Q&Q Test 3
Nominal scale type
(name) subjects fall into categories, but one category is not considered to be higher or lower than another * used for mode
How are null hypothesis stated?
- No difference between groups M1 = M2 - The true difference between groups is zero: M1 - M2 = 0 - The observed difference is due to sampling error
Suppose a fellow student gave a report in class and said, "The average is 25.88". What additional information should you ask for? Why?
Average of what? (mean, median, mode?) Average can refer to multiple aspects of data.
What are 3 common ways for describing data?
Central Tendency Dispersion of scores Frequency distributions
how is effect size evaluated?
Cohen's D - used for experiments having 2 groups
Name a trait that inherently lends itself to nominal measurement. Explain your answer.
Ethnicity or Marriage Status- It can be made categorical and there is no mathematical order to the results and no category is higher than the other. It is what it is.
Why is effect size important to consider in an experiment?
It is considered good practice when presenting empirical research findings in many fields, it plays an important role in meta-analysis which summarize findings across studies in a specific area of research; can help determine sample size.
How does SD affect curve shape?
Larger standard deviations lead to wider AND lower bell curves (platykurtic) Smaller standard deviations lead to narrower AND taller bell curves (leptokurtic)
What is Central tendency?
Mean median mode
What are the 4 different scales?
Nominal Ordinal interval ratio
What are the properties of normal distribution and non symmetrical?
Normal distribution: actually a family of frequency distributions * Only certain characteristics are normally distributed (IQ) *If the distribution is normal 34% of the participants lie 1 SD above the mean, and 34% lie 1 SD below the mean - 68% are within ± 1 SD of the mean
What is skewness?
Skewness refers to the positon of the tail of the distribution - Negative- tail in negative direction - Positive- tail in positive direction
a 2-way ANOVA
Statistic = F Used when there are 2 independent variables effect size is calculate by: Omega squared
a 1- way ANOVA
Statistic = F Used when there is 1 independent variable, and 3 or more groups effect size is calculate by: Omega squared
A chi-square
Statistic = x2 (x squared) Used when there are 2 nominal variables, scores are frequencies effect size is calculate by: Cramer's V
How is hypothesis testing conducted?
T-Test - a two group comparison * theoretical range between -5 and +5 *bigger differences yield a larger t value - hypothesis testing based on group mean, SD, and sample size
what factors do you consider when determining sample size?
There are many ways of doing this: - If the population is small enough, include everyone in the study (conduct a census); - Use a sample size of a similar study; - Use published tables; - Use formulas to calculate sample size; OR ideally, conduct a pilot study and calculate the effect size. - If the effect size is small (i.e., there is a subtle effect of the IV on the DV), it may be necessary to boost sample size to increase the likelihood of obtaining significant results. (this may be the best way to decide upon sample size) ***if effective it should show the same results regardless of sample size
Dispersion of scores
Variability and standard deviation
Imagine that you have conducted an experiment and are now analyzing the results. You will be conducting a 2-tailed t-test in which you are setting the overall alpha at 0.05. Draw a sampling distribution for t and indicate what area of each tail would be "shaded in" as the region of null rejection. If your calculated value for t equals 3.98 and the critical value for t equals plus or minus 2.63, will you reject the null hypothesis? Why or why not?
You would reject the null hypothesis because the t value exceeds the critical value
What is a type II error?
accidentally not rejecting the null when it should be rejected your results are actually "real" but your calculated statistic is too small to allow the null hypothesis to be rejected
What is the null hypothesis?
belief that the observed differences reflects sampling error or threats to internal validity rather than a real difference between groups
What is a 2-tailed test?
conducted if you are not expecting more or less, you are simply expecting a difference - m1 does not equal m2 - alpha is no longer 5%, it is 2.5%on each side of the distribution
What is a 1-tailed test?
conducted if your researcher hypothesis suggests a direction to your finding - either more or less of something *more of something --> right side tail (positive t value) *less of something --> left side tail (negative t value)
Bar graphs
data are a tally of different categories
Histogram
data are tally that can be described as a range of numbers - Frequency histogram: shows score frequency * not a bar chart because x axis is quantitative * discrete scores on the x axis vs range of values -Frequency polygons: based on frequency histogram * if you draw continuous line through midpoint of each column (also referred to as frequency distribution) *have different shapes (normal distributions are symmetrical) (may have a variable number of peaks)
Interval Scale Type
differences between scores have equal value, but there is no absolute zero (date) *used for mean
what do you do when effect size are equal?
