Advanced Statistics Test
In class, we discussed two key questions that could be addressed if Moniz had conducted a clinical trial. What are those questions?
How big is the effect? Could it be random chance?
What is the definition of a mean?Your definition should state the most important things to know about a mean.You may answer this question by writing the lyrics to the song.
If you pick someone at random and you want to bet The mean is the score you expect to get
A numerical value based on data from a sample that indicates something about a population.
Inferential Statistics
All of the cases in which a researcher is interested.
Population
The probability of making a correct decision if the null hypothesis is false.
Power
sd(xbar)
Sampling Error Almost perfectly in shape as the sample size increases beyond 30 Smaller as the sample size increases
In the process of computing a standard deviation, Zelda lost one degree of freedom. What did Zelda do that caused her to lose one degree of freedom?
She calculated a mean ********
A word that means: "if the null hypothesis is true, then the results from the sample are extremely unusual.
Significant
The general term for a numerical value based on data from a sample (that may indicate something about the sample or something about the population).
Statistic
Covariance Equation
Sum(x-xbar)(y-ybar) / n-1 CAN BE NEGATIVE
What is the definition of the standard deviation?Your definition should state the most important things to know about a standard deviation.You may answer this question by writing the lyrics to the song.
The Standard Deviation is used to measure things Its how far the average person strays from the mean
What is xi? What value is x hat equal to? What is ei? What is the mean of ei? What commonly calculated statistic is essentially the mean of | ei |
The score on x for case i the mean how much case i deviates from the mean zero standard deviation
Draw Pictures that illustrate d-statistic effect sizes of 1, .8, .6, .4, .2
- Draw Bell Shaped Curve - Mark off and # the sd units - Draw a line for the mean of the treatment group - Draw the curve for the treatment group - Label the means and direction of the outcome variable - Write the d-stat value, and indicate effect size - Finally writ the percent in the tail (round to nearest 10%) --- % thats still under the untreated mean (% / .5)
The association between clinician confidence and accuracy - 120.What is the name of the statistic? - 121.What is the value of the effect size?
Correlation .1
The association between parenting and child delinquency - 134.What is the name of the statistic? - 135.What is the value of the effect size?
Correlation .2
The association between therapeutic alliance and psychotherapy outcome - 118.What is the name of the statistic? - 119.What is the value of the effect size?
Correlation .3
The association between marriage quality and life well-being - 130.What is the name of the statistic? - 131.What is the value of the effect size?
Correlation .4
The association between self-compassion and (lack of) psychopathology - 124.What is the name of the statistic? - 125.What is the value of the effect size?
Correlation .5
Study where scores for all the variables are determined by assessment and there are NO manipulated variables.
Correlational Research
The effectiveness of cognitive therapy for treating depression - 116.What is the name of the statistic? - 117.What is the value of the effect size?
D - Stat .8
The effectiveness of behavioral couple therapy for treating relationship distress - 132.What is the name of the statistic? - 133.What is the value of the effect size?
D-Stat .6
The effectiveness of cognitive behavior therapy with motivational interviewing for treating alcohol use disorder - 128.What is the name of the statistic? - 129.What is the value of the effect size?
D-Statistic .2
The effectiveness of dialectical behavior therapy for treating borderline personality disorder - 122.What is the name of the statistic? - 123.What is the value of the effect size?
D-Statistic .4
The effectiveness of prolonged exposure for treating post-traumatic stress disorder - 126.What is the name of the statistic? - 127.What is the value of the effect size?
D-Statistic 1.0
A numerical value based on data from a sample that indicates something about the sample.
Descriptive Statistics
What is a limitation of Correlational research
Determining Cause
The average of all the values for a population of values from which a single value can be randomly sampled.
Expected Value
Study that has at least one variable with scores determined by an assessment, and at least one manipulated variable produced by the researcher forcing cases into groups.
Experimental Research
What is a limitation of experimental research?
