PSY 203 Exam 2

Steps to finding Linear Regression

1. Compute r 2. Compute slope 3. Compute Y intercept 4. Substitute values into linear regression equation 5. Plot the regression line

Significance Test for Pearson r/ Assumptions

1. Random sample of X-Y pairs and that each variable is an interval or ratio variable 2. Y scores and X scores represent a normal distribution and they represent a bivariate normal distribution 3. the null hypothesis states that the population correlation is 0 -otherwise we use a different procedure

How to calculate the single sample t test

Compute estimated standard deviation (Sx) Compute the estimated standard error of the mean (Sx bar) Compute tobt

Computing the independent sample t-test

Compute estimated variance/ pooled variance Compute estimated standard error (standard error of the difference) Compute tobt

Strength and Effect size for dependent t test

Compute rpb (assign value based on study) then r2 effect size: - .10 - .29 = Small effect - .30 - .49 = Medium effect - .50 - 1.0 - Large effect

Predictor Variable (LR)

Use X to predict Y like in the SAT (score predicts how well they will do in college)

Powerful studies

We seek a powerful design that produces likely to be significant data maximizes the difference between means through strong manipulation It eliminates extraneous variables that will minimize differences between groups

Finished linear regression equation that describes the regression line

Y'= 1.44(X)+ 1.47 - numbers can change but needs Y' and X to plot the line sub in values of X to find Y'

Linear Regression Equation

Y'= bX + a b= slope (indicates how slated the line is and what direction the slant is)- no relationship is a horizontal line, positive linear relationship= positive slope, and negative linear relationship= negative slope a= y intercept (value of Y at the point where the regression line intercepts or crosses the Y axis) X= given X value This equation produces the value of Y' at each X and thus defines the straight line The slope and intercept describe how starting at a particular value, the Y scores change as the X changes

t-tables interpolation procedure for single sample t-test

You will not find a critical value for every df between 1 and 120 1. Examine the critical values for df above and below the df of your sample Ex: 1 tailed test, a=.05, df=49 -tcrit (df=40)= +1.684; tcrit (df=60)=+1.671 if both FTR or R you know will be that because its in the middle if not do the steps to get it

Y intercept for linear regression

a= Y bar- (b)(X bar)

Independent t-test

also known as between group/ subjects, independent groups

Dependent t test

also known as dependent groups, repeated groups, matched samples, and related samples

Making decisions for probability

any sample may poorly represent one population and accurately represent another population Based on probability- (can also look at frequency- more frequent more likely to occur and represent the population and vise versa) Whether the sample represents the population: - if the sample is likely to occur when the population is sampled then the sample represents the population -If the sample is unlikely to occur when the population is sampled then the sample does not represent the population

Errors in Probability

anytime we reject a sample we may be wrong anytime we retain/fail to reject a sample we may be wrong but errors are not likely because the decision making is based on probability

b (slope for linear regression)

b= N (∑XY) - (∑X/ (∑Y)N(∑X2) -(∑X)2

logic of hypothesis testing

getting a number can be be produced by sampling error (Ho; nothing happened) or real relationship in nature (Ha; something happened) Unless everyone undergoes the testing we will never know if it actually works so we can never prove null and we can determine likelihood based on probability

Interpretations of z test

if the zobt lies in the ROR then it is unlikely to occur due to chance or sampling error so you reject Ho; results are significant If the data is significant then it implies that the relationship found in the study represents a real relationship found it nature (reject Ho); p< .05 If the data is nonsignificant it implies that the relationship is likely to have occurred by chance without there being a relationship in nature; we failed to reject Ho; p>.05

Inferential Statistics

tells us what we could expect to find if we could perform a study on the entire population These bets have a high probability of being correct (probability and how we make statistical decisions) Take sample data and apply it to the population- it reflects the population

Statistical Notation for Single Sample t-Test

tobt tcrit Estimated population variance- s2x = ΣX2 - ((ΣX)2/ N)/ N-1 Estimated population standard deviation square root of the variance above

Probability

used to describe random chance events Based on how often the event occurs over the long run Population of events= all possible events that can occur in a given situation Probability of an event= the event's relative frequency in the population A probability can never be less than 0 or greater than one Probabilities of all events must add up to one

