Hi Muhammad
Typically a t-test is used to examine the differences between the means of two groups. For example, in an experiment you may want to compare the overall mean for the group on which the manipulation took place vs a control group.
However, if you have more than two groups, you shouldn't just use multiple t-tests as the error adds up (see familywise error) and thus you increase your chances of finding an effect when there really isn't one (i.e. a type 1 error). Therefore when you have more than two groups to compare e.g. in a drugs trial when you have a high dose, low does and a placebo group (so 3 groups), you use ANOVA to examine whether there any differences between the groups.
To examine whether there are differences between the groups you would use the F-ratio, which essentially measures the improvement due to fitting the model i.e. the group means versus the grand mean of scores for all participant and compares this against the error remaining in the model, which is the difference between the actual scores and the respective means of the groups. Therefore, the F-test is the ratio of systematic variance : unsystematic variance, so higher scores are better.
Going a little beyond your question, an ANOVA only tells you that there are differences between your groups, not where they lie. Therefore you would use a priori contrasts to test hypothesised differences between the groups or post-hoc tests to examine where the differences lie.
Perhaps this video may be useful to you as an intro.
https://www.youtube.com/watch?v=SULO2-gjZoY
Regards
Tom
Hi Muhammad
Typically a t-test is used to examine the differences between the means of two groups. For example, in an experiment you may want to compare the overall mean for the group on which the manipulation took place vs a control group.
However, if you have more than two groups, you shouldn't just use multiple t-tests as the error adds up (see familywise error) and thus you increase your chances of finding an effect when there really isn't one (i.e. a type 1 error). Therefore when you have more than two groups to compare e.g. in a drugs trial when you have a high dose, low does and a placebo group (so 3 groups), you use ANOVA to examine whether there any differences between the groups.
To examine whether there are differences between the groups you would use the F-ratio, which essentially measures the improvement due to fitting the model i.e. the group means versus the grand mean of scores for all participant and compares this against the error remaining in the model, which is the difference between the actual scores and the respective means of the groups. Therefore, the F-test is the ratio of systematic variance : unsystematic variance, so higher scores are better.
Going a little beyond your question, an ANOVA only tells you that there are differences between your groups, not where they lie. Therefore you would use a priori contrasts to test hypothesised differences between the groups or post-hoc tests to examine where the differences lie.
Perhaps this video may be useful to you as an intro.
https://www.youtube.com/watch?v=SULO2-gjZoY
Regards
Tom
I was writing the same as Tom has written. A 't' test does not allow for more freedom and is confined to compare two groups. However, ANOVA has more independence and can be used between two groups as well as more than two groups and will help you in measuring the variance from the mean for each group.
Hi Jon
Taking what you have said at face value - you would typically use a t-test to compare two means (although it doesn't really matter) - attached is an example write up for both a t-test and anova.
Cheers
Tom
YOU CAN ALSO READ THIS:
A z-test is used for testing the mean of a population versus a standard, or comparing the means of two populations, with large (n ≥ 30) samples whether you know the population standard deviation or not. It is also used for testing the proportion of some characteristic versus a standard proportion, or comparing the proportions of two populations.
Example:Comparing the average engineering salaries of men versus women.
Example: Comparing the fraction defectives from 2 production lines.
A t-test is used for testing the mean of one population against a standard or comparing the means of two populations if you do not know the populations’ standard deviation and when you have a limited sample (n < 30). If you know the populations’ standard deviation, you may use a z-test.
Example:Measuring the average diameter of shafts from a certain machine when you have a small sample.
An F-test is used to compare 2 populations’ variances. The samples can be any size. It is the basis of ANOVA.
Example: Comparing the variability of bolt diameters from two machines.
Matched pair test is used to compare the means before and after something is done to the samples. A t-test is often used because the samples are often small. However, a z-test is used when the samples are large. The variable is the difference between the before and after measurements.
Example: The average weight of subjects before and after following a diet for 6 weeks
T-test and F-test are completely two different things.
1. T-test is used to estimate population parameter, i.e. population mean, and is also used for hypothesis testing for population mean. Though, it can only be used when we are not aware of population standard deviation. If we know the population standard deviation, we will use Z-test.
For eg. Suppose a data suggests that the average height of boys between 10-16 years in city X is 6 Feet. So, we want to test this hypothesis,whether the height of boys between 10-16 years in city X is less than, more than, or equal to 6 Feet. For doing so, we will take some samples, say 2000, and find out the height of boys between age 10 to 16 years. We will calculate the standard deviation of the 2000 boys, and calculate the t-statistic=
X bar = sample mean
u= pop mean
S= sample standard deviation
n= sample size
df= n-1
Once we calculate t-statistic, we will compare it with the critical value. Suppose, we takeα=.05, as it is two tailed test, α/2= .025, we then look at the table value for t, withdegrees of freedom =n-1, 2000-1, and α/2=0.25 which is=±1.96.
Once we get the t-value, we will compare whether our t-statistic is greater than +1.96 or less than -1.96. . If it is greater than +1.96 or less than -1.96, we reject the null hypothesis, which means, that the average height of boys in city X is not equal to 6 feet. If our t-statistic is between ±1.96, we fail to reject the null hypothesis, which means, that the average height of boys in city X is equal to 6 feet. This is when we conduct hypothesis testing.
2. We can also use t-statistic to estimate population mean:
Eg. Suppose,a large conglomerate like TCS(Indian IT company), which has employees more than 300,000. So, TCS wants to estimate average over time an employee works for the company, in a week. So, it is might not be possible to get required data(hypothetical situation, though these days it might be possible) from all employees. Therefore, the company takes a sample, say 3000, and finds the number of extra hours of work, employees have done in week. With the help of the sample mean and sample standard deviation; for the entire population- one can estimate the range of average number of extra hours of work, employees have done in week.
Confidence interval to find out the range= x̅±tα/2,n-1 *S/√n ≤Ų≤ x̅±tα/2,n-1* S/√n.
3. t-statistic is also used for finding out the difference in two population mean with the help of sample means.
For eg, suppose, if we want to understand buying behaviour of customers from two cities for a particular product. We want to understand whether there is any difference in buying behaviour in these cities,or is it similar.
F-statistic
Z statistic or t-statistic is used to estimate population parameters- population mean & proportion. It is also used for testing hypothesis for population mean or population proportion.
Unlike Z-statistic or t-statistic, where we deal with mean & proportion, Chi-square or F-test is used for finding out whether there is any variance within the samples. F-test is the ratio of variance of two samples.
Eg. Suppose, in a manufacturing plant there are 2 machines producing same products, and the management wants to understand, whether there is any variability among the products produced by these two machines. Researcher will take samples from both the machines and find out the variability, and test it against the null hypothesis, i.e. the prescribed limit.
F-statistic also forms the basis for ANNOVA.
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