Exam 2 Flashcards
interval estimate
based on our sample statistic, range of sample statistic we would expect if we repeatedly sampled from the same population. Confidence interval
point estimate
summary statistic - one number as an estimate of the population (what we’ve been doing so far). Mean
how to create a confidence interval for a z statistic
- draw a normal curve with the sample mean at the center
- indicate the bounds of the confidence interval on either end of the drawing
- look up the z statistics for the lower and upper ends of the confidence interval in the z table. (always -1.96 and 1.96 for 95% confidence interval)
- convert the z statistics to raw means for each end of the confidence interval (Mlower = -z(σM)+Msample) (Mupper = z(σM)+Msample)
- check your answer; each end of the confidence interval should be exactly the same distance from the sample mean
confidence interval
an interval estimate based on the sample statistic; it includes the population mean a certain percentage of the time if we sample from the same population repeatedly
effect size
shows how much two populations don’t overlap (the further apart, the bigger the effect size)
cohen’s d
measures effect size by assessing the difference between two means using standard deviation. d= (M-u)/σ
meta-analysis
a study that involves the calculation of a mean effect size from the individual effect sizes of many studies (adds statistical power by considering many studies at once. Helps resolve contradictory findings)
file drawer analysis
statistical calculation done 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 power
a measure of the likelihood that we will reject the null hypothesis, given that the null hypothesis is false. Affected most directly by sample size. Between 0.00 and 1.00 (0%-100%). Minimum of 0.80 (80%) probability needed to conduct a study
By increasing statistical power, the probability of making a _____ error is _____
Type II, decreased
As the overlap between distributions being compared decreases, the effect size:
increases
Power can be thought of as the percentage…
of the distribution of means, centered around the sample mean, that falls within the critical cutoff regions, where the null hypothesis can be rejected
A 95 percent confidence interval of (167, 185) is calculated. What is the sample mean?
176
The _____ estimate acknowledges the amount of uncertainty in the _____ estimate by reporting the margin of error
interval; point
standard deviation when estimating from a sample
s = √Σ(X-M)^2/(N-1)
only thing that differs is - 1 in denominator
t distribution size when samples are small
wider and flatter than z distribution
t distribution size when samples are large
closer to z distribution shape
standard error for t statistic
sM=s/√N
s means standard deviation for sample
t statistic
the distance of a sample mean from a population mean in terms of the estimated standard error
t statistic formula
t = (M-μM)\sM
only thing different from a z statistic formula is that you use estimated standard error in denominator
single-sample t test
used to compare data from one sample to a population for which we know the mean but not the standard deviation (ex: comparing the mean of a sample against an expected value)
degrees of freedom
the number of scores that are free to vary when we estimate a population parameter from a sample (df)
degrees of freedom formula
df = N - 1
dot plot
a graph that displays all the data points in a sample, with the range of scores along the x-axis and a dot for each data point above the appropriate value
steps to create a dot plot
1: determine the lowest score and highest score of the sample
2: draw an x-axis and label it, including the values from the lowest through highest scores
3: place a dot above the appropriate value for every score
t distributions
similar to the z distribution, except we must estimate the standard deviation from the sample
we consider ____ instead of N when we assess estimated test statistics against distributions
degrees of freedom
to conduct a single-sample t test, we follow the same six steps of hypothesis testing as the z test, except we estimate the ____ before we calculate standard error
standard deviation from the sample
small effect size for Cohen’s d
0.2
medium effect size for Cohen’s d
0.5
large effect size for Cohen’s d
0.8
paired-samples t test (dependent-samples t test)
compares two mean for a within-groups (every participant is in both samples). Used to analyze the data from many studies. Participants have two scores (one score in each condition) (ex: before and afters)
distribution of mean differences
used for paired-samples t test
order effects
how a participant’s behavior changes when the dependent variable is presented for a second time (also called practice effects). When responses are influenced by the practice of having already completed the tasks once
counterbalancing
minimizes order effects by varying the order of presentation of different levels of the independent variable from one participant to the next
what’s in the center of a paired-samples t test curve?
sample mean difference
In which statistical test do we calculate a difference score for each individual, take the mean of the difference scores, and perform a single-sample t test on them to compare two sample means?
paired-samples t test
For the paired-samples t test, the comparison distribution:
contains means of difference scores
r^2
another measure of effect size (t^2obs / t^2obs + df)
small effect size for r^2
0.01
medium effect size for r^2
0.09
large effect size for r^2
0.25
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
formula for calculating degrees of freedom in an independent-samples t test
dftotal = dfx + dfy
pooled variance
weighted average of the two estimates of variance- one from each sample- that are calculated when conducting an independent-samples t test
To determine the critical values for an independent-samples t test, we need to know the:
total degrees of freedom
independent-samples t test uses
a distribution of differences between means
