Exam 3 Flashcards
What are the uses of statistics in research?
- Provide a description of the research sample (descriptive statistics)
- Perform statistical tests of significance on research hypotheses (inferential statistics)
What do descriptive characteristics characterize?
- Shape
- Central tendency (averages)
- Variability
What do descriptive statistics do?
*Provide a description (“picture”) of the dataset
Include
–frequency distributions
–measures of central tendency
–measures of variability
*These statistics illustrate the characteristics of a sample
–allow comparison of the sample to other samples
What does a table of rank ordered scores do?
*Shows how many times each value occurred (frequency)
What is a histogram?
- A bar graph
- -composed of a series of columns
- -each representing a score or class interval
What is a normal distribution? (bell shaped)
- Most scores fall in the middle
- Fewer scores found at the extremes
- Symmetrical
- Mean, median and mode represent the same value
- Important assumption for parametric statistics
What is a skewed distribution?
- asymmetrical
- to the right or left
- distribution of scores above and below the mean are not equivalent
- there are specific statistics appropriate to non-normal distributions
What is a positive skew?
- Skewed to the right (tail points to the right)
- Most scores cluster at low end
- Few at high end
what is a negative skew?
- Skewed to the left (tail points to the left)
- Most scores at the high end
- Few at low end
What is mode?
Score that occurs most frequently
What is median?
Value above which there are as many scores as below
What is the mean?
Sum of scores divided by number of scores
How do you measure variability?
- Range
- Percentiles; quartiles
- Variance
- Standard Deviation
- Coefficient of variation
What is range?
Difference b/w highest and lowest values in the distribution
What is percentile?
Percentage of a distribution that is below a specified value
What is variance?
Measure of variability in a distribution, equal to the square of the standard deviation
What is standard deviation?
Descriptive statistic reflecting the variability or dispersion of scores around the mean
What is coefficient of variation?
Measure of relative variation as a %
—(SD/mean) *100
What is a standardized score?
*Expresses scores in terms of standard deviation units
What is inferential statistics?
- Decision making process
* Estimate population characteristics from data from a sample
What is statistical inference?
- Draw valid conclusions from research data
- –Does the sample represent the population?
- Probability and sampling error
What is probability?
- Likelihood an event will occur given all possible outcomes
- p represents probability e.g. p=0.50 that a coin flip will be heads
- Used in research to make decisions about how well sample data estimates characteristics of a population
- Did differences we see b/w treatment groups occur by chance or are we likely to see these differences in the larger population?
- Estimating what would happen to others based on what we observe in our sample
What is sampling error?
- Estimating population characteristics (parameters) from sample data
- -Assumes that samples are random i.e. individuals randomly drawn from the population
- -And that samples represent the population
- Sampling error: sample values and population values differ
Give an example of sampling error
- *Say there are 1000 000 people over the age of 55 years in the population with population mean age of 67 and SD of 5.2 years
- We randomly select 15 people and find that mean age is 62 yrs and SD is 2.7
- A second sample of 15 people might have age of 73 and SD of 6.4
- -i.e. means and SD will very likely differ with each time we sample
What is the sampling error for a single sample?
- Sampling error of the mean for a single sample is sample mean (Xbar) minus population mean (µ)
- If drew many (infinite) samples would see varying degrees of sampling error
What would the plot of sample means be?
- The shape of a normal curve
- -Mean of all sample means will equal population mean
- The distribution of sample means is called a “sampling distribution of means”
- Predictable properties of normal curve
- –use the concept of the “sampling distribution” to draw inferences from sample data
What is standard error of the mean?
- Sampling distribution is a normal curve
- -Can establish its variability
- Standard deviation of sampling distribution of means is called standard error of the mean (SEM)
- –Estimate of population standard deviation
*SEM = SD/√n, where SD=sample SD and n=sample size
What is a confidence interval?
- Can use sample mean as an estimate of population mean
- -Point estimate
- -Single sample value will not be a true estimate of population mean
What is the interval estimate of mean?
- Interval which contains the population mean
- Range of values which contain the population mean
- –Confidence interval (CI)
What are the ranges of scores of CI?
- -Boundaries (confidence limits)
- -Contains the population mean
- Boundaries based on sample mean and SEM
- Expressed as 95% confidence interval
- CI= X ± Z (SEM) where z=1.96
- “We are 95% confident that the population mean falls within this range of values.”
What is a null hypothesis?
- No difference
* H0: μA = μB
What is an alternative hypothesis?
- Is a difference
* H1: μA ≠ μB
What are hypothesis testing based on?
- Your statistical tests are based on the null hypothesis only: rejecting or failing to reject H0
- If p ≤ 0.05, we reject the null hypothesis and accept the alternative hypothesis
- If p > 0.05, we fail to reject the null hypothesis
What is hypothesis direction?
- Directional vs. Non-directional alternative hypothesis
- -Non-directional do not specify which group will be greater in value than the other
- —-E.g. H1: μA ≠ μB Population A will have different strength to Population B (greater or lower not specified)
- -Directional specifies which group will be greater than the other
- —-E.g. H1: μA > μB Population A will have greater strength than Population B
