RMS II Final Exam (USI)

Dr. Pilot

What is an ANOVA?

• Analysis of Variance (group differences in variance)

• Can compare more than 2 groups

• 1 test instead of 3 independent T-tests

What letter represents the ANOVA statistic?

F

What is the Null hypothesis for an ANOVA?

• No difference is seen

• H_o = μ₁ = μ₂ = μ₃ = μ₄ = …

What is the Alternative Hypothesis for an ANOVA?

• Difference is seen

• H₁ = At least 1 μ is different

How do you determine if there is a systematic effect in an ANOVA?

• If there is a treatment (systematic) effect, F > 1

• If there is no treatment. (systematic) effect, F = 1

How do you decide whether to reject or fail to reject a hypothesis in an ANOVA?

• If F calculated < F critical = fail to reject the null / no effect is present

• If F calculated > F critical = reject the null / effect is present

What letter represents sample size?

n

What letter represents total participants?

N

What letter represents mean?

M

what letter represents a group?

j

What letter represents groups?

k

What letter represents individual scores?

Y

What represents mean of means (grand mean)?

M_G

How do you find SS between when computing for F-calculated in an ANOVA?

∑n (M_j - M_G)²

How do you find SS within when computing for F-calculated in an ANOVA?

∑ (Y_ij - M_j)²

How do you find SS total when computing for F-calculated in an ANOVA?

∑ (Y_ij - M_G)²

How do you find F- Calculated when computing for F in an ANOVA?

MS between / MS within

How to find df between when calculating F- calculated in an ANOVA?

k - 1

How to find df within when calculating F- calculated in an ANOVA?

N - k

How to find df total when calculating F- calculated in an ANOVA?

N - 1

How to find MS between when calculating F- calculated in an ANOVA?

SS between / df between

How to find MS within when calculating F- calculated in an ANOVA?

SS within / df within

When and why do you complete a Post Hoc?

• When you see a p - value of less than 0.05

• To identify which groups differ from each other

When do you use a repeated measures ANOVA (one-way between subjects ANOVA)?

When there are 2 or more conditions for each participant

What letter represents person total in a Repeated Measures ANOVA?

P

What letter represents treatment total?

T

What letter represents grand treatment total?

G

What do you use to find F- critical on the graph provided?

Use df_BT and df_e to get the relevant information for your F- critical

How to find between tx (SS_bt) when finding F- calc in a Repeated Measures ANOVA?

SS_bt = ∑ (T²)/n - (G²)/N

How to find within tx (SS_w) when finding F- calc in a Repeated Measures ANOVA?

add all sum of squares of each condition together

How to find between sub (SS_bs) when finding F- calc in a Repeated Measures ANOVA?

SS_bs = ∑ p²/k - G²/N

How to find Sum of Squares Error (SS_e) when finding F- calc in a Repeated Measures ANOVA?

SSe = SS_w - SS_bs

How to find df between (df_B) when finding F- calc in a Repeated Measures ANOVA?

k - 1

How to find df within (df_w) when finding F- calc in a Repeated Measures ANOVA?

N - k

How to find df total (df_T) when finding F- calc in a Repeated Measures ANOVA?

N - 1

How to find MS between tx (MS_bt) when finding F- calc in a Repeated Measures ANOVA?

MS_bt = SS_bt / df_bt

How to find MS error (MS_e) when finding F- calc in a Repeated Measures ANOVA?

MS_e = SS_e / df_e

How to find F- calc in a Repeated Measures ANOVA?

MS_bt / MS_e

What is a correlation used for?

Used to see a statistical relationship between 2 variables (x & y)

What is an example design of a Correlation?

Relationship between episodes of SpongeBob watched and audible laughs

What are the characteristics of a correlation?

• Direction

• Form

• Strength

How is direction in a correlation measured?

Postive (+) or negative (-)

How is form in a correlation measured?

linear (straight line) or non-linear (curved line)

How is strength in a correlation measured?

-1, 0, +1

• Perfect correlation = 1 or -1

• No correlation = 0

What does a positive (+) correlation look like?

• X-axis increases

• Y-axis increases

  • Ex: more studying, better grades

What does a negative (-) correlation look like?

• X-axis increases

• Y-axis decreases

  • Ex: more food you eat, less you have of it

What does a Pearson Correlation do and what letter represents it?

• Measures degree + discretion

  • Must be linear!!!

• Represented by the letter r

What is a Pearson correlation used for?

• Prediction

• Validity

• Reliability

• Theory verification

How do you fin Pearson Correlation?

r = SP / √SS_xSS_Y

How to find Sum of Products when conducting a Pearson Correlation?

SP = ∑ (X - M_x) (Y - M_Y)

Does Correlation equal Causation?

• No

• correlation does NOT equal causation

What can have an affect on correlations?

• Outliers

  • Extreme X or Y values

  • May inflate pr deflate correlation

What is Spearman Correlation?

• Uses Pearson formula

  • scores are converted to ranks

• Measures relationship consistency

• ordinal, interval, + ratio scales

• Non-linear relationships

What is Point-Biseral Correlation?

• Uses Pearson formula

  • one continuous variable

  • one dichotomous variable

When do we do a Regression?

• Fitting a linear model to the data to predict the values of an outcome variable (DV) from on or more predictor variables (IV)

What is the goal of a Regression?

Predicting outcomes

How are straight lines defined in a Rgression?

• Slope (or gradient) of the line (usually denoted as b)

• Y- intercept (known as the intercept of the line a)

How to find outcome in a Regression?