One tailed test for probability

we can place the entire region of rejection in only one tail of the distributions only testing if mean is too far above OR too far below the population mean but not both Criterion is .05 and the critical value from the z-tables is either +1.64 or -1.64

Pooled variance/ estimated variance for independent t test

weighted average of the sample variances formula: S2pool = (n1 - 1)s21 + (n2 - 1)s22/ (n1 - 1) + (n2 - 1) produces the estimated variance of any of the populations of recall scores represented by our samples

When are dependent sample t test preformed

when an experiment involves 2 conditions or matched groups or repeated design with dependent samples, the probability that a particular score will occur in one sample is influenced by the pair score in the other sample

Confidence interval for the difference between Ms

- Describes a range of differences between 2 μs, anyone of which is likely to be represented by the difference between our 2 sample means - Conclusion: we are 95% confident that the difference hypnosis makes is, on average, between .91 and 5.09 correct answers *specific problem

Does the sample data represent a particular raw score population (probability)

1. Create a sampling distribution from raw score population we think the sample might represent 2. select the criterion probability (ex: .05) 3. Determine the critical value (ex: +- 1.96) 4. Compute a z-score for the sample mean 5, make a decision based on where the z score falls -reject or fail to reject the sample mean as being representative

Summary of hypothesis testing/ steps of hypothesis testing

1. Create the statistical hypotheses; Ho and Ha 2. Select appropriate parametric or nonparametric procedure 3. Select the value of a 4. Collect data and compute obtained value of the inferential statistic 5. Set up the sampling distribution; one or two tailed and determine critical value 6. Compare obtained value to critical value 7. Interpretations- reject Ho results are significant; fail to reject Ho results are nonsignificant

Assumptions for Linear regression

1. Homoscedasticity - Y scores should be equally spread out around Y' (predicted scores) and the regression line throughout the relationship (Sy' will accurately describe the spread and predict the error in prediction)- this is always assumed - Heteroscedasticity (spread is not equal throughout relationship) 2. Y scores at each X represent an approximately normal distribution (68% of all scores fall between +- SD from the mean; 68% of all Y scores will be between +_ Sy' (Standard error of the estimate ) from the regression line)

Summary of Testing a CC

1. Make sure your study meets the assumptions of r, rs, or rpb 2. Create either a two tailed or one tailed Ho and Ha 3. Compute the CC from the sample data (robt) 4. Obtain rcrit 5. if robt is beyond rcrit then reject ho and results are significant 6. if robt is not beyond rcrit then it fails to reject Ho and results are not significant 7. For significant results compute coefficient of determination and perform linear regression

Significance Testing for rpb/ Assumptions

1. Random sample of X-Y pairs and that each variable is an interval or ratio variable 2. Y scores and X scores represent a normal distribution and they represent a bivariate normal distribution 3. the null hypothesis states that the population correlation is 0 -otherwise we use a different procedure Those were same as r but rpb also has 4. assumes a random sample of pairs of scores where one score is from a dichotomous variable and one is from an interval or ratio variable df= N-2

Significance Testing for rs/ assumptions

1. Random sample of X-Y pairs and that each variable is an interval or ratio variable 2. Y scores and X scores represent a normal distribution and they represent a bivariate normal distribution 3. the null hypothesis states that the population correlation is 0 -otherwise we use a different procedure Those were the same as r but rs also has 4. assumes a random sample of pairs of rank-ordered scores df=N-2

Factors affecting probability

1. Sampling with replacement -previously selected samples are placed back into the population before drawing again -Ex: deck of cards; the population is always 52 2. Sampling without replacement -we do not replace any previously selected samples before drawing again Ex: deck of cards; population is 52, then 51, etc. -with fewer possible outcomes the probability is larger on the second draw and so on

Statistical Notation for Hypothesis Testing/ the z test

> greater than < less than >- Greater than or equal to <- Less than or equal to ≠ Not equal to

