Exam 2 Study Guide – Methods of InquiryOverall Data Analysis- Errors are impossible numbers (outside the possible range)- Outliers are in the possible range, but exceptional. Could be an error or a true score from an unusual participantMeasures of Central Tendency- Median – the “middle” score (50% of scores below and 50% of scores above)- Mode - Most frequently occurring score- Mean - Arithmetic average or mean (sum of scores divided by number of scores)- Normal Distribution – Mean=Median=ModeMeasures of Variability- Range – Officially = (highest score – lowest score)- Variance –The sum of squared deviations of the scores around the mean divided by either N or n-1- Standard Deviation – The square root of the variance.Effect Size or Effect Magnitude- An index of the strength of the relationship between the IV and the DV that is independent of sample size. - Cohen’s d is one measure of “size of effect” or effect magnitude.- For d, a value of .20 indicates a small magnitude effect, .50 a medium magnitude effect, and .80 a large magnitude of effect.- d is a ratio of the difference between the means at two levels of an IV divided by the standard deviation of the population. (the difference between means divided by a measure of variability or dispersion)- As variability increases (standard deviation increases), d decreases (lower effect size).Power- Effect size is one measure that affects the “power” of a statistical analysis and it is used in making decisions about how large a sample size should be used in order to be sufficient to produce a reasonable level of “power”.- Power is the probability of correctly rejecting a false null hypothesisMeta-analysis- Because the standard deviation is used as the “denominator” for this measure, it is independent of (not affected by) sample size. Thus, you can compare effect sizes across research studies using various sample sizes. - This type of comparison is called a “Meta-analysis”Null Hypothesis Significance Testing (NHST)- H0 – Null Hypothesis – a hypothesis of “no difference” - The samples come from the same population and differ only due to chance. - HA – Alternative Hypothesis- says the means are truly different as a result of the effect of the different levels of my IV.- The samples come from different populations.- Power: the probability of correctly rejecting a false H0. - The probability that there really IS an effect of IV and you correctly detect this and say there is an effect of the IV. - “Power” is used to describe the ability of a particular statistical test to detect a true effect of an IV.- Sensitivity is the term used to describe the likelihood that a DESIGN will be able to correctly detect a true effect of an IV- Type I Error – when you claim there is an effect of IV, but in reality the differences weredue to chance alone. - Probability Type I Error = α (alpha)- Type II Error – when you miss a true effect of the IV - The IV had an effect and you said differences were due to chance- Probability Type II Error = β (beta)- Type II errors are much more common than Type I errorsWhat affects Power?- Sample size: as sample size increases, power increases- Effect size: as effect size increases, power increases- Statistical test used will actually affect power- (ex: repeated measures designs has more “power” (sensitivity) than independent group designs)- α affects power: as alpha increases, power increases- alpha (α) and beta (β) have a “reciprocal” relationship. (as one goes up, the other goes down)- Easiest way to increase power=increase sample sizeAlpha, Power, and Beta Relationship- Alpha and Power are the same, when one increases, the other increases - Beta is the reciprocal of both Alpha and Power- When Power/Alpha increase, Beta decreases- If you let α (alpha) increase, β (beta) will decrease (you lower the chance of missing a true effect of the IV)- since power = 1- β (beta), power will increase (you increase the chance of correctly detecting a true effect of the IV)Analysis of Variance (ANOVA)- The greater the difference between means, the larger “t” will be.- As variability increases, “t” decreases. - Can only use a t-test if 1 IV and 2 levelsFor each different design, there is a different “model” of ANOVA- 1 IV independent group designs (Random group, Matched group, Natural group) all use a1-way between subject ANOVA.- 1 IV repeated measures designs (complete/incomplete) use a 1-way repeated measures ANOVA- 2 IVs both as between subject manipulations use a 2-way between subject ANOVA- 2 IVs with one manipulated as a between subject manipulation and one manipulated as a repeated measures use a 2-way mixed design ANOVAF ratio- F = (Variance due to the IV and chance)Variance due to chance- Variance due to the IV is called Primary Variance!- Suppose only chance is at work and there is no effect of the IV.- If no effect of the IV then F will be close to 1 - As primary variance increases, F increases. The larger F is, the more likely it will be considered “Significant”Steps to Calculating an F-ratio1. Partitioning (dividing) the sum of squares (SS)- SS= “the sum of the squared deviations of the scores around the mean”- All SS formulas have the same basic structure. - The basic formula for SS= ∑(x−´x)2- The SS is a measure of variability (not “variance”). It is the top portion (numerator) of the variance formula- Partitioning means to “divide”. Break up total SS(variability) into parts that represent the different “sources” of the variability (primary variance, chance)- You can “partition” or break apart the SS. You can also put them back together again2. Calculating df (degrees of freedom)- For each F ratio, there are TWO df numbers reported, one for the source that appears in the numerator and one for the source that appears in the denominator.- Example: FIVA (#,#) = 5.3333. Convert SS to variance (MS) mean square- You convert your measure of variability (SS) into a measure of variance by dividing the SS by the df. The basic formula for variance is always SS/df.- In ANOVA we give “variance” a special name: “Mean Square” or MSMS = SSdf = variance4. Calculate the Fratio- F is a ratio of two mean squares (MS)- The numerator of the F-ratio is the variance (MS) for the effect of the IV and chance while the denominator is the variance (MS) due to chance alone.1 – way between subject summary