Statistical Analysis Review (Quantitative Analysis)

To check if there is a difference in the LPs between leaders from high MSROs and low MSROs, a non-parametric independent sample test is conducted using SPSS software, see Table 1. According to the results, mean for high MSRO leaders is 8.56 and low MSRO leaders is 7.00 whiles the p-value = 0.0001 which is less than .05 significance level. Therefore, the null hypothesis Hₒ is rejected and H1 is accepted. There is a significant difference in LPs between the two (2) leader groups.

Table 1: Independent Sample Test for Hypothesis 1

Hypothesis 2 – There is a strong relationship between MSRs and the LP of both high and low MSROs

Correlation is used to check how strong the relationship the two variables is. To interpret the correlation matrix, we need to look at the significance value (p) for reach value of r. A strong positive relationship can be overserved between the dependent variable (Medicare Star Ratings) and the independent variable (Leaders from high MSROs), where the value of Pearson r is .834 and the p > .05 (p = .001), therefore the H1 should be accepted and the H0 rejected. Since the p-value is significant, a significant correlation exists between the two variables. See Table 2

The results of the test also indicate that there is also a strong positive relationship between MSR and leaders from low MSROs. The value of the Pearson r is .817 and the p > .05 (p = .000), therefore the H1 should be accepted and the H2 rejected., a statistically significant correlation exists between the two variables since p-value is significant, see Table below 2

Table 2: Correlation between MSR and LP of leaders of high MSROs and low MSROs.

The Model Summary table in Table 3 provides R and R2 values. The R value represents the simple correlation which is .839 (the "R" Column), and it indicates a high degree of correlation. The R2 value (the "R Square" column) indicates how much of the total variation in the dependent variable MSR can be explained by the independent variable (Leadership practices of both high & low MSROs). In this case, 70.4% can be explained, which is very high. See Table below 3

The Coefficientsa table in Table 3 shows the beta weight and significance value for the individual independent variables. The regression model is perfect at 70.4% only, then the beta coefficient is .126 for leaders from low MSROs with p-value of .379, which is statistically insignificant. For leaders from high MSROs, the beta coefficient is .392 and p-value is .057, which also statistically insignificant. This implies that each variable is not predictive enough on its own to be statistically significant. However, the sample provides enough evidence to conclude that the model is significant but not enough to conclude that the individual variable is significant. The p-value is 0.000 for the overall model in the ANOVA in Table 3, hence H0 is rejected as a result.

Table 3: Linear regression of MSR and LP of leaders of high MSROs and low MSROs.

Hypothesis 3 - In comparison to other 4 models (thus Model the Way, Challenge the Process, Enable Others to Act, Encourage the Hearts), practicing the “Inspire A Shared Vision” model is very significant in helping leaders influence the attainment of high MSR in MCOs.

The below correlations matrix (Table 4) provides details of the dependent variable (MSR) and the five (5) principles of the independent (Leadership Practices) to determine the association between each principle and the dependent variable. The first correlation between Medicare Stars ratings and Challenge the Process (R3) model, where Pearson r is .850 and p-value is .000, this shows there is a strong positive relationship as p value is less than .01. For the relationship between MSR and Enable Other to Act (R4) model where the Pearson r is .566 and p-value is .000 this shows there is also a strong positive relationship as p value is less than .01. The relationship between MSR and Encourage the Hearts (R5) model as the Pearson r is .557 and p-value is .000, this shows there is a strong positive relationship as p-value is less than .01. The relationship between MSR and Inspire the Heart (R2) model as the Pearson r is .874 and p-value is .000, this shows there is a strong positive relationship as p-value is less than .01. The relationship between MSR and Model the Way (R1) model as the Pearson r is .622 and p-value is .001, this shows there is a strong positive relationship as p value is less than .01.

Table 4: Correlation between Medicare Stars ratings and the Five (5) leadership models.

Hierarchical Regression for Medicare Stars rating and five (5) principles

The Model Summary in Table 5 below provides the R and R2 values for the two (2) models of hierarchical regression in the first (1st) model. The R-value represents the simple correlation which is .863 (the “R” column), which indicates there is a high degree of correlation between the variables. The R2 value (the “R Square” column) indicates how much of the total variation in the dependent variable (Medicare Stars rating) can be explained by the independent variable Model the Way(R1), Challenge the Process(R3), Enable Others to Act(R4), and Encourage the Hearts(R5). In this case, 74.50% can be explained, which is very high. There model 1 is statistically significant. The p-value in ANOVA table (Table 5) is .000.

In the second (2nd) model, the R value represents the simple correlation and it is .909 (the “R” column), which also indicate a high degree of correlation. The R2 value (the “R Square” column) indicates how much of the total variation in the dependent variable (Medicare Stars rating) can be explained by the independent variable (Model the Way, Challenge the Process, Enable Others to Act, and Encourage the Hearts). Here, 82.60% can be explained, which is very high. It implies that when the other four (4) variables were added to Inspired the Vision (R2) principle, the r-square increases. This model increases the model’s predictive capacity in predicting the attainment of high Medicare Stars ratings in a statistically significant way by increasing the percentage accounted for by 8.1%. See Table 5

The F-ratio in the ANOVA table tests whether the overall regression model is a good fit for the data. Table 5 shows that the independent variables statistically and significantly predict the dependent variable, F(5, 64) = 60.673, p < .0005, thus the regression model is a good fit of the data. All five (5) predicators accounted for a significant proportion of unique criterion in the final regression model. As seen in the chart (Figure 1), there is a strong positive correlation between the two (2) variables.