Creating probability distributions

Consists of the relative frequency of every event in a population 1. Empirical Probability distribution -observe a random sample to represent the population -Ex: observe Dr. Smith for 18 days; he is cranky on 6 of the them; relative f of Dr. Smith's crankiness is 6/18 or .33 - so what is the probability of him being cranky today: .33 -probability of him not being cranky today: .67 2. Theoretical Probability Distribution -don't need to observe because it is something we already know -model of the rel f of events in the population -Ex: tossing a coin; rel f of heads is .50 and rel f of tails is .50

Significance tests for correlation coefficients for single sample t test

Correlation study is another type of single sample study Ex: examine the relationship between a man's age and his housekeeping abilities r=-.45, does this describe the relationship in the population too? we need to determine if this is significant -Value doesn't say if it is statistically proven so we have to run a test Recall the parameter for a CC= p (rho)

How do you control for order effects for dependent t tests

Counterbalance half of the RPs perform condition 1 then condition 2 while the other half performs condition 2 then condition 1 this way every variable has the opportunity to experience all three effects.

Dependent t test assumptions

DV involves ratio or interval scale Normally distributed data raw score populations represented by data have homogenous variance N in the 2 conditions much be equal Must involve dependent samples

Critical Value for probability

Defines the value required for a sample to fall into the region of rejection -determined by criterion probability -look up corresponding z from the z tables -.025 probability = z of +-1.96 for two tailed test or .05 probability = z of +- 1.64 for one tailed test -ROR begins at +-1.96 or +- 1.64 thus that is the critical vale Decisions: -If the absolute value of our sample z-score is larger than the critical value then we reject it (there is significance) -if the absolute value of our sample z-score is smaller or equal to the critical value, then we retain/ fail to reject it

How to compute the confidence interval for single sample t test

Formula: (sx)(-tcrit) + X < μ < (sx)(+tcrit) + X μ: unknown value represented by sample mean X: computed from sample data sx: computed from sample data tcrit: 2-tailed tcrit at α for our df ** Always use 2-tailed critical values even if you performed a 1-tailed hypothesis test

Computing probability

Formula: P(event)= number of outcomes that stratify the event/ total number of possible outcomes Ex: drawing a king from a deck of cards 4 kings in deck so 4/52= .076

Statistical Hypotheses

Ha : μ1 - μ2 ≠ 0 -We expect the conditions to differ, thus sample means and the corresponding μs they represent should differ as well Ho : μ1 - μ2 = 0 -There is no difference between conditions, thus both sample means represent the same population of scores

Statistical hypotheses for a Correlation Coefficient

Ho: p=0 -implies predicted relationship does not exist Ha: P=/0 -implies that r represent a real relationship in the population One tailed- Positive correlation Ho: ρ <- 0 Ha: ρ > 0 One tailed- Negative Correlation Ho: ρ >- 0 Ha: ρ < 0

Which design do you chose for dependent t test

How many RP variables must be controlled? if numerous do repeated measures design if only a few then - identify the most serious variable and control it by matching -balance most important variables and/or limit population and use a between subject design

Statistical notation for probability

Odds are expressed as fractions or ratios Ex: the odds of wining are 1 in 2 Chances are expressed as a percentage Ex: there is a 50% chance of winning Probability is expressed as a decimal (symbol= p; p(A)= probability of event A) Ex: the probability of winning is .50

Describing the strength using rpb

Only compute rpb when your results are significant Formula: rpb = √ (tobt )2/(tobt )2 + df *square root the entire formula You must decide whether rpb is positive or negative based on the data

Understanding the single sample t-test

Parametric procedure used to test the null hypothesis for a single sample experiment when the standard deviation of the population must be estimated Assumptions -one random sample of interval or ratio scores -raw score population forms a normal distribution -SD of raw score population is unknown and so will be estimated

Categories of inferential statistics

Parametric statistics- procedures that require certain assumptions about the raw score population- strict assumptions -Assumptions: population of dependent scores forms a normal distribution and scores are interval or ratio scores Nonparametric statistics- procedures that do NOT require assumptions about the raw score population, used with nominal or ordinal dependent scores, and used with skewed distributions of interval or ratio scores- no strict assumptions: uses nominal and ordinal data and skewed data Purpose: for deciding whether the data reflect a relationship found in nature or whether sampling error is misleading us

