Final Flashcards
In responding to the rating scale, one teenager circled 6 and another teenager circled 3. Would it be correct to say that one teenager watched twice as much of the reality shows?
No, because the measurement is not ratio
If you remove an outlier what would happen to the standard deviation?
Standard deviation would decrease
For the scores in the distribution s=9.5. Interpret this statistic
On average, scores are 9.5 points from the mean.
No need to say above/below because standard deviation is always positive (values are derived from squaring something)
Which one of these cases represent a reason where you would prefer to use the standard deviation instead of the range?
You prefer to use a measure that mathematically takes into account all numbers in the sample
If a distribution has no mode, the standard deviation would be?
None of the above (you have no idea what the standard deviation would be)
If you wish to decrease the likelihood of committing a Type 1 error, what could you do?
Decrease alpha
Researchers measure two variables, and they report that r=.40. For this correlation, they also report that p=.03. What does this tell you about the correlation?
The likelihood of the correlation occurring by chance is 3%
If we incorrectly fair to reject the null hypothesis, we have committed a
Type 2 error
What is the main difference between an independent groups t test and a one-way ANOVA?
The number of groupes
The researcher measured the variables, calculated and reported r(4)=.27. Comparing this result to the sampling distribution for a two-tailed test. Which of the following is true?
p>.05 The correlation has a high likelihood of occurring by chance
Imagine that a researcher proposed collecting data from a sample of 42 individuals and calculating a correlation coefficient to describe how 2 variables are related. She will then want to know the likelihood that the correlation occurred by chance. Determine the critical values for evaluating a correlation coefficient from a sample size N=42
-.304 and +.304
The average difference between the value of the population parameter and values of the samples statistic from multiple samples is called
Standard error
Scores are normally distributed mew=20 and pie=2. Determine the probability of getting a score between the mean and 25
.4938
The phrase statistically significant indicates that a research result
Has a low probability of occurring by chance
Comparing sampling error to standard error is analogous to comparing
One difference to the average of many differences
Why and when do we include an effect size in our conclusion?
An effect size tells us about the magnitude of the effect if there is a statistically significant test statistic
Se=2.15
The average error in predictions of Y is 2.15 points. Given that the range of Y is 2 to 7, this is a large amount of error
“The Roles of Combat Exposure, Personal Vulnerability, and Involvement in Harm to Civilians or Prisoners in Vietnam-War-Related PTSD”
Which variable is the dependent variable
PTSD
In the research cited in the previous item, combat exposure was determined using the military-historical measure. This measure consists of 4 categories of probably severity of exposure: very high, high, moderate, and low. In this measure discrete or continuous?
Discrete
This measure consists of 4 categories of probably severity of exposure: very high, high, moderate, and low. What is the scale of measurement?
Ordinal
What is the term for the low probability area of a sampling distribution?
Critical region
What does it mean to say that a research result has a high probability?
It has a high likelihood of occurring by chance
What does it mean when we report that a correlation is not significant?
The correlation is between -0.1 and +0.1
Which of the following studies will have the highest power?
The effect size is medium, and the study has N=350
Another name for the critical region of a sampling distribution is the rejection region. Why is this an appropriate term for the critical region?
Because the null hypothesis is rejected in the research result is in the critical region
What is the total number of variables in a two-way ANOVA?
3 (2 IV, 1 DV)
When group sizes are equivalent, how do you calculate marginal means?
Calculate the mean of the group means
Formula for z score from raw score
X-M/s
Report the z score of -.125
.125 points below the mean
Formula for raw score from z score
x=M+zs
Normal distribution rule
68-95-99.7
Scatterplot set up
IV on x axis
DV on y axis
Direction of scatterplot relationships
Positive: high scores on x associated with high scores on the y, low scores on x associated with low scores on y
Negative: high scores on x are associated with low scores on y (inversely proportional)
Correlation coefficient
Statistical measure of the relationship between 2 variables. Pearson r correlation measures the degree and direction of linear relationships
Descriptive statistics. Does not tell you why the variables go together.
r values and meanings
Not significant/No relationship: between -.1 and .1
Weak: +-.30
Interpret a correlation coefficient of optimism and depression r=-.70
There is a strong negative correlation between optimism and depression. People who are more optimistic tend to be less depressed.
Negative: There is a (strength) (direction) relationship between (IV) and (DV). As (IV) increases, (DV) decreases
Positive: There is a (strength) (direction) relationship between (IV) and (DV). As (IV) increases, (DV) also increases
Coefficient of determination r2/proportion of variance
Tells how much variability can be explained by its relationship with its other variable
(r2 value) of the variance in (DV) is explained by (IV)
Interpret the proportion of variance value of parental involvement and children’s school achievement, r2=.05
5% of the variance in children’s school achievement is explained by parental involvement.
