Explain The Differences Between Nominal, Ordinal, Interval And Ratio Data: Statistics Assignment, TCD, Ireland

Part 1 Questionnaire and Basic Statistics

1. Explain the differences between nominal, ordinal, interval and ratio data.

2. Design two questions, one each, that provide ordinal and ratio data. Make the questions relevant for your industry. Give one example of each kind of analysis that could be used with each of these questions.

3. Explain the various sources of bias in a survey, e.g. relating to sampling or question-wording. How does the bias arise? How does bias affect results and what remedies can reduce bias?

4. For the table in the excel tab “GenderAge”, Complete the following tasks.

Be sure to fully label graphs

1. Make a frequency table of ages (use 15-year intervals: “< 20”, “20 to 34”, etc) for each gender, and include a column for relative frequencies (%), and cumulative relative frequencies (%).

2. Make a histogram of ages for either male or female gender, using relative frequencies.

3. Make a clustered bar chart of ages for both genders together, using relative frequencies. Label the heights of bars (%).

4. Calculate descriptive statistics for each gender.
Describe the differences in distribution between genders, based on the frequency tables, histograms, and descriptive statistics.

5. Make a contingency table for age ranges “< 35”, “35 to 64”, “≥ 65” and compare the two genders.

6. Explain why mean and standard deviation are useful for some distributions but not so useful for other distributions.

For this section, you will use the tab“Normal” in the workbook.

1. Give two examples of data that one might expect to be normally distributed.

Using one of these examples, describe why the data has a normal distribution shape. Refer to randomness and the variety of individual items. E.g. why is there a bunching of values (a higher density) around the middle of the distribution and fewer and fewer values towards the high and low ends of the distribution?

2. A survey has previously found the amount spent on a particular service each month. The survey used a very large sample size so that the mean amount is highly accurate. The mean value is shown in cells D4.

3. A new survey has sampled 5 different groups, labeled 1, 2, 3, 4 & 5, to see if the amount spent by each group is different from the given mean from the earlier survey. 50 people were randomly sampled from each group. The data is shown in the table in D9:H58. Below the table, the mean and standard deviation for each sample is calculated in D62:H63.

4. For these 5 groups, make a table, with one row per group, showing: group means, sample standard deviation, standard error of the mean (SE), 90% confidence interval, and 95% confidence interval, for each sample. Also using the confidence interval state (Y/N) if we should accept the null hypothesis that the group has the same mean as for the previous survey.
Show one example of your calculation for SE and 90% CI.

5. Explain the general principle of hypothesis testing, referring to null and alternative hypotheses, confidence level, p-value, accepting/rejecting the null hypothesis.

6. Using the mean and standard deviation of Group 1 in D62:D63

7. For the values A. B, C in D66:D68, calculate the probability of:

8. getting a value less than A

9. getting a value more than B

1. Show your calculations for the following:

2. For the probability P1 in D38, find the value such that
the probability of someone paying less than that value is P1.

3. For the probability P2 in D39, find the value such that
the probability of someone paying more than that value is P2.

Part 3 Regression Analysis

For this part, use the tab “Trend” in the workbook.

Three datasets are shown in B5:G36. They each contain 30 rows. The “x” and “y” columns are responses to two questions collected from a survey. The three datasets are taken from three samples taken randomly from the same population.

1. Make a separate chart for each of the datasets, “Data 1”, Data 2 and Data 2.
Add axis labels “x variable” and “y variable”, and title, e.g. “Data 1 Trendline”.

2. For each chart, add a linear trendline, showing the equation and .

3. For each dataset, what is the level of correlation: very low, low, medium, high, very high? Is it positively or negatively correlated?

4. From looking at the data by eye, does each dataset look correlated. Explain.

5. Explain why the datasets might have different correlations (positive, negative, strength) even though they come from the same population.

6. In F6:N19, regression analysis output is shown for the datasets.

7. Using 90%/95% confidence and the p-value, are the slope and/or intercept values significant for each of Data 1, Data 2 and Data 3.