Experimental Hypotheses for inferential statistics

Predict the outcome we may or may not find if the hypotheses predict a relationship, but no direction for change in DV then it is a two tailed if the hypotheses predict a relationship and there is a direction of change in DV, then it is a one tailed test- look at the alternate for which tail (Takes pill for IQ and when they take it the researchers think IQ will decrease so it is in the left tail)

Y' (Y prime)

Predicted Y score - best prediction of a Y score at a given X Summary of Y scores for an X based on the entire linear relationship formed across all X-Y pairs Value of Y falling on the regression line

Z-test (inferential statistics)

Procedure for computing a z-score for a sample mean on the sampling distribution of means Assumptions: -Random sample of scores -DV is approximately normally distributed -We know M and population SD (σx) Set up the sampling distribution by 1. choosing alpha (criterion); symbol= a; usually .05 2. locate region of rejection; one or two tailed 3. determine the critical value (zcrit); z-score that marks the region of rejection

Proportion of Variance- linear regression

Quantitatively evaluates the usefulness or importance of a relationship Coefficient of Determination: -changes in X and changes in Y that are correlated - Other names: good variance/ variance accounted for/ non-error movement- want variance accounted for higher than variance not accounted for -proportion of variance accounted for = r2 -proportional improvement in accuracy when using the relationship of X to predict Y instead of using Y to predict y -Proportion of variance in sample that is nor error variance -Reflects differences in Y that are correlated to changes in X Coefficient of Alienation: -Other names- bad variance/ error variance/ movement that is not correlated - Y moves but X doesn't -Proportion of variance not accounted for = 1-r2 - Proportion of total error remaining -Reflects differences in Y that occur when X does NOT change Good variance and error variance should equal 0

Making decisions about a sample mean for probability/ Steps

Random sample of SAT scores from TCNJ with an X bar (mean of random sample)= 550 and M= 500 (population mean) Is the sample representative of the population? 1. calculate z-score for mean 2. Locate mean on sampling distribution to determine likelihood 3. Retain or reject sample as representative of the population a high frequency (X bar is close to M on normal distribution) is a likely sample so you retain it a low frequency (X bar is far from M on a normal distribution) is an unlikely sample so you reject it Closer is good; far is bad

Degrees of freedom for single sample t-test

Shape of the t-distribution is actually determined by N-1; when we compute Sx, we use N-1 The larger the df, the closer the t-distribution is to forming a normal curve -dfs greater than 120, t-distribution is identical to normal curve thus critical values are the same as in the z-distribution (∞) -dfs between 1 and 120, first use df to identify appropriate t-distribution df= # of scores that are free to vary -for variance you need the mean and all but one score

Sampling distribution of r (CC)

Shows all possible values of the CC that can occur when samples are drawn from a population where p=0 Different values of r are plotted robt= our CC We compare robt to rcrit Just like t-distribution, the shape of the r distribution changes slightly based on the N of the sample df=N-2 Stronger relationship away from 0; lower frequency

Setting up the experiment for inferential statistics

Single sample experiment- mean from a sample tested under one condition is used to infer the corresponding M and this is compared to a known M for another condition to see if a relationship exists Ex: 1 pill condition- randomly select 1 sample of RPs and give each 1 pill; give IQ test; sample mean represents M of IQ scores for all people when they have taken 1 pill No pill condition: population of IQ scores over the years from people who have taken the IQ test M=100

Linear Regression

Statistical procedure for describing the best fitting straight line that summarizes a linear relationship (draw a regression line through the data on a scatterplot is a best fitting line)

Steps for interpolation procedure for single sample t-test

Step 1: total distance between the known bracketing dfs Step 2: Distance between the upper bracket df and target df Step 3: Proportion of the distance that the target df lies from the upper known bracket (step 2 divide step 1) Step 4: total distance between the bracketing values Step 5: multiple step 3 times step 4 Step 6: add or subtract step 5 from upper or lower bracket- supper: subtract upper

Strength of relationships and prediction errors (Linear regression)

