Exam 2 psych 210
Reporting Your Results of paired sample t test
(M helvetica = 14.0,M comic sans = 12.6, t(4) = 2.33, p > .05).
minimum statistical power to conduct a study
0.8 (80%)
The Five steps of STEP 3 calculating the comparison distribution in an independent sample t test
1. Calculate the corrected variance for each sample 2. Pool the variances (take the average of the two sample variances) 3. Convert the pooled variances from square standard deviation (variance) to squared standard error (divide the pooled variance by the sample size) 4. Add the two variances (squared standard errors), one for each distribution of the sample means, to calculate the estimated variance of the distribution of differences between means 5. Square root it to get the estimated standard error
What are the steps for calculating a confidence interval for a single sample t test?
1. Draw picture 2. indicate bounds 3. look up t stat 4. Convert t value to a raw mean
Considerations to keep in mind when running meta analysis testing (during step 1)
1. Make sure the necessary statistical information is available 2. Only select studies where participants meet the specific criteria 3. Eliminate studies based on research design
Data Transformations
1. Transform a scale variable to an ordinal variable. 2. Use a data transformation such as square root transformation to "squeeze" the data together to make it more normal. Remember that we need to apply any kind of data transformation to everyobservation in the data set.
What are the 6 steps of hypothesis for a single sample t test?
1. identify the population, distribution, and assumptions 2. State the hypothesis 3. What are the characteristics of the comparison distribution 4. Identify the critical values, degrees of freedom (look up the df at 0.05 in the t table) 5. Calculate 6. Decide
How t distributions are more versatile than z distributions. They are used when:
1. when we don't know the population standard deviation 2. we compare two samples
What are the 5 steps for calculating a Confidence Interval?
1.Draw a picture of the distribution 2. Indicate the boundries of the Confidence Invt 3. Finds Z stat that falls at 95 % (1.96) 4. Turn Z stat into raw mean 5.Check that the confidence interval makes sense
What does t(4)=2.87, p<0.05 mean?
4 is the df 2.87 is the t stat p<0.05 is the critical value
paired samples t-test(dependent)
A test used to compare two means for a within-groups design, a situation in which every participant is in both samples (before and after)
pooled variance
A weighted average of the two estimates of variance—one from each sample—that are calculated when conducting an independent-samples t test.
When computing power:
Always use z distribution (even for t test)
Mean of paired and independent:
Are both 0
Difference between cohen's d and r square
Cohen's d= There's a significant difference between the means, but how much of the population is R squared= Shows how much influence the iv has on the dv. How much of the variability in the data can be explained solely by the experiment
Forest plot
Confidence interval for the effect size of every study
What does a confidence interval do for us?
Confirms findings of Hyp tests and adds detail
What is the comparison distribution for an independent sample t test
Distribution of differences between means
What is the comparison distribution for a paired single sample t-test?
Distribution of mean difference scores
What is the comparison distribution for a z-test and single sample t test?
Distribution of means
What is the name of the fourth assumption to be used in an independent samples t-test?
Homogeneity of variance
T-Test's tell us:
How confident we can be that the sample differs from the larger population. They are used when parameters aren't known
Three bad ways to increase power
Increase the alpha turn a 2 tailed test into a 1 tailed test Increase the variance of the distributions
What does increasing sample size due to significance?
Increases the significance
DoIndependent samples t-test increases or decreases variability in data?
Increases variability
How do you turn a Z score to raw score for Confidence Interval?
M lower=M sample- Z(σ M) M Upper=M Sample + Z(σM)
What is the significance value of α?
Probability of rejecting the null that is true (Type 1)
What are 2 ways to increase effect size?
Reduce variability within populations Make mean differences larger (less overlap)
Three steps to creating a dot plot
STEP 1: We determine the lowest score and highest score of the sample STEP 2: We draw an x-axis and label it, including the values from the lowest through highest scores STEP 3: We place a dot above the appropriate value for every score.
Effect size?
Size of the difference, and is unaffected by the sample size (how much two populations do not overlap)
Proportion of variance(r^2)
Small: 0.01 Medium: 0.06 Large: 0.14
difference between statistical significance and effect size
Statistical significance= difference between two means exist Effect Size= puts a number to it Cohen's d and R^2= measures of effect size
Steps for Calculating CIs (paired sample t test)
Step 1. Draw a normal curve with the sample difference between means in the center. Step 2. Indicate the bounds of the CI on either end, writing the percentages under each segment of the curve. Step 3. Look up the t values for lower and upper ends of the CIs in the t table. Step 4. Convert the t values to raw differences
Calculating the Estimated Population SD
Step 1: Calculate the sample mean Step 2: Use the sample mean in the corrected standard deviation formula
The major difference between Single sample and paired sample t tests
Step are essentially the same, but for paired sample we must create different scores for every participant (distribution of mean differences, M1-M2 and μ1- μ2)
Define Homogeneity of Variance
The 2 populations the samples are selected from must have equal variances
True/False: Two samples drawn from the same population will have different t-stats even if they have the same size mean
True
Type I is to αlpha , as ______ is to ______
Type 2, beta
If the treatment has a small effect, what is the likely outcome for a hypothesis test evaluating the treatment?
