Significance Testing: One-Sample T-Test

What is the central limit theorem and when can it be used?

The CLT says that regardless of the shape of the population raw score distribution, the following is true: The larger the "N" of one's sample, the greater the degree to which the sampling distribution of the mean approaches normality.

What do we include in our writing when we are assessing for normality?

1) KS- test 2) Skewness and kurtosis 3) Histogram - mention (unimodal or bimodal) 4)Normal Probability plots (normal and detrended) 5) Measures of central tendency (mean, median, mode) 6) Measures of dispersion (SD, variance, range, and interquartile range) 6) CLT- if sample size is 30 or more.

What are the assumptions for a One-sample t-test?

1) Normality 2) Central Limit theorem 3) Independence within the Sample

What are the steps when conducting a One- t-test?

1) state null hypothesis (i.e"IN THE POPULATION, the mean ___ = a specified value.) 3) state the alternative hypothesis (i.e "IN THE POPULATION the mean _____ does not equal a specified value. 2) Check for normality (9 things I need to report). 2) calculate your t-critical. (t = sample mean - population mean/ s/square root of n). 3) run your t-test 4) Check to see where your t-statistic from tests you run, whether it fall into the area of rejection or not. 5) look at p-values for significance.

What is an example of a t-test?

A neurologist is testing the effect of a new drug on response time by injecting 100 rats with a dose of the drug. The mean response time for rats not injected with the drug is 1.2 seconds. The mean response time for rats that were injected with the drug is 1.05 seconds. The mean

What is a One- Sample t-test?

A one sample t-test compares the mean of a population against a specified value (given in problem). In other words, we have a specified value against which we are comparing the population parameter (mean).

What are the steps for conducting a One- sample T-test on SPSS?

Analyze> Compare means> One sample t-test> enter your hypothesized population value into the test value> enter the variable name? and click okay.

How do we assess normality of data of a one sample t-test?

Assess with measures of central tendency, K-S test, histogram, and normality graphs. and CLT may be considered as well,, depending on the circumstances.

Can you state the various hypothesis for a One-sample t-test in english?

Ha: THE POPULATION MEAN does not equal the specified value. (2-tailed) Or Ha: THE POPULATION MEAN is greater than/ less than a specified value. (Ha: M > value or M< value).

What is the Null hypothesis for a One sample t-test?

It is Ho: M = Specified value Ha: M doe snot equal a specified value. (two- tailed) OR Ha: M> specified value (right side table) Ha: M< specified value (left sided)

Graphs what does the K-S test do?

It tells us whether the data is statistically significantly different from a normal distribution. Ha: sample distirbution equal to that of a ND Ho: sample distirbution stat sig different than ND. Here we want to retain the null (p>0.05) so that we conclude that our sample scores are normally distributed as in the population.

What are some examples on how we could report whether the assumptions of normality have been meet when analyzing our Normal Probability Plot?

Our normal probability plot shows an equal number of scores both above and below the best fit line. These scores hug the best fit lines, with some minor deviations toward the upper end of the tail. Overall scores fall in linear pattern close to the line of fit and thus assumptions for normality are met. - the normal probability does not show scores that hug around the best fit line, but rather shows a strong non-linear relationship pattern. Specifically, it shows a quadratic bowed-down pattern. this quadratic bowed down pattern is indicative of a negatively skewed data set. Therefore the assumptions for normality are not met.

What is the assumption of normality for a One-sample t-test?

Scores of the variable being studied are normally distributed IN THE POPULATION. 2) Independence within the sample (no connection amongst the scores obtained) - have faith that researchers considered the assumption of independence when designing the study.

What are the general interpretations of a normal probability plot?

Skewness: Postive skewness is bowed upward and Negative skewness is bowed downward> Kurtosis: Leptokurtic - heavy clustering in the center, gaps and then heavy tails. Platykurtic-

What is the rule of thumb for use of CLT?

The greater the non-normality, the larger the "N" needs to be in order for the CLT to counteract it. 2) if N is roughly symmetrical and unimodal and N is at least 30, CLT will allow us to use a parametric test. 3) Do not have to invoke CLT unless other normality tests are suggesting that the distribution is not normal, and sample size bigger than 30. ** Does not hurt to mention it as long as N is really large!

What are some examples on how we could report whether the assumptions of normality have been meet when analyzing the histogram?

The histogram shows a unimodal distribution that is slightly skewed to the left, but for the most part appears to be normally distributed. The histogram represents a multimodal negativley skewed distirbution which deviates from that of a normal distribution.

How do we interrupt, in words, the K-S test when assessing normality?

The k-test is significant (p<.05) suggesting that the assumptions of normality have not been met.

How do we interpret Skewness in words, when assessing for normality?

The skewness statistic (______) divided by it's standard error falls within the normal z- interval of -3 and 3, thus normality can be assumed.

What is an example on how we would report whether the assumptions of normality are met or not?

When addressing our measures of central tendency we notice that mean (89.3

So when do we want to use a One-Sample T-test?

When we want to test the hypothesis that the population mean is equal to a particular value and when you don't know the standard deviation of the population.

How do we interpret kurtosis in words, when assessing normality?

the distribution is leptokurtic in nature, with scores clustering in the center and at the tails. This leptokurtic distribution is indicate of a positive Similarly kurtosis statistic (______) divided by its standard error, gives us a z-score of ____, which falls in between the normal z-score range of -3 and 3, which is consistent with the assumptions of normality.

What is the purpose of a one sample t-test?

we want to draw conclusions about the population from which our sample is drawn. A significance test allows us to make an inference about the value of a population parameter.