institutions in Malaysia, higher learning institutions in Sabah are expected to follow the lead, despite the state lagging in its development. This has certainly impacted the overall productivity and performance of students in Sabah. Therefore, this study aims to explore the challenges of the implementation of virtual learning among students in Sabah. More specifically, this study seeks to identify vulnerable groups among students based on their geographical location. To achieve the objective of this study, a survey has been conducted on a total of 1,371 students in both private and public higher learning institutions in Sabah. The sample selection for this study was determined using a purposive sampling technique. Based on Principal Component Analysis (PCA), it was found that there are five challenges in virtual learning faced by students in higher learning institutions in Sabah. These are the unconducive learning environment (var(X) = 20.12%), the deterioration of physical health (var(X) = 13.40%), the decline of mental health (var(X) = 12.10%), the limited educational facilities (var(X) = 10.14%) and social isolation (var(X) = 7.47%). The K-Means Clustering analysis found that there are six student clusters in Sabah (Cluster A, B, C, D, E & F), each of which faces different challenges in participating in virtual learning. Based on the assessment of location, almost half of the total number of districts in Sabah are dominated by students from Cluster A (9 districts) and Cluster B (4 districts). More worryingly, both Cluster A and Cluster B are classified as highly vulnerable groups in relation to the implementation of virtual learning. The results of this study can be used by the local authorities and policymakers in Malaysia to improve the implementation of virtual learning in Sabah so that the education system can be more effective and systematic. Additionally, the improvement and empowerment of the learning environment are crucial to ensuring education is accessible and inclusive for all societies, in line with the fourth of the Sustainable Development Goals (SDG-4).
... Therefore, quantitatively, at the same time, insight is given to help describe the research findings. We used IBM's SPSS [28]. Another suggestion guidelines provided by Cohen that Pearson's correlation coefficients not far from 0.24 and 0.36 would have a medium effect in establishing the strength of a correlation [29]. ...
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Flowers are a part of tourist attractions. The existence of gardens and flowers in a tourist spot affects the perception of visitors. This research aims to determine the perceptions and impressions of tourists from Indonesia who have visited Hungary. Data obtained from online surveys through the Whatsapp group of Indonesian students. Furthermore, the data obtained processed and counted to find out the tendency of the flowers impression to visitor. The data obtained shows that flowers have an influence on impressions for visitors in Hungary. Flowers impression correlates versus selfie activity, willingness to referral and attention to flower’s colour with lower than the given p-value of 0.05. They are 0.002 for selfie, 0.020 for willingness to referral, and 0.01 for colour intention respectively.
... Prior to establishing causal relationships, Pearson's product-moment correlation coefficient analysis was performed (Niño-Zarazúa, 2012;Pallant, 2010) to examine the relationship between the DEO (as measured on an interval scale of 10 to 60) and two independent variables: the perceived degree of access to information (as measured on an interval scale of 9 ...
... needed to be measured continuously in interval or ratio scales(Niño-Zarazúa, 2012). For this reason, the analysis was performed to examine the strength and direction of the correlation between each of the two interval-scale independent variables (access to information and perceived level of competence) and each of the three dimensions of the dependent variable as well as their combined measurement.Independent samples t-tests were used to compare the mean scores on each of the three dimensions of the dependent variable and their composite measurement, for the different groups of the categorical explanatory variables. ...
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