The below table (Table 5) shows the results for the hierarchical regression coefficient between the two (2) models. In the first (1st) model, the dependent variable is Medicare Stars ratings and the independent variables are Model the Way[R1], Challenge the Process[R3], Enable Others to Act[R4], and Encourage the Hearts[R5]. In this model, as the regression model is perfect which 74.50% only, then the beta coefficient for Challenge the Process (R3) is .693 and the significance value is .000. This result shows the relationship between the two (2) variables is significant. The beta coeffect for Enable Other to Act (R4) is 102 where p-value is .054. The beta coefficient for Model the Way (R1) is .114 where p-value is .310.

In the second (2nd) model, the dependent variable is MSR and the independent variables are: Inspire a Vision (R2), Model the Way(R1), Challenge the Process(R3), Enable Others to Act(R4), and Encourage the Hearts(R5). Also, the p-value in ANOVA table (Table 5) is .000 as well, therefore the H0 is rejected for the 2nd model. In this model, the regression is perfect which is 82.6% only, then the beta coefficient for Challenge the Process (R3) is .388 and significance value is .000. This result indicates the relationship between the two (2) variables is significant. The beta coeffect for Enables Other to Act (R4) is .063 and p-value is 0.156, which shows the relationship is statistically insignificant. The beta coeffect for Model the Way (R1) is -.58 and p-value is .555, which is also statistically insignificant. The beta coefficient for Encourage the Heart (R5) is -.21 and p-value is .790, which is also a statistically insignificant relationship. But when Inspire a Vision (R2) is added to the other four (4) variables, then the beta coefficient for Inspire a vision (R2) is .575 and p-value is .000. It implies that, in comparison to the other four(4) variables: Model the Way[R1], Challenge the Process[R3], Enable Others to Act[R4], and Encourage the Hearts[R5], practicing Inspire a Vision [R2] principle is very effective in enabling leaders influence the attainment of high Medicare Stars rate in MCOs.

Table 5: Hierarchical Regression for Medicare Stars rating and five (5) principles

Figure 1: Histogram and Scatterplot for Medicare Stars rating and five (5) principle

Hypothesis 4 – The leaders’ leadership style contributes to a leader’s ability to influence the achievement of high Medicare ratings for MCO.

Correlation is used to check how strong the relationship the two variables is. To interpret the correlation matrix, we need to look at the significance value (p) for reach value of r. In Table 5, a moderate positive linear relationship exists between the dependent variables (Medicare Stars ratings) and the independent variables (the leadership styles of leaders from low Medicare Star ratings organizations), where Pearson r is .392 and the p-value is .20 at 0.5 level of significance. Hence, the p-value is statistically significant. From this result, a correlation exists between Medicare Stars ratings and leadership style of leaders from low MSROs.

In comparison to the correlation that exists between MSR (dependent variable) and the leadership style of leaders from high MSROs (independent variable), a moderate positive linear relationship exists between the two (2) variables, where Pearson r is .329, see Table 5. However, the p-value is .54 at .5 level of significance. The p-value is not significant ([p > 0.5], p= .54) unlike the p-value of the correlation of Medicare Stars ratings and the leadership styles of leaders from MSROs ([p > 0.5], p= .20), though there is a positive correlation.

Table 5: Correlation between MSR and leadership style of high and low MSROs.

Table 6 below provides the R and R2 values. The R value represents the simple correlation which is 0.685 (the "R" Column), which indicates a high degree of correlation. The R2 value (the "R Square" column) measures the strength of the relationship between the model and dependent variable MSR. In this case, 47.00% can be explained, which is low.

Table 6 below also shows the results for the simple linear regression between the dependent variable (Medicare Stars ratings) and the independent variables (leadership style). This regression model is not perfect as it is only 47%, then the beta coefficient is .200 and a significant value is .001 for leadership style of leaders from low MSROs and it is statistically significant. The beta for leadership style of leaders from high MSROs is .180 and p-value is .000, which is also statistically significant.

Table 6: Hierarchical Regression for Medicare Stars rating and leadership styles of leadership from both low and high MSROs.

Hypothesis 5 – The Leaders’ of Years of Experience (YoE) is effective in enabling leaders influence the attainment of either a high MSRs in MCOs

The correlation matrix below (Table 7) measures the strength and direction of the relationship between the two (2) variable. There is a weak positive linear relationship between the dependent variable (MSR) and independent variable (years of experience of leaders from high MSROs), where Pearson r .109, and p-value is .267 at 0.5 level of significance. Hence, it is statistically insignificant. This means a correlation does not exist between MSR and YoE of leaders from high MSROs.