Coefficient of non-determination 1-r2
95% of the variance in children’s school achievement is not explained by parental involvement
Additional uses of correlation
Validity (does it measure what it’s supposed to measure), reliability (consistency of measurement), prediction (if 2 variables are related, we can use the data to create a model to predict the value of one variable for the other variable)
Regression
Statistical technique for determining the best-fitting straight line for a set of data (Scatterplot)
Regression line equation
Yhat=bX +a
Yhat=predicted value of Y (DV) score
X=known value of X (IV) score
b=slope of regression line, tells how shallow or steep the slop is and is the predicted change in the DV variable given a one-unit increase in the IV
a=predicted value of the DV given a value of 0 on the IV
Regression example: To predict children’s vocab score from quality of care, a=10
If quality of care is 0, then we predict a vocab score of 10
Write the regression equation
Regression model to predict final exam score (scale 0-50) from average quiz score.
b=19.71 a=-15.41
Yhat=19.71X-15.41
Yhat=predicted final exam score
X=known average quiz score
Standard error if the estimate (Se)
Avg amt of error in the predictions. Mean of all the errors, doesn’t tell exactly how much error there will be in a single prediction
Small <10%
Moderate 10-29.99%
Large >30%
Interpretation of Se
The average error in predictions of (DV) is (#) points. Given the range of (DV) scores, this seems like a (S,M,L) amount of error.
Interpret the Se score of 3.52 used to predict depression from optimism. Depression range is 3-18
The average error in predictions of depression is 3.52 points. Given the range of depression scores, this seems like a moderate amount of error.
Se/range of DV
3.52/15=23.47
Beta and multiple regression
Standardized regression coefficient. Indicates the predicted change in the DV in std deviation units. Beta values can be + or - but interpretation focuses on its magnitude, no sign.
X3 contributes the most to the prediction of Y. X2 is less important, and the beta value of X1 is so close to zero that it contributes little, if anything, to the prediction of Y.
R
multiple correlation coefficient. Correlation between DV and all the IVs taken together
R2
Proportion of variance in the DV that is explained by the set of IVs included in the multiple regression.
(R2) value of the variance in (DV) is explained by the set of IVs
Probability
The likelihood of an outcome occurring by chance. Reported as proportions, p
Interpretation of p value
The likelihood that (name of statistic) occurred by chance is (p value)
Interpret the p value
r=-.23, p
The likelihood that the correlation occurred by chance is less than 4%
2 assumptions of probability
Random sampling: each individual in the population has an equal chance of being selected
Sampling with replacement: each individual in the sample is returned to the population; keeps probabilities constant across sampling
What are the steps to solve this? what is the probability of randomly selecting a score above 43? M=40 and s=3
1) Draw out distribution
2) Calculate z score and put it on the drawing
3) Use std deviation table to find p value
4) Column C to find above/below. Column B to find a score BETWEEN 2 numbers
If proportion of the distribution includes the mean and tails, use 1-p
Low probability
IF you chose a value at random, you would NOT expect it to be from this region
High probability
Corresponds to a large proportion of the distribution, usually .95 or more. If you chose a value at random, you would expect it to be from this region almost all the time. Most typical scores in the distribution
Sampling distribution
Used to determine the likelihood of a value of the statistic occurring by chance alone. Used to determine probability.
Expected value
Mean of all values of the sample statistics. um=u
Sampling error
For a single sample, the difference between the sample statistic and the population parameter
Standard error
The average difference between values of the sample statistic and the value of the population parameter
As n increases, standard error decreases. The bigger the sample, the more accurately the sample mean represents the population mean
Central limit theorum
As sample size n increases, the sampling distribution of sample means will approach a normal distribution
Using the sampling distribution r to determine probability of r steps
1) Calc degrees of freedom (n-2)
2) Look up that number in the r table, look under .05
3) That number is the CV. Mark it off in the sampling distribution
4) Indicate where r falls in
5) p>alpha or p
2 interpretations of the sample result (hypothesis testing)
1) The result is due to chance/error
2) The result is not due to chance. The sample accurately reflects what is really happening in the population
Inferential stats allows us to evaluate these 2 possibilities. In order to do this, we must use probability and hypothesis testing
2 types of hypothesis
H0: There is no effect, no relationship, no difference, nothing real in the population. IV does not affect DV. parameter=0
H1: There is an affect. IV affects DV. parameter not equal to 0
p (rho) vs u (mu)
p is used for population correlation while r is used for sample correlation
H0: p=0
mu is used for population MEAN while M is used for sample mean
H1: u1-u2=0
Steps in hypothesis testing
1) State the hypothesis. State the null and alternative in words and in parameter notation
2) Set alpha to define low probability
3) Use table (collect data compute/sample statistics)
4) Determine p. Draw and label sampling distribution and evaluate if r is in the high/low probability area
5) Make a decision about the null hypothesis. If p<a>alpha, fail to reject H0. This means the probability of obtaining the sample result by chance is so high that we conclude that is due to chance
Conclusion after step 5) There is a significant relationship between sleep quality and anxiety, r(28)=-.44,p</a>
Statistical significance
When the null hypothesis is reject, findings are said to be statistically significant.
