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BECK - L3: PSYC5212
Terms in this set (59)
Which is least affected by outliers? Mean, median, mode, range, standard deviation?
Define 95% confidence interval
an interval constructed such that the true population mean μ will fall within this interval in 95% of samples
What are the 2 sources of bias?
1. outliers 2. violations of assumptions (about the data)
How do you define an outlier in terms of z scores?
a standardised score or z score less than -3 or greater than 3 are categorised as outliers
how many Standard Deviations from the mean is a z score of 3?
the data point is 3 standard deviations from the mean.
How can you spot an outlier?
use z scores, or using box plots or histograms. box plots give row number.
what is the range of z scores for 95% of participants in a normal distribution?
will have a range of z scores between 1.96 and -1.96
what is the difference between statistical and conceptual hypotheses?
conceptual: a predicted relationship between the IV and DV. e.g attention span of ADHD kids not the same as the attention span of TD children. What is IV and DV? No mathematical symbols. Statistical - a mathematical relationship exists between two or more means, eg μADHD < 7mins
Why is the preference to investigate non-directional hypotheses?
We always examine the non-directional alternative hypothesis because it is always possible to reject the null, but find an effect (e.g., difference between means) completely opposite to what we thought would occur). we cant have 2 alternate hypotheses!
what does the significance level/ threshold of 0.05 or 5% mean in hypothesis testing?
we reject the null hypothesis when the sample mean is so extreme that it would occur under a true null hypothesis less than 5% of the time.
what is another term for significance level?
what is p or significance value?
the probability of making a type-1 error using the current data sample.
what is a type one error
probability of rejecting the null hypothesis for a sample when it is actually correct (rejecting H0 when it is actually true). This is making a false positive - assuming it's from a different population when it is not.
what percentage do we accept in making a type one error?
we accept up to 5% chance of making a type one error
if p is larger than or equal to 0.05 (p ≥ 0.05) we will reject or accept the null hypothesis?
type one error is too high, so we fail to reject the null hypothesis.
if p is equal to .05 (p = .05), we will accept or reject the null hypothesis?
type one error is too high, so we fail to reject the null hypothesis. We retain the null hypothesis.
if p is less than .05 (p < .05), we will accept or reject the null hypothesis?
chance of making type one error not high, so we reject the null hypothesis.
If the p value is .10, what percentage chance will you be making a type one error?
there is a 10% chance of making a type one error and rejecting the null hypothesis by mistake.
what is the assumption or null hypothesis for tests of normality?
The null-hypothesis of this test is that the population is normally distributed. Thus, on the one hand, if the p value is less than the chosen alpha level, then the null hypothesis is rejected and there is evidence that the data tested are not normally distributed.
what does it mean if p = .02 in a test for normality?
p < .05 therefore reject the null hypothesis that the population is normally distributed.
What does the Shapiro-Wilk test give us?
Shapiro-Wilk tests the null hypothesis that a sample x1, ..., xn came from a normally distributed population. if P < .05 we reject the null hypothesis that the sample is normally distributed. If greater than .05 we can retain the null that the population is normally distributed and passes the assumption of normality.
how can we use ratio of skewness in assumption of normality testing?
Standard Error of Skewness. The ratio of skewness to its standard error can be used as a test of normality (that is, you can reject normality if the ratio is less than -2 or greater than +2).
which test is more conservative? Shapiro-wilk or Kolmogorov-Smirnov test?
Kolmogorov-Smirnov is more conservative, Shapiro-Wilk is more statistically powerful and likely to give a smaller p value, so go with Kolmogorov-Smirnov (bigger p value, more likely to retain null)
how do you calculate ratio of skewness?
The ratio of skewness is skewness divided by standard error. If between -2 and 2, the shape of distribution probably resembles a bell curve. If smaller than -2 or or larger than + 2, you are probably dealing with a violation of normality.
What are the 3 main assumptions about the distribution of scores?
1. independence (of error)
2. Normality - sample data comes from population which is normally distributed
3. homogeneity of variance: samples should come from populations that have equal variability of scores
a ratio skewness falls within the range of -2 to -2. is it likely to meet the assumption of normality?
Ratio skewness score -5. is it likely to meet assumption of normality?
which is the least important assumption?
Normality. Because the larger the sample (N bigger than 30) gross deviations from normality do not affect or bias the outcome of parametric tests. Because of Central Limit Theorem
what is central limit theorem?
regardless of population shape, parameter estimates of that population (e.g. the mean) will have a normal distribution provided the samples are big enough.
what's a more pressing concern than assumptions of normality?
What is statistical power?
1 minus beta.