Outcome = (a + bx) + error

How to find a in a Regression?

a = M_y - bM_x

How to find b in a Regression?

b = SP / SS_x

How to find r- statistic in a Regression?

r = SP / √SS_x(SS_y)

• Note: similar as in a correlation

How to find regression sum of squares in a Regression Analysis?

r²SS_Y

How to find residual sum of squares in a Regression Analysis?

(1-r²) SS_Y

How to find regression df in a Regression Analysis?

Always equals 1

How to find residual df in a Regression Analysis?

n - 2

How to find regression mean of squares in a Regression Analysis?

SS regression / df regression

How to find residual mean of squares in a Regression Analysis?

SS residual / df residual

How to find F in a Regression Analysis?

MS regression / MS residual

What is Pearson’s Chi Square?

An analysis used to determine if two categorical variables are related

What are the general hypotheses for Pearson’s Chi Square?

• H₀ = No relationship exists

• H₁ = A relationship exists

What is an example design of Pearson’s Chi Square?

Whether men cheated on their partner + how happy they were in their current relationship

• 2 variables:

  • Happiness

    • Happy or unhappy

  • Fidelity

    • Faithful or cheater

How do you calculate expected frequencies for Pearson’s Chi Square?

model of expected frequency = (row total x column total) / N

What is the equation for Pearson’s Chi Square?

X² = ∑ (observed_ij - model_ij)² / model_ij

How do you find degrees of freedom in Pearson’s Chi Square?

(number of rows - 1) x (number of columns - 1)

• df = (r-1)(c-1)

How do you determine of you reject or fail to reject the null hypothesis for Pearson’s Chi Square?

X² calc > X² crit = reject null hypothesis

• there is a relationship between the 2 variables

• all groups are NOT equal

What are standardized residuals

• Z-scores

• The difference between what model predicts and what is observed

• Directly related to chi square

How do you calculate standardized residual?

residual_ij = observed_ij - model_ij / √model_ij

What is the factorial design of a 2 Way ANOVA?

• IV = factor

• similar to one way ANOVA, use the linear model

What is the linear model of a 2 Way ANOVA?

outcome = b₀ + b₁A + b₂B + b₃AxB

• b₀ = constant

• b₁A = IV 1

• b₂B = IV 2

• b₃AxB = interaction

What is a 2 Way ANOVA and what does it do?

• “2 × 2” design

• 1 dependent variable

• 2 independent variables with 2 levels

• Evaluates multiple hypotheses

What is an example design of a 2 Way ANOVA?

• DV = test scores

• IV 1 = Stereotype threat

  • Levels: threat & no threat

• IV 2 = Gender

  • Levels: female & male

What are the hypotheses for a 2 Way ANOVA?

• H₀ (null hypothesis): μ_A1 - μ_A2 = 0

• H₁ (alternate hypothesis): μ_A1 - μ_A2 ≠ 0

What are the interaction hypotheses for a 2 Way ANOVA?

• H₀ : no interaction, mean differences are explained by the main effects

• H₁ : interaction is present, mean differences are not predicted by the main effects

What is skewness?

• Asymmetry in the normal distribution

• Skewed distributions pile up on one side, leaving a “tail” of a few extreme values on the other side

  • Positively Skewed = tail goes to the right (towards positive numbers)

  • Negatively Skewed = tail goes to the left (towards negative numbers)

What is kurtosis?

Measure of how heavily the tails of a distribution differ from the middle

What are the types of kurtosis?

• Leptokurtosis

• Platykurtosis

What is Leptokurtosis?

More values in the tails than close to the middle

What is Platykurtosis?

Fewer values in tails and fewer close to the mean

What is the Central Limit Therom?

If the population is normally distributed, with a large enough sample then the sampling distribution will also be normally distributed

What is a P-P Plot (Probability-Probability Plot)?

Plots a cumulative probability of a variable against the cumulative probability of a normal distribution

What is Levene’s Test?

tests the null hypothesis that the variances in different groups are equal

• Note: you do NOT want a significant levene’s test

What is Type 1 Error?

False Positive - Rejecting a true Null Hypothesis

What is Type 2 Error?

False Negative - Failing to reject a false Null Hypothesis

What is a confound?

• A variable other than the IV that differs systematically between conditions

  • Invalidates experiment

    • Unclear whether difference are due to IV or confound

  • Must be eliminated at all costs

What does a Between-Subjects (Independent) design look like?

• Independent measures

• Individual differences

• Differences due to IV

• Participants experience one condition

• Typically requires random assignment

• At least 2 distinct groups (control and experimental)

What does a Within-Subjects (Repeated) Design look like?

• Repeated measures

• Difference due to IV

• Participants experience all conditions

  • All levels of the IV

• No need for random assignment

  • Tested against your prior behavior

What is a T- Test?

To determine if there is a statistically significant difference between the means of two population samples

ANOVA is necessary to evaluate mean differences among three or more treatments in order to...

Minimize the risk of Type 1 error

An industrial/organization psychologist is interested in employee efficiency. The researcher wants to see if scores on the Myers-Briggs personality test predicts work performance. What analyses would they use to answer this question?

Regression

" In an independent measures ANOVA, individual differences contribute to the variance in the numerator and in the denominator of the F ratio. For a repeated measures ANOVA, what happens to the individual differences in the numerator of the F ratio? "

They do not exist because the same individuals participate in all of the treatments