Statistically significant - low probability of the results occurring by chance alone
Errors in hypothesis testing
Type I Error: false positive. H0 is true but we decide to reject (H0 is false). Concluding there is an effect when there is no effect in reality. Incorrect rejection of the null hypothesis.
Type II Error: false negative. H0 is not true but we decide to fail to reject (H0 is true). Concluding there is no effect when there is a real effect. Incorrect acceptance of the null hypothesis
Power (null hypothesis significance testing)
The likelihood of correctly detecting a real effect(correct rejection of null). The likelihood of getting a statistically significant result
Power increases as sample size and effect size increases
With a large enough sample, even a very small effect will be statistically significant
Effect size (null hypothesis significance testing)
A measure of the magnitude of the research result. How big is it? If r is a significant value, then we calculate r2
Estimation
Inferential technique used to sample statistic to estimate the value of a population parameter
2 types of estimates
1) Point estimate: value of the sample statistic is used to estimate the population parameter. Ex: mean
2) Interval estimate: range of values used to estimate the population parameter. Confidence intervals; start with the point estimate and include a margin of error
Confidence
The probability that the interval contains the true value of the parameter; the percentage of confidence intervals that include a value that matches the population parameter
Confidence levels and corresponding z values
Confidence level 95, z=1.96
99, z=2.58
Formation for reporting a confidence interval
__% CI [LL,UL]
Ex: Average American watches 5 hours of TV per day, 95% CI [4.55,5.45]
There is a 95% probability that the interval contains the value of the population mean. We are 95% confident that one of the values in the interval matches the value of the population mean
Calculating CI
M+-z(s/sqrtn)
What affects the width of a confidence interval of the mean?
As confidence level increases, width increases.
As standard deviation increases, width increases.
As sample size increases, confidence interval width decreases.
Narrower interval is more precise, wider interval is less precise
Evaluate a mean difference
Mean difference = 0 indicates no difference
If the CI includes the value of 0, we conclude that the mean difference is not significantly different from 0. No difference in the population
If the CI does not include 0, then we conclude the mean difference is significantly different from 0. There is a real difference in the population
Compare group means
CI overlap then the comparison is inconclusive and t-tests will need to be done
CI don not overlap, conclude that there is a significant difference between group means. The means are statistically different.
t-test
Used when the DV is continuous and the sample result consists of one or two means
Types of t-test
Related samples: repeated measures (within-subjects) and matched-subjects
Independent samples: used to determine if means from2 unrelated groups are significantly different. Between subjects
t
Little overlap = large absolute val of t. groups are different from each other
More overlap = smaller abs value of t
t depends on variability
Equation for independent and related samples t-test
Independent: M1-M2/SE
Dependent: Md/SE
Hypothesis testing with t-test steps
1) State hypothesis. Independent groups: u1=u2
Related groups: H0:uD=0
2) Set alpha
3) Compute t with formulas
4) Determine probability of t by drawing distribution, CR, CV, mark off t. df for independent: n1+n2-2
5) p>alpha or p
Calculate r2 after a significant t-test equation
t2/t2+df
interpreting r2 effect size values
r>.10 Weak r2>.01 small
r>.30 Moderate r2>.09 medium
r>.50 Strong r2>.25 Large
r>.70 Very strong r>.49 very large
r2=(-2.11)^2/(-2.11)^2+20=.18
18% of the variance in mood is explained by food. This is a medium effect size.
ANOVA
2 IV, 1 DV. Hypothesis test used to evaluate mean differences between 2+ groups
2 sources of variance (ANOVA)
Between groups variance: differences between group means. caused by the IV plus some error
Within groups variance: spread or dispersion os scores within each group. Caused by error
F statistic
F=betweengroupcariance/withingroupariance
Small F value = less statistically significant
Large F value = more statistically significant difference
Computing F
F= MSbetween/within
Between group variance df: number of groups-1=k-1
Within group variance df: total number of scores - number of groups = N-k
ANOVA summary table
Source: Between, Within, Total
SS: SSbetween, SSwithin, SStotal=add those 2
SS between/ SSwithin=MS between
MSbetween/MSwithin=F
Post-hoc tests
Pairwise comparisons made after finding that F is significant (H0 rejected). Used to determine which pairs of means are significantly different. Control the overall probability of Type I error and protect against alpha inflation
Effect size for ANOVA
n2 eta squared = SSbetween/SStotal. Proportion of variance in the DV that is accounted for by the IV.
Ex: 47% of the variance in depression scores is accounted for by treatment
How to report ANOVA results
Complete sentence states the conclusion in words followed by the notation for the test statistic, df, and probability. IF significant, include eta squared (Effect size)
Treatment had a significant effect on depression, F (3,16)=4.68,p
Step 1 state hypothesis for ANOVA
H0: u1=u2
H1: Not all u’s are equal
