Pooled Standard Error Spss
Contents |
performs t-tests for one sample, two samples and paired observations. The single-sample t-test compares the mean of the sample to a given number (which you supply). The independent samples t-test compares the difference in the means how to find p value in spss from the two groups to a given value (usually 0). In other words, it how to interpret one sample t test results in spss tests whether the difference in the means is 0. The dependent-sample or paired t-test compares the difference in the means from the two how to interpret independent t-test results spss variables measured on the same set of subjects to a given number (usually 0), while taking into account the fact that the scores are not independent. In our examples, we will use the hsb2 data set.
Spss Paired T Test
Single sample t-test The single sample t-test tests the null hypothesis that the population mean is equal to the number specified by the user. SPSS calculates the t-statistic and its p-value under the assumption that the sample comes from an approximately normal distribution. If the p-value associated with the t-test is small (0.05 is often used as the threshold), there is evidence that the mean is different from the hypothesized value. If the p-value pooled standard deviation calculator associated with the t-test is not small (p > 0.05), then the null hypothesis is not rejected and you can conclude that the mean is not different from the hypothesized value. In this example, the t-statistic is 4.140 with 199 degrees of freedom. The corresponding two-tailed p-value is .000, which is less than 0.05. We conclude that the mean of variable write is different from 50. get file "C:\hsb2.sav". t-test /testval=50 variables=write. One-Sample Statistics a. - This is the list of variables. Each variable that was listed on the variables= statement in the above code will have its own line in this part of the output. b. N - This is the number of valid (i.e., non-missing) observations used in calculating the t-test. c. Mean - This is the mean of the variable. d. Std. Deviation - This is the standard deviation of the variable. e. Std. Error Mean - This is the estimated standard deviation of the sample mean. If we drew repeated samples of size 200, we would expect the standard deviation of the sample means to be close to the standard error. The standard deviation of the distribution of sample mean is estimated as the standard deviation of the sample divided by the square root of sample size: 9.47859/(sqrt(200)) = .67024. Test statistics f. - This identifi
1. Check any necessary assumptions and write null and alternative hypotheses.There are two assumptions for the following test of comparing two paired sample t test spss interpretation independent means: (1) the two samples are independent and (2)
Spss Independent T Test
each sample is randomly sampled from a population that is approximately normally distributed.Below are the possible null
Spss Output Interpretation
and alternative hypothesis pairs:Research QuestionAre the means of group 1 and group 2 different?Is the mean of group 1 greater than the mean of group 2?Is the http://www.ats.ucla.edu/stat/spss/output/Spss_ttest.htm mean of group 1 less than the mean of group 2?Null Hypothesis, \(H_{0}\)\(\mu_1 - \mu_2=0\)\(\mu_1 - \mu_2=0\)\(\mu_1 - \mu_2=0\)Alternative Hypothesis, \(H_{a}\)\(\mu_1 - \mu_2 \neq 0\)\(\mu_1 - \mu_2> 0\)\(\mu_1 - \mu_2<0\)Type of Hypothesis TestTwo-tailed, non-directionalRight-tailed, directionalLeft-tailed, directional2. Calculate an appropriate test statistic.This will be a ttest statistic. The calculations for these test statistics can get quite https://onlinecourses.science.psu.edu/stat200/node/60 involved. Below you are presented with the formulas that are used, however, in real life these calculations are performed using statistical software (e.g., Minitab Express).Recall that test statistics are typically a fraction with the numerator being the difference observed in the sample and the denominator being the standard error.The standard error of the difference between two means is different depending on whether or not the standard deviations of the two groups are similar.Pooled Standard Error Method (Similar Standard Deviations) If the two standard deviations are similar (neither is more than twice of the other), then the pooled standard error is used: Pooled standard error\[s_p \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}\]\(s_p\) = pooled standard deviation Pooled standard deviation\[s_p=\sqrt{\frac{(n_1-1)s_1^2 + (n_2-1)s_2^2}{n_1+n_2-2}}\] Test statistic for independent means (pooled)\[t=\frac{\bar{x}_1-\bar{x}_2}{s_p \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}\]Degrees of freedom for independent means (pooled)\(df=n_1+n_2-2\)Unpooled Standard Error Method (Differing Standard Deviations)If the two standard deviations are not similar (one is more than twice of the other), then the unpooled standard error is used: Unpooled standard error\( \sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}\)Test statistic for independ