Statistical Insights: Blood Pressure, Cancer, Baseball, and Hypertension

Question 1: Investigation of the effect of calcium on reducing blood pressure

Observational studies suggest that there is a link between calcium intake and reduced blood pressure, and that it is strongest in African-American men. To investigate this twenty-one African-American men participated in a double-blind experiment. Ten of the men took a calcium supplement for 12 weeks while the remaining 11 men received a placebo. Researchers measured the blood pressure of each subject before and after the 12-week period. For investigating the effect of calcium on reducing blood pressure the appropriate statistical test will be an independent sample t-test as independent-samples t-test relates the means between two unrelated groups in the context of same continuous, dependent variable. If you need further assistance with this analysis, consider seeking statistics dissertation help to ensure accurate results and interpretations.

Assumption of the test

1. First assumption of the test is that dependent variable will be continues. According to the sample, change of bold pressure which is dependent variable, is continuous in nature.

2. Second assumption of the test is that independent variable surely will contain two independent, categorical groups. According to the test sample, treatment, which is independent variable, have two independent categories – placebo and calcium.

3. Third assumption of the test is that observations are independent. In the test sample, the data are collected randomly so, it can be concluded that observation are independent. No outlier is detected and data is almost normally distributed according to the Q-Q plot.

Hypothesis of the test

Null hypothesis (H0): the two population means are equal means the mean of change of blood pressure of nicotine treatment is equal to the mean of change of blood pressure blood pressure of placebo treatment Alternative hypothesis (H1): Means are not equal

Result

According to the result of the group statistic, it can be concluded that the mean of change of blood pressure of calcium treatment is -7.2 which is meant that the blood pressure is reduced than before and the mean of change of blood pressure of placebo treatment is .0909 which is meant that the blood pressure is almost same as before (figure 1).

According to the result of independent sample test, the associated p-value of t-test of equality of mean is .009 and 0.010 which are less than significance level 0.05 (figure 2). So null hypothesis is rejected and alternative hypothesis which depicted that means the mean of change of blood pressure of nicotine treatment is not equal to the mean of change of blood pressure blood pressure of placebo treatment.

It can be concluded from the result of mean and t test, that calcium has a significant effect in reducing blood pressure.

Question 2: Determine association between the socioeconomic status of patients and cancer grades of different cancer types

To determine whether there is a relationship between the socioeconomic status of patients and tumor stage at presentation, in patients with breast, colorectal, ovarian and lung cancer, Chi square test has been chosen. The chi-square test for independence is used for discovering any type of association or relationship between two categorical variables.

Assumption of the test

First assumption of the test is that independent variable will be categorical. According to the sample, the socioeconomic and tumor stage presentation, both are categorical.

Second assumption of the test is that independent variable consist of two or more categorical, independent groups. According to the sample, the socioeconomic and tumor stage presentation, both have 3 or more independent group.

Hypothesis of the test

Null hypothesis (H0): Two independent variable are independent of each other.

Alternative hypothesis (H1): Two independent variable are independent of each other.

The case of breast cancer

According to the table of chi square test, the value of the test statistic is 6 and the corresponding p-value of the test statistic is p =.199 which is p-value is greater than chosen significance level (α = 0.05) (figure 3). So null hypothesis is accepted and it can be concluded that there is not such enough evidence to prove an association between socioeconomic group and tumor size in the case of breast cancer.

The case of colorectal cancer

According to the table of chi square test, the value of the test statistic is 12.001 and the corresponding p-value of the test statistic is p =.213 which is p-value is greater than chosen significance level (α = 0.05) (figure 4). So null hypothesis is accepted and it can be concluded that there is not such enough evidence to prove an association between socioeconomic group and tumor size in the case of colorectal cancer.

The case of ovarian cancer

According to the table of chi square test, the value of the test statistic is colorectal and the corresponding p-value of the test statistic is p =.213 which is p-value is greater than chosen significance level (α = 0.05) (figure 5). So null hypothesis is accepted and it can be concluded that there is not such enough evidence to prove an association between socioeconomic group and tumor size in the case of ovarian cancer.

The case of lung cancer

According to the table of chi square test, the value of the test statistic is 6 and the corresponding p-value of the test statistic is p =.199 which is p-value is greater than chosen significance level (α = 0.05) (figure 6). So null hypothesis is accepted and it can be concluded that there is not such enough evidence to prove an association between socioeconomic group and tumor size in the case of lung cancer.

In conclusion, there is not such enough evidence is proved association between two independent variable the socioeconomic status of patients and the cancer grades for each of the different cancer types.

Question 3: Investigation of the impact of different factor on between the numbers of team wins of US baseball teams

A study was conducted to investigate whether a relationship exists between the numbers of team wins for some US baseball teams with other criteria. For investing the impact of different factor on wining of the football, multiple regression is chosen. Multiple regression is an extent of simple linear regression. It is needed when dependent variable is forecasted on the basis of the value of two or more independent variables.

Assumption of the test:

First assumption of the test is that dependent variable will be continues. According to the sample, number of win of the football team, which is dependent variable, is continuous in nature.

Second assumption of the test is that independent variable surely will be continuous or categorical. According to the test sample, all the independent variables are continuous in nature

Third assumption of the test is that observations are independent. In the test sample, the data are collected randomly so, it can be concluded that observation are independent. No outlier is detected in the sample. Multicollinearity is also done which depicted that there is no problem of it according to the VIF result (Figure 8). According to the Q-Q plot, residuals are normally disturbed.

Result

For exploring the impact of winning of the team, size of team stadium, attendance at matches, earned run average, number of home runs, and number of stolen bases these variables are analyzed. According to the result of model summary, the model is able to explain 64.5 % of the dependent variable which is not bad as per value of R square (figure 7). Significance value of four dependent variables is greater than 0.05 these variable does not significantly contributing to the model. Significance value of only one variable, attendance at matches, is equal to 0.05 which depicted that is significantly contributing to the model (figure 8).

It can be concluded that, all independent variable is predicting 64% of the dependent variable according to the model. However attendance at matches within all independent variables have grate impact in winning football matches.

Question 4: Investigation of the effect of new calcium-channel blocker drug treatment for hypertension.

A survey was done for understanding the effect of new calcium-channel blocker drug treatment for hypertension. All participants showed systolic blood pressure within the range 150 – 170 mm Hg when randomly allocated to one of the five conditions. To investigate variances observed in all conditions for the different drug treatments, one-way ANOVA test is chosen. The test is needed for determining if there are any statistically significant variances between the means of three or more independent variables.

Assumption of the test

1. First assumption of the test is that dependent variable will be continues. According to the sample, decrease of bold pressure which is dependent variable, is continuous in nature.

2. Second assumption of the test is that independent variable surely will contain two independent, categorical groups. According to the test sample, different treatment, which is independent variable, have five independent categories.

Hypothesis of the test

Null hypothesis (H0): there is no statistically significant difference between the five types of drug treatments.

Alternative hypothesis (H1): there is statistically significant difference between the five types of drug treatments.

Result

The ANOVA table shows that the p-value or the significance value of the analysis comes out to be 0.000, which is lesser than 0.05 (figure 9). It means that obtainable null hypothesis is rejected and the alternative hypothesis is accepted. That is, there is statistically significant difference between the five types of drug treatments.

It can concluded that all the type of calcium-channel blocker drug treatment haven’t similar impact in reducing blood pressure of the participants.