Explaining Natural Phenomena (As an experiment is not the natural world
Estimating x hat and e(i)
Find mean mean = x hat e(i) how far score is from mean (can be positive or negative)
Computing a Correlation
Find sd1, find sd2 (from ss and variance) Find covariance Compute Correlation
Find D-Statistic
Find sum of squares for two groups - Find total degrees of freedom - Find Pooled SD - Find d-statistic
58.What is depicted by this row of numbers (-4, -3, -2, etc.)? 59.What is depicted by this row of numbers (10, 20, 30, etc.)? 60.What is depicted by this double headed arrow? 61.What is depicted by this long vertical line (crossing the numbers 0, 50, 72, 44) 62.What is depicted by this row of numbers (0, 10, 20, etc?) 63.What is depicted by this row of numbers?(0, 0, 1, 1, 8, etc.)?
Z-Scores at top T-Scores 2nd from top Standard Deviation between z scores the mean Unstandardized Raw Scores Percentiles
The probability of committing a type I error if the null hypothesis is false.
Zero
How does decreasing the sample size change the shape of the t-distribution?
The t-distribution will become flatter
Size of Correlation
Trivial = Less than .1 Small = Greater or equal to .1 Medium = Greater than or equal to .3 Large = Greater than or equal to .5
Effect sizes
Trivial = Less than .2 Small = greater than or equal to .2 Medium = greater than or equal to .5 Large = greater than or equal to .8
A person's average score on a test if he or she were assessed an infinite number of times.
True Score
sd^2 - sd^2(measure)
True Variance True Variance = Total Variance - Measurement Error variance
The extent to which a scale measures what it is supposed to measure.
Validity
Given SD find Variance and sum of squares
Variance = sd^2 Sum of squares = Variance x (n-1)
The term used when the expected value is not equal to the parameter.
Bias
The set of cases from which a researcher collects data.
Sample
Distributions Chart --- Standard Deviation --- Standard Error of Measure --- Standard Error of Estimate --- Standard error of the mean, the correlation, mean difference, beta (Sampling Error)
--- Pertains to observations of a single case and deviations around a sample mean --- Pertains to observations of a single case and deviations around a true score --- pertains to observations of different cases and deviations around a predicted value --- pertains to observations of different samples and deviations around a population parameter
(sd^2 true)/ sd^2
---Reliability ---True Variance/Total Variance Estimated by --- Chronbach's Alpha --- correlation between 2 alternate forms --- A test retest correlation
Z Score Chart - Finds amount below z-score --- % higher --- % lower --- % more extreme
1. 1 - z score chart 2. z - score chart 3. (z-chart x 2)
Memorized area under Curve Questions --- % of cases falls between mean and score 1 sd --- % of cases between 1 sd and 2 sd --- % of cases above 2 sd
1. 34% 2. 14% 3. 2%
In significance testing, what determines the probability of committing a type II error if the null hypothesis is false?
Beta
The probability of committing a type II error if the null hypothesis is false.
Beta
A standard error of measure indicates the typical magnitude of [101]__________ from the linear equation [102]__________, where the subscripts [103]__________ .
101. e(ai) 102. x(ai) = true(i) + e(ai) 103. a and i stands for assessment occasion and individual
A standard error of a mean difference indicates the typical magnitude of [104]__________ from the linear equation [105]__________, where the subscripts [106]__________ .
104. e(sp) 105. (ybar - ybar) = (mew - mew)(p) + e(sp) 106. s and p stand for sample and population
A standard error of estimate indicates the typical magnitude of [107]__________ from the linear equation [108]__________, where the subscripts [109]__________ .
107. e(is) 108. y = (prediction(s), based on x(is)) + e(is) 109. i and s stand for individual and sample
A standard error of the correlation indicates the typical magnitude of [110]__________ from the linear equation [111]__________, where the subscripts [112]__________ .
110. e(sp) 111. r(sp) = p(p) + e(sp) 112. s and p stand for sample and population
A standard error of a mean indicates the typical magnitude of [113]__________ from the linear equation [114]__________, where the subscripts [115]__________ .
