unit 3 - ch 12 - Distribution & 1-Way ANOVA Flashcards

Question

the big picture [ look at picture on docs ] X to x double bar =

Answer 1

SStotal Distance between these is two distances

Answer 2

SSwithin Sum of the squares within Remaining distance is how x bar to x double bar

Answer 3

Sum of squares between

Answer 4

Variation due to chance Sample with a lot of dispersion the length of sum of squares lengthens Sample with little dispersion the length of sum of the squares within shortens Square before we sum = 0 (don't want this so) SSwithin = sigma(x -xbar)^2 Sum of the squares (SS)

Answer 5

Relationships samples have to each other If 4 sample are spread out then SSbetween lengths If 4 samples are stacked on top each other then SSbetween will shorten Relationship between samples control shape Sigma (xbar - xdouble bar)^2

Answer 6

between term / within term Divide total variation into these two

Answer 7

Total variation can be portioned into 2 distinct parts-- between and within -- and those 2 components can be compared to determine which is affecting the data to a greater degree

Answer 8

reject the null

Answer 9

fail to reject null small numerator Small distance between Large within Chance randomness and error

Answer 10

Ho mewW = mewVoba = mewTequila = mewEnergy Alternative is not this but with =/= This is WRONG some of these can be equal to each other H1 = not all population means are equal OR “at least one population means are equal” Wtv but H1 is a sentence

Answer 11

Single factor -> type of drink Variance SS > Between > Within > Total Formula for variance (X - xbar)^2 Sum of the squares aka numerator of the variance

Answer 12

ANOVA (sigma(x -xbar)^2)

Answer 13

MSbetween = MSwithin

Answer 14

additive (as the lines show)

Answer 15

dfbetween and dfwithin

Answer 16

P value of F crit

Answer 17

P < a = REJECT P > a = FTRN TS > CV = REJECT TS < CV = FTRN One tail-Right tail because the TS positive because everything is always squared (think of formula)

Answer 18

Not all population means are equal Rejected so different drinks impacts people’s ability to get through the levels of the game. Tequila did NOT impair people from progressing through the game; it actually made them better. That is because ___. Social game or game that rewards risk or rewards aggression Factor is the reason for variation (type of drink) FACTOR IS APART OF CONCLUSION NOT RANDOMNESS Look at means.. Tequila is higher than other means!!!!!!!! This is how we know the factors are not equal and we may be REJECTING THE NULL

Answer 19

B/W = TS TS is around 1 always positive 1!!!!! Further away = reject Close to TS = FTR Null Ho says that 2 groups compared are equal If they are equal TS = 1 Num and Denom can be big or small F distribution is skewed Df num and Df denom Steep decline because it can't go negative but can get larger

Answer 20

For hypothesis tests comparing averages among more than two groups, statisticians have developed a method called

Answer 21

The purpose of a one-way ANOVA test is to determine the existence of a statistically significant difference among several group means. The test actually uses variances to help determine if the means are equal or not.

Answer 22

Each population from which a sample is taken is assumed to be normal. All samples are randomly selected and independent. The populations are assumed to have equal standard deviations (or variances). The factor is a categorical variable. The response is a numerical variable.

Answer 23

The distribution used for the hypothesis test is a new one. It is called the F distribution, invented by George Snedecor but named in honor of Sir Ronald Fisher, an English statistician. The F statistic is a ratio (a fraction). There are two sets of degrees of freedom; one for the numerator and one for the denominator.

Answer 24

1. Variance between samples: An estimate of σ2 that is the variance of the sample means multiplied by n (when the sample sizes are the same.). 2. Variance within samples: An estimate of σ2 that is the average of the sample variances (also known as a pooled variance). SSbetween = the sum of squares that represents the variation among the different samples SSwithin = the sum of squares that represents the variation within samples that is due to chance.

Answer 25

To find a "sum of squares" means to add together squared quantities that, in some cases, may be weighted. We used sum of squares to calculate the sample variance and the sample standard deviation in Chapter 2 Descriptive Statistics. MS means "mean square." MSbetween is the variance between groups, and MSwithin is the variance within groups.