It is the probability of rejecting the null hypothesis (no association exists) when it is truly false. Thus, that implies that the study will be able to find a true relationship (fail to reject alternative) when its present.
difference between alpha and beta?
alpha: probability of making a type 1 error (rejecting null when actually true) - telling old man he is pregnant
beta: probability of making type 2 error (accepting the null when it is actually false) - telling pregnant lady she is not pregnant
What transformations deal with violation of normality?
log 10 to reduce positive skew. If lowest score is zero, add constant of 1.
square root to reduce positive skew. If lowest score is -2, add positive 2.
What are some objective methods for normality testing?
Skewness ratio, and p-values for shapiro-wilk and kolmogorov smirnov tests.
Which is more powerful and likely to generate a smaller p value? Shapiro-wilk or kolmogorov smirnov?
shapiro-wilk more powerful and likely to give smaller p. use when you have small N/ sample size.
which is more conservative and more likely to give larger p value? Shapiro-wilk or kolmogorov smirnov?
Kolmogorov smirnov is more conservative and likely to give larger p value. use when you have larger sample size.
what do kolmogorov smirnov and shapiro-wilk test for?
assumptions of normality
if the p value for a shapiro-wilk test is less than .05, is the population likely to be normal or not normal?
value of the Shapiro-Wilk Test is greater than 0.05, the data is normal. If it is below 0.05, the data significantly deviate from a normal distribution
what are 2 subjective tests for assumptions of normality?
Histograms and QQ graphs, you have to eyeball them.
Why is the test of normality a shortcut?
It's a shortcut because we are eventually interested in the shape of the sampling distribution of the means. Even if you have a skewed distribution but you have a large sample, your Sampling Distribution Of The Mean will STILL turn out to be normal, REGARDLESS.
What is far more important than the assumption of normality?
The assumption of homogeneity of variance
how do we evaluate the assumption of homogeneity of variance?
The Levene's Test
What are 4 ways to deal with violations of normality?
1. non-parametric tests
2. Transform scores (log 10, square root, reciprocals, reverse scoring)
which transformation deals with positively skewed data?
log 10 and square root
which transformation deals with negatively skewed data?
reverse scoring. then you need to run another transformation.
When can you ignore the assumption for homogeneity of variance?
when group sizes are equal. we only violate or reject the assumption of homogeneity of variance when you have unequal group sizes.
What is the difference between exclude cases list wise and exclude cases pairwise?
In listwise deletion a case is dropped from an analysis because it has a missing value in at least one of the specified variables. The analysis is only run on cases which have a complete set of data. Pairwise deletion occurs when the statistical procedure uses cases that contain some missing data.
pairwise includes missing data or no missing data?
includes cases which have some missing data
why is the assumption of normality important?
What is the relationship between sample size and objective methods of testing normality (e.g. Kolmgorev-Smirnov and Shapiro-Wilks, and ratio skewness)
the larger your sample, the more likely you are to generate a smaller p-value and reject the null hypothesis (which is to state you would be rejecting that the assumption of normality). The irony is as you increase the normality, the less you care about normality.
I have N = 356, and my Shapiro-Wilks value is p < .001? Does this mean I should reject the null (which is rejecting assumption of normality?).
No. As your sample size increases past 30 the p value gets smaller and smaller for your assumption of normality. Therefore the larger your sample, the less concerned you should be about this statistic.
Difference between normality plot and detrended normality plot for normal data...
normality QQ plot is a straight line, de-trended becomes more scattered the more normal the data is.
if you need to Log 10 males, do you need to do same with females?
Yes. if you do one transformation you will need to do the same for the other group.
what is the assumption of homogeneity of variance?
Homogeneity or equality of variance compares the variance between the two or more groups. important only when you have more than one group of participants.
How do you assess normality when you have different groups? That is, do you examine the overall sample or each individual group? Why?
You examine the overall sample to check whether it follows a normal distribution or bell curve. Sample data come from a population that is normally distributed. This assumption is the shape of the sample distribution that is taken from the population.
What is a common transformation used to deal with violation of the homogeneity of variance assumption?
power transformation. can find this on spread and level plot.
For HOV, when should you use transformed data and when should you use untransformed data?
You use untransformed data when a Levene's test reveals a p>.05 (retain the null that the assumption of homogeneity of variance is met). When Levene's test generates p<.05, reject the null, that means assumption of HOV is violated. They are different. Use power transformation, use transformed variables to run another Levene's test.
For HOV, do you divide into separate groups (e.g. males and females on each of day 1, 2 and 3?)
In HOV you need to separate according to sex (put into factor list). E.G. Hygiene day 1: p value = .03. Smaller than .05. Must reject the null hypothesis. Null was no difference between average amount of variance in males vs females for hygiene on day one. Reject - that means assumption of HOV is violated. They have different variance.
de-trended QQ plot - a subjective check of normality
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