Strength of r value determines errors in predictions- stronger r is the less movement/ if r (relationship of X and Y) is weaker there are more errors in our predictors so Standard Error rises minimum error occurs when r=+-1 Maximum error occurs when r= 0 SE is at max and = SD of Y score in sample (no idea what that means) As r gets smaller, S2y' (variance of Y scores-error) and Sy' (standard error of the estimate) get larger as r gets larger, S2y' and Sy' gets smaller so weaker relationships produce greater errors and stronger relationships produce smaller errors

Order effects for dependent t test

The influence of performing a series of trials 1. Practice effects- you get better at the task as you do more trials 2. Fatigue effects- you get worse at the task as you do more trials because you are tired 3. Carry over effects- the experience of any one trial that influence score on subsequent trials (you didn't like how you had to do one trial so you used the technique from the last trial) 4. Response sets- developed a habitual response for subsequent trials

Independent t-test/ between subject experiment statistical notation

There are 2 means: X1 bar and X2 bar Estimated Variance: S21 and S22 N=total number of scores in a study n1 number of scores in one condition and n2 number of scores in second condition

t-distribution novelty

There are many versions of the t-distribution each having a slightly different shape -the shape depends on n -larger samples tend to represent the population more accurately -each has different critical values Only use the version of the t-distribution that has the same N as our sample

How to know which control approach to use (independent)

They are not mutually exclusive Consider: How important is the variable? -the more likely it will influence results, the more likely it needs to be actively controlled Statistical power vs internal and external validity -more counterbalancing= greater variability= less power= more validity - limiting the population= increased power=reduced external validity

The role of inferential statistics

To see if there is an error or unique and exciting data and it allows us to catch that error in the data Sampling error- results when chance produces a sample statistic that is not equal to the population parameter it represents Ex: measure height of males and females and by chance males are short and females are tall so you conclude that females are taller than males although this isn't true it just was in that study Inferential statistics are used to decide whether sample data represent a relationship in the population- use probability to determine likelihood

Independent Samples t-test Assumptions

Two independent samples DV measures interval or ratio scores Population of raw scores forms a normal distribution Populations represented by the samples have a homogeneous variance -true variance of the populations represented by the samples is the same -There is a test to determine this, but for now we will assume this is true Not required that each condition have the same n

Hypothesis for dependent t test

Two tailed Ho: MD = 0 Ha: MD=- 0 One tailed: still set to zero but < and > change depending on study

Independent Sample T-test

Used to analyze a two sample experiment that consists of independent (different) samples Each participant serves in only one condition Randomly selected for a condition without regard for who else has been selected for other condition Use a between subject design when it is appropriate to compare RPs in one condition to a completely different group of RPs in another condition

One-tailed test in hypothesis testing

Used when we predict the direction in which scores will change Ex: IQ pill- we predict the pill will make you smarter -Ha-M> 100 -H0-M<- 100 .05 is the entire one tail

Criterion Variable

Variable where scores are being predicted like in GPA (GPA is predicted by grades?)

Linear Regression Statistical Notation

Variance and Standard deviation computes for Y instead of X Variability for the Y scores is reflected by their different vertical positions on Y axis (the larger the variance or SD for Y, the more the Y scores will be vertically spread out)- we know x we want to predict y vertical spread= variability of y

The standard normal curve in probability

We assume that scores form a normal distribution The proportion of area under the curve for scores in any part of the distribution equals the probability of those scores Same techniques with z-scores and z-tables apply to probability OR means to add areas or probabilities together beyond means use column c then add between use column b and add?

Interpretations for independent t test

Compare tobt to tcrit df= (n1 + n2)- 2 Compute confidence interval if reject

Statistical notation for dependent t test

Compute difference scores D= difference score when we subtract one raw score from another D bar= mean of the difference scores S2D= estimated variance of the difference scores MD= mean of the population difference scores

t-distribution

All possible values of tobt compute for random sample means from the raw score population Means greater than M have positive values of t Means less than M have negative values of t The larger the absolute value of t the farther it and its corresponding sample mean are from M The larger the t, the lower the corresponding sample means relative frequency and probability