Type II error
Why is including unpublished studies important in meta analysis?
Unpublished studies have better chance of showing null results (i.e.. there was no difference)
When is a paired sample t-test used
When comparing differences Within group designs with 2 sample means
When do we use a single sample t-test?
When we know the population mean, but not the standard deviation
What are some criticisms of, or concerns regarding, traditional hypothesis testing?
You can't report a significant difference without reporting the size of the difference observed (i.e. the effect size) or the associated confidence intervals -you need an effect size of a certain test in order to see if a certain study has meaningful or important results · Arbitrary significance—not based on actual consequences of type 1 error · Dichotomous logic--black and white! · Overemphasis on significance · Inadequate attention to other factors that influence significance- i.e. sample size, variance(poor control)
file drawer analysis
a statistical calculation, following a meta-analysis, of the number of studies with null results that would have to exist so that a mean effect size would no longer be statistically significant
statistical significance
a statistical statement of how likely it is that an obtained relationships between two variables occurred by chance
point estimate
a summary statistic from a sample that is just one number used as an estimate of the population parameter
error bars
a vertical line used in a bar graph or histogram to indicate the confidence interval around a group mean
What does Cohen's d use to estimate effect size?
accesses the difference between means, using the standard deviation instead of standard error(If standard deviation increases, so does d)
confidence interval
an interval estimate that includes the mean we would expect for a sample stat a certain % of the time (in this class 95%) if we sampled from the same population
Independent Sample t-test are used for what type of design?
between group design (comparing two means)
meta-analysis
calculating the mean (average) effect size from the individual effect sizes of more than one study
What is the formula for calculating effect size with a single sample t-test?
d=(m-µ)/s
Critical Value ___________ as degrees of freedom increases
decreases
R^2
determines the proportion of variance in the dependent variable that can be explained by the independent variable.
Order effects
how a participants behavior changes when the dependent variable is presented for a second time
Three good ways to increase power
increase the sample size (N) (most commonly used) increase the difference between means decrease standard deviation
T-Statistic
indicates the distance of a sample mean from a population mean in terms of the estimated standard error
In regards to effect size, what does it mean when there is a bigger mean difference?
less overlap and larger effect size
In regards to effect size, what does it mean when there is less variability? (steeper curve)
less overlap and larger effect size
t distribution is a distribution of _________
means
Counter Balancing
method to reduce order effects in within group designs by varying the order of presentation of different levels of the independent variable from one participant to the next
Degrees of Freedom
n-1
The Logic of Meta-Analysis
o STEP 1: Select the topic of interest o STEP 2: Locate every study that has been conducted and meets the criteria o STEP 3: Calculate an effect size, often Cohen's d, for every study o STEP 4: Calculate statistics and create appropriate graphs
Calculating Power
o Step 1: Determine the information needed to calculate power - Population mean, population standard deviation, sample mean, sample size, standard error (based on sample size) o Step 2: Determine a critical z value (1.96) and raw mean, to calculate power o Step 3: Calculate power: the percentage of the distribution of the means for population 2 that falls above the critical value o Calculate the Power
Variance Accounted for
r^2. Another measure of effect size
interval estimate
range of values within which the true population value is estimated to fall (margin of error)
What does the confidence interval mean?
that with repeated samples, we should get a sample mean within the interval 95% of the time
Statistical power
the ability to reject the null hypothesis, given that the null is false(the probability that we will reject the null when we should reject the null, and thus avoid a type II error)
What is the p-value?
the probability of obtaining at least as extreme results, given the null hypothesis is true
If you can't find the exact DF on the t table, which DF should you uses?
the smaller one
How do t distribution look different than z distributions?
they are wider and fatter(they look more like Z as N/df increases)
When the Confidence interval is constructed around the null Hypothesis...
this is where we would expect the sample mean to fall 95% of the time
When the Confidence interval is constructed around the research Hypothesis...
this is where we would expect the true mean to fall 95% of the time
What is Cohen's d used for?
to estimate effect size
Independent Samples t-Test
used to compare two means for a between-groups design, a situation in which each participant is assigned to only one condition (ex. Reward versus Punishment, Anxious versus Non-anxious)
When is statistical significance obtained?
when the p-value is less than the significance level (alpha or α)(0.05).