either treatment can be recommended
Pie charts
have made a tally or are expressing the results as %
how do effect size and sample size interact?
if affect size is small- may miss subtle effects of IV on DV if effect size is large- can be limited importance - results can expensive to replicate ** The larger the effect size, the smaller sample size you will require and the smaller the chance that you will not notice a change
What is variance?
it finds out how different the field of scores are from the average
What is effect size?
magnitude of experimental effect measurement of effectiveness of the treatment Independent variable - if IV causes big change in DV, there is a large effect size
Ordinal Scale Type
measurements are ranked from high to low strongly agree to strongly disagree *used for median
bigger samples
more reliable
smaller samples
more subject to sample bias
What is standard deviation?
most commonly reported measure of variance average dispersion of scores around the mean - low sd: less spread -high sd: more spread Square root of variance for a set of cores provide estimate of how representative the mean is for the set of data
Type 1 error is reduced by:
notice that as the amount of the distribution set aside as the rejection area (alpha) decreases, the chances of incorrectly rejecting the null hypothesis decreases too * this is the major way of decreasing probability error referred to as: decreasing p value or decreasing alpha
What is kurtosis?
refers to the "peakedness" of the distribution
the only way to support a research hypothesis is to...
refute the null hypothesis
What does alpha represent?
region of rejection when a researcher identifies 5% of the distribution as the region of null rejection -->set alpha at 5% if two tailed test, both sides together don't exceed 5%
if the calculated Chi-square exceeds a critical value, the null hypothesis is...
rejected
Ratio Scale Type
same as interval scale, but absolute zero exists (mph) *used for mean
It is possible that results reflect...
sampling error or threats of internal validity
frequency distributions
several ways of describing the number of subject that are similar along the given characteristic or measured dependent variable Graphed: pie chart, bar graph, histogram, frequency histogram, frequency polygons
a correlation test
statistic = r used to determine the direction and strength of relationship between two continuous variables effect size is calculate by: r2 (r squared)
a t-test
statistic = t used when there is 1 independent variable, and 2 groups effect size is calculate by: Cohen's d
What factors affect power?
statistical significance criterion used magnitude of the effect of interest in population sample size used to detect effect (SAME AS WAY TO REDUCE type II error)
Discuss 3 important factors that affect statistical power in an experiment
statistical significance criterion used - where you set alpha magnitude of the effect of interest in population sample size used to detect effect
type II error occur because..
studies lack statistical power (the probability that you will detect a false null hypothesis)
Foundational statistics
the only way we an support research hypothesis is by rejecting the null hypothesis it is always assumed that the alternate or research is wrong until you find evidence to thin otherwise
Whatever level you reject the null hypothesis at equals..
the probability you're making a type 1 error or less if alpha = 5% ; there is a 5% chance of type 1 error
rejecting the null hypothesis does not guarantee that ...
the results are real because values are generated by chance alone
What is a type 1 error?
the situation in which the null hypothesis is mistakenly rejected - threat to internal validity - nothing is really going on in the study (bias sample)
Type II error is reduced by:
the statistical criterion used in the test - whether you set alpha at .05 or .01 (.01 can make it too hard to reject null that the real effect is missed) the magnitude of the effect of interest in the population - if experiment is done on a robust phenomenon, it will be easier to demonstrate effect experimentally (big phenomenon = big experimental effect) -examining a robust phenomenon increases power the sample size used to detect the effect - increasing sample size may increase power (bigger the sample, better chances of detecting true magnitude of experimental effects)
why is it that when you reject the null, it is unlikely (but not impossible) that your results could still reflect a true null hypothesis?
threats to internal validity or sampling error
What is a Chi-square (x2) design?
used if you did a study in which you obtained frequencies and your two variables where categorical (nominal) i.e. pollling situation test determines whether there is significant association between the two variables
Why do researchers desperately guard against Type II errors?
you lack statistical power and you retain the null. Therefore, hypothesis appears invalid. the effect is so small it is overlooked.
