research analysis quiz 3

sampling error

difference between sample statistic and true population parameter

Σ

sigma, sum

μ

mu, population mean

x̄

sample mean

independent variable

variable that is manipulated or categorized in study to observe its effect on another variable (dependent)

mean of z distribution

0

how are z score and standard deviation related?

z score represents how many standard deviations a data point is away from a mean of a distribution

standard deviation and what is the equation

measure of the amount of variability or dispersion in a data set

indicates how spread out the values in a data set are around mean (average)

smaller = data points closer to mean

standard error

how much the sample mean or any other sample stat is expected to vary from true population mean

estimate of variability or precision of the sample mean

smaller = sample mean is more accurate estimate of population mean

order of hypothesis testing

1) state hypotheses

2) set decision criterion

3) collect sample data

4) calculate statistics

5) make a decision

type one error

statistical test incorrectly rejects a true null hypothesis

conclude there is an effect or relationship when there is none

false positive

type two error

fails to reject a false null hypothesis

conclude there is no effect or relationship when there is one

false negative

Z test

compare sample mean to known population mean

test if sample mean is significantly different from a known population mean

sample size larger than 30

normal distribution

population standard deviation is known

ANOVA

means of three or more groups to determine if at least one group mean is significantly different from others

test the hypothesis that all groups means are equal

data are independent, normal distributed within each group

homogeneity of variance

one way or two way

two way ANOVA

compares means across two factors allowing interaction effects

t test

compares means of one or two groups

similar to z test BUT

sample size is small (n<30)

normal distribution

one sample t test, independent sample t test, paired sample t test

one sample t test

compare sample mean to known value often a population mean

one tailed t test (left)

lower tail

is sample mean significantly less than population mean?

alt hypothesis - sample mean less than population mean

null hypothesis - sample mean greater than or equal to population mean

one tailed t test (right)

upper tail

is sample mean significantly greater than population mean

alt hypothesis - sample mean is greater than pop mean

null hypothesis - sample mean less than or equal to pop mean

large sample effect

does not direct affect standard deviation of individual sample but better estimate of populations true standard deviation

lead to smaller standard errors, more likely to be closer to population mean

more normal in shape even if population distribution itself is not normal due to central limit theorem

sampling distribution gets narrower estimate more precise

paired t test

two related samples or observation that are paired in some way

before and after, matched samples, dependents, etc

individual (independent) t test

means of two independent or unrelated groups, no relationship with each other, normal distribution, homogeneity of variances

variances of the two groups are roughly equal not use welchs t test

effect size

used to quantify the magnitude of a different for relationship observed in a study

determine how strong or meaningful the effect is

Pearson’s r

correlation

strength and direction of linear relationship between two continuous variables

eta squared n2

for ANOVA

measure proportion of the total variance in dependent variable that is explained by independent variable

if n2 is small, it suggest other factors are more important than study method

omega squared (w2)

for ANOVA

assessing effect size in ANOVA more conservative than eta

total variance

include everything that could influence scores

between group variance

part of variance that is explained by study method

variability due to difference between means of groups

how much group mean difference from overall mean of entire sample

Measures how much the average weight loss for each diet (A, B, and C) differs from the overall average weight loss across all participants.

cohens d

mean difference

most commonly used to measure the effect size between two groups

measures the size of difference between two groups in standard deviation units

one way ANOVA vs one way t test

groups are independent of each other

test if there is significant difference between groups

t test - 2 groups

anova - 3 or more groups

why use an ANOVA?

compare multiple groups

avoid risk of type 1 error

determine whether there is a significant difference in group means while analyzing in the data

analyze more complex designs including interactions

what do we do after we find a significant effect in an ANOVA test?

usually follow up with a t test

examine effect size visualize results check assumptions

within group variance

variability within each group

how much individual data points within each group deviate from their respective group mean

Measures how much the individual participants' weight loss values within each diet group (A, B, or C) differ from their respective group means.

mean

measure of central tendency in a data set

average value of all data points

variance

spread or dispersion of data of far data points are from the mean

f ratio/statistic

used in ANOVA
compare variability between groups to variability within groups

whether the means of three groups or more are significantly different from each other

can never equal 0 unless there is no variability

closer it is to 1.0 less of an effect there is of the independent variable in the data

t value/t statistic

larger the sample size the closer t is to the z

is used in t test

determine whether the difference between two sample means is statistically significant

measures of the difference between observed sample stat and hypothesized population parameter

how many standard errors the sample mean is from population mean (one sample t test)

how many standard errors the difference between the means of two groups is from zero

what happens if our limits test fail in our t test?

means assumption of normality independence or homogeneity of variance is violated

can affect the validity of results

adjust test using welchs t test or non parametric tests

sampling distribution of the mean

take multiple random sample and calculate mean for each sample

plot them

the distribution it forms = this

approx equal to pop mean

sample size increase then it gets narrower estimate more precise

bonferroni correction

running one hypothesis test = 5% chance of type one error

running multiple tests, each test has 5% chance of false positive, probability of making at least one type 1 error increases

helps control this by adjusting significance level

reduces type 1 but increase type 2

full standard deviation vs standard deviation

full - population

other - sample

full variance vs variance

estimated standard error

standard error formula

sum of squares

z score

anova formula

t test formula