8 Common Techniques in Descriptive Statistics Flashcards
What are the main topics covered in this chapter?
- Understanding frequencies and percentages
- Calculating percent change and percent difference
- Discovering confidence intervals
- Understanding z-scores
Define frequencies in the context of descriptive statistics.
A count of occurrences of specific values within a variable.
What is a frequency table?
A table that lists every reported value in a variable and how many times they occurred.
What is the purpose of a contingency table?
To hold more than one variable and show the relationship between them.
How do you calculate frequency?
- Arrange values in order.
- Create a table of possible values.
- Count occurrences of each value.
What is the difference between count and probability in statistics?
Count is the number of occurrences, while probability is the count divided by the total number of occurrences.
What are percentages in relation to frequencies?
Percentages represent the portion of the whole that each value accounts for.
List the steps to calculate percentages.
- Find the frequencies.
- Divide each frequency by the total number of values.
- Multiply each frequency by 100.
Fill in the blank: Percent change is concerned with how a single value has changed from point A to point _______.
[B]
What is the formula for calculating percent change?
C = ((x2 - x1) / x1) * 100
True or False: Percent change can yield negative results.
True
What is the main focus of percent difference?
Comparing two values without a designated starting point.
What is the formula for calculating percent difference?
Percent difference = (|x1 - x2| / ((x1 + x2) / 2)) * 100
Fill in the blank: Percent difference will never have a _______ value.
[negative]
What type of data do frequencies and percentages commonly apply to?
Qualitative variables
What happens to the complexity of frequency tables as more variables are added?
Complexity increases exponentially.
What type of chart represents frequencies?
Bar charts
What type of chart represents percentages?
Pie charts
True or False: Percent change and percent difference are calculated the same way.
False
What is the key difference between percent change and percent difference?
Percent change references a starting value; percent difference treats both values equally.
How would you describe the relationship between percent change and a variableβs starting point?
Percent change is always reported in reference to a starting value.
What is the significance of understanding confidence intervals in data analysis?
What is a z-score used for in statistics?
What is the formula for calculating percent difference?
Percent difference = (|π₯π₯1 - π₯π₯2| / ((π₯π₯1 + π₯π₯2) / 2)) * 100
What is the first step in calculating percent difference?
Subtract one value from the other and drop any negative signs.
True or False: Percent difference can have negative values.
False
What does a confidence interval represent?
A range including the mean of your sample.
What is the most common alpha value used for confidence intervals?
0.05
What confidence level corresponds to an alpha of 0.05?
95%
What is the equation for calculating a confidence interval?
CI = π₯π₯Μ Β± t (π / βπ)
What does π₯π₯Μ represent in the confidence interval equation?
The mean of the sample.
What is the purpose of a z-score?
To compare a single value to a normal distribution.
Fill in the blank: A z-score reports how many _______ your chosen value is from the mean.
standard deviations
What is the equation for calculating a z-score?
Z = (π₯π₯ - ππ) / ππ
What is the first step in calculating a z-score?
Subtract the mean from your value.
How do you find the upper confidence interval?
Add the result of the previous step to your mean.
How do you find the lower confidence interval?
Subtract the result of the previous step from the mean.
What does βtβ represent in the confidence interval equation?
A value from a t-distribution confidence table.
What is the standard deviation of the sample in the hotdog sales example?
1.12
What is the sample size in the hotdog sales example?
9
What is the mean of the hotdog sales example?
8
What is the result of the confidence interval calculation for the hotdog sales?
Lower confidence interval = 7.31, Upper confidence interval = 8.69
What type of analysis is most appropriate for comparing a single articleβs reads to other articles?
Z-score
What is the confidence level if the alpha is 0.01?
99%
True or False: The percent change measures the objective difference between two values.
False
What do you need to calculate percent change?
A starting value and an ending value.
What is the percent change if the starting value is 200 and the ending value is 240?
20%
What is the second step in calculating percent difference?
Find the average of the two values.
What is the third step in calculating confidence intervals?
Find the square root of your sample size.
What is the significance of the degrees of freedom (dfs) in the context of confidence intervals?
Sample size minus 1.
What does a z-score of 1 indicate in terms of standard deviation?
The value is 1 standard deviation above the mean.
