Lecture 4 Flashcards
What are descriptive statistics?
Methods for organizing and summarizing data
example: table or graph
A descriptive value for a population is called a __________
parameter
a descriptive value for a sample is called a ___________
statistic
What does the Mu symbol represent?
The mean for a population
NOT a sample
Frequency Distribution vs Grouped Frequency Distribution
Frequency distribution- presents organized picture of entire set of scores
Grouped frequency distribution- Some statistics are grouped together to accomadate for a wider range of scores
If the scores in a population are measured on an interval/ratio scale and the N is large…. the data will present as a ___________
smooth curve instead of a jagged histogram
T or F: a smooth curve shows the exact frequency of every score
F
Describe a normal distribution
symmetrical bell shape
What is a skew of frequency distribution?
Nonsymmetrical distribution of data
What kind of skew is this?
Positive skew
What kind of skew is this?
Negative skew
What is Kurtosis of a graph?
The “peakedness” of the distribution
Leptokurtic vs Platykurtic
Describe the Kurtosis of a graph
Leptokurtic = High, thin peak
Platykurtic = lower/broader peak
How does a stem and leaf distribution work?
Each score divided into stem and leaf
the stem contains the first digit(s) and the leaf contains the final digits
example: 3//3582 represents the scores 33 35 38 32
What are 3 measures of central tendency?
Mode Median and Mean
Bimodal vs Multimodal
Having 2 modes vs having multiple modes
Mode definition
Most frequently occuring number
What kind of data is appropriate for using a Mode?
All types: Nominal, Ordinal, Interval, and Ratio
Median definition
If the scores are listed smallest to largest, it is the midpoint of the list
If odd numbers, it’s the middle number
if even numbers, its the average of the middle 2 numbers.
What kind of data is appropriate for use of the median
Ordinal Interval and Ratio data
NOT nominal
What is one advantage of using the Median?
It is relatively unaffected by extreme scores
The Mean can be used as a representation of central tendency for what kind of data?
Interval and Ratio
NOT Nominal or Ordinal
When should we not report the mean?
When there are extreme scores that will pull the mean in one direction
When you’re using a nominal scale
In a central distrubtion, the mean and median will ____________
Always be equal and always be in the middle
(mean, median, mode)
In a skew, what stays in the middle of the curve?
What is skewed most towards the tail?
What is in the middle?
Mode
Mean
Median
Descriptive statistic vs inferential statistic in variability:
A descriptive statistic measures the degree to which scores are spread out
Inferential statistic measures how accurately an individual score or sample represents an entire population
A _______ variability means scores will more liekly give a good view of the whole population
Low
How to measure range for this set?
4, 5, 7, 8, 9, 11
11- 4 = 7
How to calculate standard deviation for a sample?
- First calculate the variance of every score from the mean. Each score - the mean
- Square all of those numbers and add them together
- Divide by N - 1 if it’s for a sample, just N if it’s for a population
- Take the square root of the answer
what does n-1 represent when calculating standard deviaton?
Degrees of freedom
On a normal distribution __% of scores will be 1 standard deviation from the mean
70%
On a normal distribution __% of scores will be 2 standard deviations from the mean
95
On a normal distribution __% of scores will be 3 standard deviations from the mean
99
What does a Z score tell you?
Gives you context of how a score relates to other scores in the distribution
How to calculate a Z score?
(Score - Mean) / Standard Deviation = Z score
note: Z score will always be a really small number
What are inferential statistics?
Methods for using sample data to make general conclusions about a population using probability
Rather than just describing the data like descriptive statistics
When graphed on a normal distribution, probability can be defined as the ____________________ the curve
the portion under the curve
Are Z scores for populations or samples?
Populations, not samples
How to use a Z score table?
You can use a coresponding Z score to find the probability that something will fall into the body vs the tail of the graph
Z scores will only work if the data has a _______ distribution
normal
If you sample _____ people you will end up with a normal distribution
30
What is the central limit theorem?
As sample size increase it approaches a normal distribution
30 will have a more normal distribution than 15
T or F: population data can be any size or any shape, but if you have a sample of 30+ it will be very close to normal distribution
T
What is SEM (Standard Error of the Mean)
Difference between Sample Mean and True Population mean
What is the difference between SEM and SD?
Standard Deviation compares the amount of variability of a set of data, from the mean
SEM- measures how far the sample mean is likely to be from the population mean
SEM is ALWAYS smaller than SD
How do you calculate SEM?
SD of sample: 5
Sample size: 50
50/ SqRt(5)
The smaller the number = less sampling error likely
What is a point estimate vs an interval estimate?
These are ways to use estimates to represent a population
Point estimate- using the mean of your sample
Interval estimate- using a span of numbers that includes the mean
What is a confidence interval/interval estimate
Range of numbers inferred from the sample that has a known probability of capturing the true population parameter
Example: AVG GPA = 3.4 with a 95% confidence interval that it’s between 3.2 and 3.6