The correlation that exists between MSR (dependent variable) and YoE of leaders from high MSROs is a moderate positive linear relationship, where Pearson r is .583 and p-value is .000 at .05 level of significance. The p-value is significant ([p > 0.5], p= .000) unlike the p-value of the correlation of MSR and YoE of leaders from high MSROs ([p > 0.5], p= .267).

Table 7: Correlation between MSR and Years of Experience of leaders from high and low MSROs.

Table 8 below shows the R and R2 values. The R value represents the simple correlation which is 0.583 (the "R" Column), which indicates a moderate degree of correlation. The R2 value (the "R Square" column) indicates how much of the total variation in the dependent variable Medicare star rating can be explained by the independent variable leaders YoE. In this case, 29.90% can be explained, which is low very.

The results displayed in Table 8 shows the simple linear regression between the dependent variable (MSR) and the independent variable (leaders’ YoE). This regression model is not perfect as it is only 34%, then the beta coefficient for YoE of leaders from low MSROs is .346 and p-value is .000, which is statistically significant. However, the beta coefficient for YoE of leaders from high Medicare Stars is .012 and p-value is .915, which is not statistically significant. The sample provides enough evidence to conclude that the model is significant but not enough to conclude that the individual variable is significant. The p-value is 0.001 for the overall model in the ANOVA in Table 8, hence H0 is rejected as a result.

Table 8: Hierarchical Regression for Medicare Stars rating and leaders YoE

Hypothesis 6- Leadership practice is highly effective in helping a leader influence the attainment of high MSR in MCOs in regard to leader’s years of experience and leadership styles,

The correlation matrix gives details of the dependent variable (Medicare Stars ratings) and three (3) independent variables: Leadership Practice (LP), Years of Leadership Experience, and Leadership Style to check the association between the variables. See Table 9.

The first correlation relationship between MSR and leadership practice where Pearson r is .839 and p-value is .000, which shows there is a strong and significant relationship as p-value is less than .01. The relationship between MSR and leaders’ YoE is Pearson r is .533 and p-value is .000, this indicates there is a moderate and significant relationship as p-value is less than .01. The relationship between MSR and leader’s leadership style is Pearson r is .197 and p-value is .102, this shows there is a weak and insignificant relationship as p-value is greater than .01, see Table 9.

Table 9: Correlation between MSR and leadership style, leadership practice and leaders’ years of experience

The Model Summary in Table 10 provides R and R2 values for the two (2) models of hierarchical regression in the first (1st) model. The R value represents the simple correlation which is .534 (the “R” column), which indicates there is a moderate positive relationship between the variables. The R2 value (the “R” Square” column) indicates how much of the total variation in the dependent variable (MSRs) can be explained by the independent variable: Leadership Practice, Leaders’ Years of Experience, and Leadership Style. In this case, 28.50% can be explained, which is very low, though the p-value is .000. There model 1 is statistically significant.

In the second (2nd) model, the R value represents the simple correlation which .846 (the “R” column), which also indicate a high degree of correlation. The R2 value (the “R” Square” column) indicates how much of the total variation in the dependent variable (Medicare Stars rating) can be explained by the independent variable: Leadership Practice, Leaders’ Years of Experience, and Leadership Style. In this model, 71.50% can be explained which is very high. This indicates that the r-square increases when leadership practice is employed in addition to leadership style and years of experience. This model increases predictive capacity in predicting the leaders’ influence in attaining high MSR in a statistically significant way by increasing the percentage accounted by 43.10% in the 2nd model. See Table 10

The F-ratio in the ANOVA table tests whether the overall regression model is a good fit for the data (Table 10). The independent variables statistically and significantly predict the dependent variable, F(3, 66) = 55,251, p-value is .000 as p < .05, thus the regression model is good git of the data.

Furthermore, the result of the hierarchical regression coefficient between the two (2) models is shown in the Coefficientsa section, Table 10. In the first (1st) model, the dependent variable is MSRs and the independent variables are: Leaders’ Years of Experience, and Leadership Style. In this model, the regression model is moderate 28.50% only, then the beta coefficient for Years of Leadership is .902 and p-value is .000. This result shows the relationship between the two (2) variables is significant. The beta coefficient for Leadership Style is .024 where p-value is .906. which is statistically insignificant.

In the second (2nd) model, the dependent variable (MSR) and the independent variables: Leadership Practice, Leaders’ Years of Experience, and Leadership Style. With this model, the regression is perfect which is 71.50%. then the beta coefficient for Leaders’ Years of Experience is .115 and p-value is .426, which is statistically insignificant. The beta coefficient for Leadership Style is -.207 and p-value is .118, which is also statistically insignificant. However, when Leadership Practice is added to the other two (2) variables, then the beta coefficient for Leadership Practice is .970 and p-value is .000. This shows that, in comparison to the independent variable in the 1st model, practicing Leadership Practice is very effective in helping leaders influence the attainment of high MSR in MCOs; hence H0 is rejected as a result.

Table 10: Hierarchical Regression for Medicare Stars rating and leadership practice, leaders’ YoE and leadership style.