113. e(sp) 114. xbar(sp) = mew(sp) + e(sp) 115. s and p stand for sample and population
A standard deviation indicates the typical magnitude of [98]__________ from the linear equation [99]__________, where the subscripts [100]__________ .
98. e(is) 99. x(is) = xbar(s) + e(is) 100. i and s stand for individual and sample
The probability of committing a type I error if the null hypothesis is true.
Alpha
Recognizing Effect Sizes
Be able to get a good estimate of a d-statistic and a correlation
Compute Mean, Sum of Squares, Variance, and SD from list of #'s
Mean = Sum(x)/n Sum of Square = Sum(x - xbar)^2 Variance = ss/n-1 sd = Square root (Variance)
You use a linear model in R to estimate the mean and standard deviation for a variable called "CSI and you get the output listed below. Based on this output, what is the mean and the standard deviation of CSI?
Mean = Under Estimate SD = Standard Error at bottom
The assumption that the population parameter for a statistic is equal to zero.
Null Hypothesis
A numerical value based on data from all the cases in a population that describes something about the population.
Parameter
The same amount of something always produces the same assessed numerical value regardless of when or how it is assessed.
Reliability
What are the lyrics for the d-statistic song? What are the lyrics for the variance and covariance song? What are the lyrics for the standard error of estimate song? What are the lyrics for the standard error of measure song? What are the lyrics for the standard error of a statistic song? What are the lyrics fort-value song? What are the lyrics for significance song?
a d-stat says how far two means are split measured by a standard deviation unit the standard error of estimate tell me what its for Got people in a sample and you guess their score Its your typical mistake, no less no more If you test me many times My scores will change and stray from true The standard error of estimate says just how far they do How much change do you typically find When a study is repeated many times Each statistic we declare will have it's own standard error A t-value is always where you divide a statistic by its standard error When the p is less than o-five i call it significant because i derive the sample was big enough to make me a hero and now i claim the effect is not 0
Visually estimate SD
about half way down is 1 sd
Bruno computed a standard deviation, but he accidentally used "n" rather than the degrees of freedom in his formula. This means that the value he obtains will be ____________________ .
biased *******
An effect size that is typically used when one variable is dichotomous
d
sd(est)
estimation error becomes smaller as effect size increases
Two distributions of sampling error that are skewed in shape.
f and X^2
An effect size that is typically used with two numerically scales variables.
r
Correlation Equation
r = COVxy / sdx x sdy
Write the formula for a standard deviation.
sd = Square root ( (sum(x - xbar)^2) / n-1 )
Pooled Standard Deviation
sqroot( (ss1 + ss2) / (df1 + df2) )
sd x sqroot(1-reliability)
standard error of measure
A distribution of sampling error that is almost normal in shape
t
What is the t-value? 92.In the t-statistic formula, what is the assumed value for the population parameter? 93.Given the assumed value for the population parameter, what is the value that indicates the amount of sampling error that was made in this study? 94.If this study were repeated over and over, what is the typical amount of sampling error that would be made in each study? 95.Given the assumed value for the population parameter, the error in this study is equal to the typical error times what value? 96.One component of the t-formula is something that is calculated from the sample, and if we knew the true population parameter for this, there would be no reason for doing the t-test. In the above example, what is this value? 97.Another component of the t-formula is something that is calculated from the sample, and if we knew the true population parameter for this, the distribution would change from a t-distribution to a z-distribution. In the above example, what is this value?
t = stat / sd(statistic) population parameter = 0 The Statistic sd(stat) t value statistic sd(stat
In significance testing, what determines the probability of committing a type I error if the null hypothesis is true?
the alpha
How does increasing the sample size change the shape of the t-distribution?
the t distribution will become more normal
Covariance Will be as large as possible Covariance will be as negative as possible Covariance will equal zero when Cannot be larger than Will equal the averaged variance when
there is a perfect positive correlation you have a perfect negative correlation you have a 0 correlation the average variance between the 2 variables you have a perfect positive correlation
d - statistic
xbar 1 - xbar2 / sd pooled
Z Score given mean and score
z = x - xbar / sd
