descriptive and inferential statistics Flashcards
What are examples of forms of raw data?
a. Questionnaires
b. Interviews
c. Objective measures
Explain descriptive vs inferential statistics
Descriptive statistics
These are basics measures
They average scores on variables and how they differ
iii. Cannot conclude statistical differences
Inferential statistics
These help make decisions about the Null and research hypotheses
They make Generalizations from the sample population
What is central tendency
used for summarizing large amounts of data into one typical or average value
Uses mean median and mode
A summary of measure that attempts to describe a whole set of data with a singe value that represents the middle or centre of its distribution
Explain what the mean its level of measurement and when it is used
Mean measures the average score for each variable.
- Level of measurement = interval and ratio
- Used when: you can, and the data fit
Explain what the median its level of measurement and when it is used
Median is the mid point of data
a. Level of measurement: ordinal
b. Used when: data include extreme scores
Explain what mode is, its level of measurement and when it is used
Mode is the most frequent score
a. Level of measurement: nominal
b. Used when: data are categorical
What are the indices of variability?
a. Range
b. Standard deviation
c. Skewness
What is the importance of descriptives?
Provide a first glance at the data
i. Describes the variability of the sample
b. Allows other researchers to understand the data
- All variables are assumed to follow a ____ distribution
normal
What is the meaning of z-scores?
the number of standard deviations a particular score is away from the sample mean
a. Different scores represent different locations on the x-axis
i. The location on the axis is associated with a certain %
b. Z-scores can be used to predict:
i. Percentage of scores both above and below a particular score
ii. The probability that a particular score will occur in a distribution
c. Z-scores are a good method to understand how scores relate to one another
i. Typically used at population level, but can be useful in samples however not always practical.
if you want to compare it to the “average” person’s weight, looking at a vast table of data can be overwhelming (especially if some weights are recorded in kilograms). A z-score can tell you where that person’s weight is compared to the average population’s mean weight
…
let’s say you have a test score of 190. The test has a mean (μ) of 150 and a standard deviation (σ) of 25. Assuming a normal distribution, your z score would be:
z = (x – μ) / σ
= (190 – 150) / 25 = 1.6.
The z score tells you how many standard deviations from the mean your score is. In this example, your score is 1.6 standard deviations above the mean
way to compare results to a “normal” population
If a z-score has a p value less than 0.05, it is deemed _ _ than the comparison
Significantly different
Reject the null
Want it to be less than .05
What is a type 1 error?
Error of optimism, resulting from rejecting the null hypothesis when it is true.
a. The probability of making a type 1 error:
- Set by researcher
(Ex. 0.01% chance of rejecting the null when it is true)
What is a type 2 error and how can risk of this be reduced?
Error of pessimism, resulting from accepting the null when it should be rejected
- Reduced by increasing sample size
- Reduced by increasing treatment effects
List the 8 steps of using a significance test:
a. State the null hypothesis
b. Establish the significance level
c. Select the appropriate test statistic
d. Compute the test statistic (obtained value)
e. Determine the value needed to reject the null (critical value)
i. This depends on:
1. Level of significance chosen (e.g. p = 0.5)
2. Degrees of freedom (based on sample size)
f. Compare the obtained value to the critical value
g. If the obtained value is greater than the critical value, reject the null
h. If the obtained value is less than or equal to the critical value, accept the null
Explain non-parametric
(Remember the measures)
a. Data are nominal or ordinal
b. Population is not normal
c. Useful in frequency data or proportions
Tests:
Chi square
Mann Whitney wilcoxan u (compares 2 samples or groups)
Explain parametric data
Data are interval or ratio level
Population from which observations are made are normally distributed
Tests:
One sample t-test
Independent sample t-test
Dependent sample t-test
What are the 3 types of t-tests?
a. One sample t-test
b. Independent sample t-test
c. Dependent sample t-test (paired t-test)
Used for parametric data
Explain one sample t-test
Compare sample mean to known population mean
Only need 1 sample of collected data but need to know mean you are comparing against
Don’t need to know population standard deviation; use info collected from sample
Explain independent sample t-test
a. Comparing results of 2 groups and the Individuals in each group are different
Ex. Male and female
Explain dependent sample t-test
paired sample
Comparing 2 means but individuals in the 2 samples are the same people
need to account for person effects within the calculation, hence the different test
Explain the difference between a 1-tail and 2-tail test:
2 tailed
- p = 0.05, the critical z =1.96
1 tailed
- p =0.05, critical z = 1.65
knowing the direction of a result is needed ot use a 1-tailed test
1 tailed tests are more lenient (will reject the null more) then 2 tailed tests
with 2 tailed tests, it is assumed we reject the null unless falls within critical regions
what types of analysis are used for experimental studies?
t-test
ANOVA (multiple types)
chi-square
what type of analysis is used for correlational studies?
bivariate correlations
regression analyses (many types)
what types of analysis are used for multivariate designs
MANOVA
hierarchial linear model
how is a z score (standard score) calculated?
z = individual score - mean of the group / population standard deviation
if the null hypothesis should be accepted and you rejected it, this is a ____ error
type 1
if the null hypothesis is false and you accept it, this is a ____ error
type 2
why should we beware large samples?
effects can be statistically significant but not clinically important
why should we beware the small sample?
it is hard to find significant differences
& no difference means little or nothing
what is the F-test
Used for tests with multiple groups
the f-test will tell us a significant difference exists somewhere between the groups but will not tell us where
- so you can reach the conclusion that significant difference does exist but need to follow up with other test to find out where
steps in f-test follow up
- post-hoc analyses (multiple types exist) - pinpoints where the difference exists
- allows to investigate difference once significant test has been found
- adjust the alpha value due to EWE
- pinpoint where differences exist
- can then reach final conclusions about groups
2-way ANOVA
Investigates the interaction between independent variables 1 and 2
1-way ANOVA
investigate tests of 3 or more population means with just 1 independent variable
If the obtained value is greater than the critical value…
Reject the null
If the obtained value is less than the critical value…
Accept the null
EWE meaning
Experiment wise error