Statistical hypotheses for inferential statistics

Alternate Hypothesis- Experiment works as predicted (Ha : μ ≠ 100)- IV affects DV -If the pill works as predicted, the the population with the pill will have a μ that is either greater than or less than 100 Null Hypothesis (says everything the Ha doesn't)- Experiment does not work as predicted (Ho : μ = 100)- IV does NOT affect DV- The sample mean produced with the pill represents a population mean equal to 100

Limiting the population- control variable (independent)

Alternative to counterbalancing Keep variable of interest constant so it can't influence the results -assume large difference in memory between females and males; only include females in study Pros: -Increase internal validity by eliminating a potential confounding -Increase power; reduce variability in scores Cons: -Restriction of range problem (little to no difference in recall scores between conditions) -Lower external validity (because of higher selectivity of ppts; can't generalize to males if there is only females in the study)

zobt (z-test)

Calculate zobt formula: zobt = X - μ/ σx bar Use standard error of the mean formula -σ x bar= σ x/√N then compare zobt to z crit

Summary of single sample t-test

Check that the experiment meets the assumptions of a t-test Create a 1 or 2 tailed Ho and Ha From sample data compute s2x (or sx); then compute sx, and then compute tobt. For the df in the study find the tcrit Make conclusions: -tobt is beyond tcrit= reject Ho; results are significant -tobt is not beyond tcrit= fail to reject ho, results are not significant if results are significant compute confidence interval

Confidence interval for single sample t test

If you reject Ho you have to estimate the population M that your sample mean represents after finding significance/ only if reject hypothesis?- all the people in the population would fall in this calculated range and we are 95% confident (bc alpha is .05) They are commonly reported: Our survey showed that 45% of voters support the president, with a margin or error of + 3% The confidence interval for a single M describes a range of values of M, any one of which our sample mean is likely to represent μlow = lowest value of μ sample mean is likely to represent μhigh = highest value of μ sample mean is likely to represent -These 2 values make up the confidence interval Logic: compute the highest and lowest values of μ that are not significantly different from the sample mean

Confidence intervals and alpha (single sample t test)

Interval was defined using a=.05 so 5% of the time the interval will be in error and will not contain the M represented by our sample mean (95% of the time we are correct) The smaller the a, the smaller the probability of error and the greater the confidence The larger the a the larger the probability of error and the smaller the confidence only compute a confidence interval when the t test results are significant/ we reject Ho

Effect size of Strength (rpb) for independent t test

It indicates how consistently differences in the dependent scores are caused by changes in the independent variable Proportion of variance accounted for is r2 Cohen's Classification System of Effect Size: - .10 - .29 = Small effect - .30 - .49 = Medium effect - .50 - 1.0 - Large effect

Importance of Linear Regression

It is used to predict an individual's unknown Y score based on his or her X score from a correlated variable

Standard Error of the estimate (linear regression)

Just square root the variance formulas Def- SY' = √Σ(Y - Y')2/ N Comp- SY' = √S2Y (1 - r2) Standard error of the estimate is the best indicator of average error with regressions

r

Linear regression- statistic that summarizes the relationship and regression produces the line that summarizes the relationship Always compute r first When r is not 0 use linear regression to further understand the relationship

Errors in decision making for hypothesis testing

Look at chart in notes Type I error -reject Ho when Ho is true -saying the IV works when it doesn't probability= alpha Type II error -fail to reject Ho when Ho is false -fail to identify the IV really does work -Probability = Beta Statistical procedures are designed to minimize type I error - more serious to say IV works when it doesn't

Random assignment -control variable (independent)

Randomly mix the participants variables so that differences are balanced out in each condition Ex: memory each of the conditions should have someone RPs with good memory and some without Assign participants in a truly random way by using random number tables Pros: usually produce balanced representative samples in each condition Cons: -not guaranteed to balance participant variables within each condition (Ex: RPs with better memory abilities in condition 1) -Does not work well with small samples -Effective balancing leads to fluctuation within conditions -could produce larger differences among scores in a given condition, results in a weaker relationship (Ex: memory abilities balance between conditions= wide range of scores within conditions; weakens relationship)- makes it hard to find significance

Significance of r (CC)

Recognize that the sample may contain some sample error Compute a confidence interval if reject Ho -find r2 (coefficient of determination) -proportion of variance accounted for by the relationship -r2 indicated the importance of a relationship because the larger it is the more accurate our predictions of a Y score from X

