Lecture 3 Chapter 3 Flashcards
What is the purpose of descriptive statistics?
Describe data only
What is the purpose of inferential statistics?
Determine likelihood of pure randomness explaining data
Name the three types of descriptive statitsics?
1) Measures of Central Tendency
2) Measures of Variability
3)Statistics for describing shapes of distributions
What are the three measures of central tendency?
Mean
Median
Mode
How to choose the right measure of central tendency?
-The type of measure of central tendency you choose depends on the level of measurement of the variable
-Measures of central tendency are linked to the levels of measurement of variables
What is the mode?
The value that occurs most frequently in a set of data
A distribution with two highest frequently occurring values is called ?
Bimodal
A distribution with three or more highest frequently occurring values is called ?
multimodal
What type of data is the best for the mode?
Nominal
Why in nominal data data best for mode?
With nominal and dichotomous data, we cannot rank the values, but can only count them
What is the median?
The middle value/score in a sorted set of data (in ascending or descending order)
How do you get the median?
Half of the scores fall above the median, and half fall below the median; it’s the center score
What type of data is best for the median?
Ordinal
Why does median not work for nominal data?
-Doesn’t work for nominal data because you can’t order the categories
-So we can’t say half of nominal categories are “less than” and half are “greater than” a particular category
What is the mean?
The arithmetic average
What is the data is best for the mean?
Normal
What is a weakness to the mean?
-A single very large (or small) number can dramatically change the mean
-The mean can be greatly influenced/swayed by outliers (scores far higher or lower than most)
What is a strength of the mean?
-The mean best describes the center of the values of a variable
-The mean provides a good representation of the entire data for a variable
What does it mean when data is normally distributed?
meaning no outliers or numbers are close to each other
How can you tell data is normally distributed?
the mean median, and mode can have the same value
what is the purpose of measures of variability?
-Describe how the values of a variable are spread out or dispersed
-Describe how much the values vary from each other
What are the three measures of variability?
- Number of categories
- Range
- Standard deviation
How do you choose the best measure of variability?
- Best to use depends on the level of measurement of the variable or type of data you have
What is the measure of variability for nominal data?
How many categories
What is the measure of variability for dichotomous data?
Range is always 1
how many categories is always 2
What is the measure of variability for ordinal data?
Range & Interquartile Range
but range is preferred
What is the measure of variability for normal/scale data?
Standard Deviation
What is the definition of standard deviation?
Is the “average distance” between each score and the mean
What does standard deviation tell us?
Tells you how far the values are spread out around the mean of the variable
What does a higher standard deviation mean?
- The higher the standard deviation, the higher the “average distance” between each score and the mean
- The higher the standard deviation, the more spread out about the mean are the individual scores in the data set
What does a lower standard deviation mean?
The average distance is smaller, meaning the scores are closer together
The mean and standard deviation can be used to calculate
“standardized scores”
What is another name for what the mean and standard deviation calculate
Z-Score
What does the z-score mean
-Z-scores tell you the number of standard deviations a score/value is from the mean
-Z-scores are expressed in terms of standard deviations from their means
What is the mean and standard deviation in a z-score?
Z-scores have a mean of 0 and a standard deviation of 1
Why is the z-score important?
-Used to compare two or more values that are part of different distributions
* Useful for comparing different groups because scores are standardized
What is the calculation for the z score?
Raw score - group mean / divided by the group standard deviation
What is the definition of normal distribution?
A theoretical distribution that provides a reference point for describing the shape of a distribution
How can we find the percentage of scores that are below or above a particular score on the normal curve?
We use the z-score calculation
what do Negative z-score tells us?
the actual raw score is below the mean
What does a Positive z-score tells us ?
the actual raw score is above the mean
What percent of the stores fall within 1 positive/ 1 negative standard deviation?
About 68% fall within +/- 1 SD from the Mean
What percent of the stores fall within 2 positive/ 2 negative standard deviation?
About 95% fall within +/- 2 SD from the Mean
What percent of the scores fall within 3 positive/ 3 negative standard deviations?
About 99% fall within +/- 3 SD from the Mean
By knowing how much area is between plus and minus 1 sd what does this help us do?
helps us to describe the spread of values of a normally distributed variable
What is the central limit theorem?
Tells us that data are often distributed approximately as the normal curve when the sample size is large
What is skewness?
*Tells us how symmetrical a distribution is
* Describes data symmetry
*Describes how the shape of a distribution of scores differ from the normal curve
If the data is symmetrical does it have a skewness?
No skewness
How do we determine the type of skewness of a distribution?
Comparing the mean, median and mode
The type of skewness of a distribution is determined by the direction that the tail trails off
What is positive skewness?
The tail trails off to the right
Where are the mean, median and mode in positive skewness?
The mean is higher than the median, which is also higher than the mode
What is negative skewness?
The tail trails off to the left
Where are the mean, median and mode in negative skewness?
The mean is lower than the median, which is also lower than the mode
What data is assumed to be skewed?
Nominal and ordinal
Many statistical tests may only be used if the data is _______?
normally distributed variables or data
How do we tell if scale/normal data are normally distributed?
-Use skewness: The mean, median, and mode must be equal (or very close) to be normally distributed
* Create a histogram (with the normal curve superimposed) and compare it to the normal curve
