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Statistics - Basic Concepts Explained

  • 20th Aug, 2019
  • 14:19 PM

Our Statistics Assignment Help Experts have explained some basic concepts of statsitics by answering the below questions. Please read the questions and answers carefully to complete your statistics coursework on time. 

 

Statistics Assignment Help - Basic Concepts

1. What are the differences between population parameters and sample statistics?

Answer - Statistics describes a sample, while a parameter describes an entire population. A sample is a smaller subset that is a representative of a larger population. 


2. Why must the researchers begin with descriptive statistics when the goal is to conduct inferential statistics?

Answer - A researcher must begin with descriptive statistics because it describes the data and summarize data to make the data even more comprehensible. For researchers to make inferences or draw conclusions about a population they use inferential statistics. Inferential statistics uses laws of probability to help researchers draw objective conclusions about population characteristics, based on information from samples. 

 

3. Imagine you are to conduct a study on how weight and age group (18-35, 36-53, and =>54 years) relate to systolic blood pressure.

a. What are the variables in this study?
Answer - Weight, Age groups and systolic blood pressure

b. What is the exposure variable? what is its type and measurement?
Answer - Weight and Age groups

  • Weight is a ratio type variable measured in kilograms.
  • Age group is a interval type variable measured in years.

c. What is the outcome variable? what is its type and measurement?
Answer - Systolic blood pressure - Blood pressure is a ratio type variable measured in torrs or “millimetres of mercury (Hg)”

 

4. Answer True or False:

  • An instrument can be reliable without being valid - True (Validity implies reliability but the converse may not be true)
  • An instrument can be valid without being reliable - False (Validity implies reliability so if an instrument is valid, then it’s reliable also)
  • Normality is assumed with all parametric statistical tests; therefore, it is important to check if the data is normally distributed or not. - False. In parametric statistical tests, the mean of the samples is assumed to be normal. Not the data itself.

 

5. Which of these charts allows a researcher to examine a possible relationship between two ratio variables

  • Histogram
  • Bar chart
  • Scatter plot
  • Line chart

6. The 95% confidence interval of sodium content level in 32 nursing home patients is 4,250 mg/day and 4750 mg/day. What does this confidence interval tell us?

Answer - The confidence interval tells us that if we took 100 such samples of patients and looked at the average sodium content level, then the value would lie within that interval at least 95 times.

 

7. The purpose of a study is to test the effect of pressure ulcer prevention in reducing the incidence of pressure ulcer in critically ill patients in intensive care units.

a. What is the null hypothesis? - Pressure ulcer prevention drug/medication has no effect in reducing the incidence of pressure ulcers in critically ill patients in ICU.

b. What is the alternative hypothesis? - Pressure ulcer prevention drug/medication has significant effect in reducing the incidence of pressure ulcers in critically ill patients in ICU.

c. What is the exposure variable and its level of measurement? - (Since there is no information in the question, we assume that these are clinical trials involving some drug) The exposure variable is the dosage level of the drug administered to the patients, which is generally measured in milligrams (mg).

d. What is the outcome variable and its level of measurement? - We can speculate that the outcome variable should intuitively be a discrete variable giving the number of ulcers that develop after (not) administering the drug or a binary variable with values 0 or 1 if the only possibility is that either there is just one ulcer or there is none (or also possibly the size of the ulcer).

e. The finding was as follows: intervention group had less pressure ulcer than the control group (p=0.005). what is the status of the null hypothesis based on this result? - We see that the p-value is 0.005 which is lower than the standard level of significance assumed for such tests (the standard level of significance is either 0.05 or 0.01). Hence, we have enough evidence to reject the null hypothesis, and we can say that the drug, statistically, has significant effect in reducing the pressure ulcers in critically ill patients in the ICU.

 

8. A type I error is made when:

  • The false null hypothesis is not rejected
  • The true alternative hypothesis is rejected
  • The true null hypothesis is rejected
  • The false alternative hypothesis is not rejected

9. A type II error is made when:

  • The false null hypothesis is not rejected
  • The true alternative hypothesis is rejected
  • The true null hypothesis is rejected
  • The false alternative hypothesis is not rejected

 

10. What type of statistics (mention all possible statistics) can be used to describe the variables:  age in years, income groups, and blood type? 

Answer -

  • Age in Years: Mean, median, mode, standard deviation, skewness, kurtosis 
  • Income group [low, medium, high]: mode, skewness
  • Blood Type: mode

 

11. Does a set of scores with most of its values below the mean have a negatively or positively skewed distribution? Provide a rationale for your answer. 

Answer - Most of the values are below the mean; this shows that there are more data points whose values are small and few data points that have very large values. Hence we can say that the data is positively skewed.

12. t-statistics = -7.9 and p-value=0.005 describe the difference between women and men for mental health score. 

a. If alpha is set to 0.05, is the p-value of 0.005 statistically significant?  - Yes

b. In a sentence, interpret the p value of 0.005 - Answer - p-value of 0.005 indicates that the probability of getting a value of the statistic more extreme than the one in the current sample (given the statistic follows the null distribution) is 0.005 (which is considered to be very low, i.e. the value of the statistic as calculated from the current sample is significantly extreme and has a very low probability of happening in general.)

13. A study found that the Pearson correlation coefficient “r” value for the relationship between serum level of cholesterol and the age of the patients in years is 0.77 and p-value was 0.002.  

a. Interpret the “r” value of 0.77 [strength and direction] and provide a rationale for your answer. 

Answer - The value of the correlation coefficient shows the linear association between 2 variables. When the absolute value of r is close to 1, the variables are said to be very highly linearly associated. In this case r=0.77 can be considered to be astrong linear association. The positive value of the correlation coefficient shows that the variables are positively linearly associated.

b. If alpha is set to be 0.05, is this “r” value of 0.77 and p-value of 0.002 statistically significant? 

Answer - Yes, if the p-value of the statistical test is less than the pre-decided level of significance, then the result is statistically significant. In this case, level of significance is 0.05 and p-value is 0.002 (<0.05). Hence, the value of r is statistically significant.
 

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