Sampling distribution of probability

Region of rejection is the area in one or both tails of the distribution where a sample mean is deemed unrepresentative -reject that means the mean represents the raw score population -sample means NOT in the region of rejection are retained (fail to reject) -(ROR)- extreme ends of the distribution/ unlikely ROR = reject mean, significant Outside of ROR= retain mean, not significant Tailed test -two tailed test: ROR is in both tails of the distribution ( a sample mean can be too far above or below the population mean -shaded is unlikely a sample mean- reject One tailed test: a sample mean is either too far above or too far below the population mean but not both Criterion -the probability that defines the sample as too unlikely to retain -Usually set at .05 or .025 in each tail of a two tailed test

Interpretation for single sample t test

Rules are the same as with the z-test tobt falls in the ROR we reject Ho; results demonstrate a relationship in the population between the independent variable and the dependent variable whenever we reject the Ho there is a chance, equal to a that we made type I error

Counterbalancing -control variable (independent t-test)

Systematically ensuring that a participant variable can't confound results Make potential confound part of selection criteria- could involve a pretest Ex: hypnosis study: gender and memory ability Mean score for hypnosis and no hypnosis conditions should be equally influenced by memory ability and gender have the same amount of males with good memory in both conditions, males with bad memory, females with good memory, and females with bad memory Pros: We can be sure significance is NOT due to confounding (higher internal validity) Cons: -less likely to find a significant relationship (greater variability within conditions) -endless variables to counterbalance -Pretest may alert ppt to purpose of study (then you get demand characteristics)

Errors in Prediction for linear regression

The error in a single prediction is the amount that a participant's Y score deviates from the predicted Y' (Y-Y')- sum of deviations around the mean is 0 Use Variance of Y scores around Y' formula- indicates how much we were off when we predict a participants score on Y from X Squaring the deviation produces an unrealistically large number for error variance so standard deviation is the better indicator of error than variance Formulas: Comp- S2Y' = S2Y (1 -r2) Def- S2Y' = Σ(Y - Y')2/ N

How to find tobt for dependent t test

calculate S2d then Sd bar then tobt

Steps for Probability

compute standard error of the mean compute z-score reject or fail to reject sample as representative

Sampling distribution for independent t test

consists of the difference between the means (what is the probability of obtaining our difference between Xs bar when Ho is true Along the x-axis are the differences between the means (X1 bar -X2 bar) The mean is the value stated in Ho Testing Ho determines where our difference in sample means lies on the distribution

Interpretations of dependent t test

draw your sampling distribution of D bar -values of D bar that are farther above or below zero are less likely to occur when Ho is true df= N-1 Run a confidence interval if reject Ho- describes a range of values for MD (use two tailed tcrit even if study is one tailed)

Standard error of the difference (Sx1 bar- X2 bar) for independent t test

estimated standard deviation of the sampling distribution of differences between the means Formula: Sx1 bar- X2 bar= the square root of S2pool times 1/n1 + 1/n2

With- in subject/ dependent design

it controls for ppts variables like gender, IQ, anything that can alter the experiment There are two types of designs: 1. Matched group designs -each RP in one condition matches a RP in the other condition(s) on one or more extraneous variables -Pro: ensures control of given participant variable; in the end know it wasn't the variable that affected the study -Con: pre-testing can increase demand characteristics; with more than 2 conditions of IV it is complicated to match 2. Repeated measures design - Each RP is tested under all conditions of an independent variable (order effects and pretest/ posttest design come into play) -Pro: eliminates confounding from RP variables -Con: RPs experience all conditions (demand characteristics); subject history, subject maturation; subject mortality; order effects

Computing tobt for independent t test

measures how far our difference in means is from 0 (difference between Ms according to Ho) Formula: tobt= (X1 bar- X2 bar)- (M1 - M2)/ Sx1 bar - X2 bar

Controlling participant variables (independent t-test)

personal characteristics that distinguish one individual from another are physical and mental ability, attitudues and emotions, personal history, etc. Produce individual differences within and between conditions we seek to control all variables through random assignment, counterbalance, and limiting the population