Document_ID:2020-07-24_06:57:50_UTC_T-TEST

Welcome to OLSPS Statistical Interpreter brought to you by OLSPS. This easy to read report was created to help you understand the analysis, and provide further guidance through your data project.

A t-test is typically used when one needs to compare the mean of a variable to a test value. The following hypotheses were tested:

Null Hypothesis: |
The mean of the variable is equal to 53. |

Alternative Hypothesis: |
The mean of the variable is not equal to 53. |

The hypotheses were tested on the following variable:

- Age in years

The output from SPSS Statistics is summarised in two tables titled ‘One-Sample Statistics’ and ‘One-Sample Test’. The following sections elaborate on the results in these tables.

The table titled ‘One-Sample Statistics’ reports some descriptive statistics about each of the variables, including the number of observations, the mean, standard deviation, and the standard error of the mean.

**N -** N is the number of observations of the selected variable in the dataset. For example, the number of observations for ‘Age in years’ is 850.

**Mean -** The mean, or average, is one of the measures of central tendency that indicates where the data are centred. For example, the mean for ‘Age in years’ is 35.03.

**Standard Deviation -** The standard deviation of a variable gives an indication of how observations in the dataset are dispersed around the mean. If a variable has a low standard deviation then the observations of the variable are less spread out, and closer to the mean of the variable. However, if a variable has a high standard deviation, then the observations will be more spread out. For example, the standard deviation for ‘Age in years’ is 8.041.

**Standard Error of the Mean -** The standard error of the mean estimates the variability among the different sample means for a given variable. The means of multiple samples of the dataset will form a distribution, of which the standard deviation will be the standard error of the mean. If the standard error of the mean for a dataset is low, then the estimate of the population mean will be more precise. A dataset with a larger sample will result in a lower standard error of the mean. For example, the standard deviation for ‘Age in years’ is 0.276.

Of the tables presented, the ‘One-Sample Test’ table is the most important as it reports the t-test results.

**t -** The t statistic is used to test the difference between the sample mean of the selected variable and a test value. This value is reported as -65.154 and can be further interpreter with the use of the ‘Sig.’ value.

**df -** The degrees of freedom of an estimate is the number of independent pieces of information that were used in calculating the estimate. There are 849 degrees of freedom for this analysis.

Here the t-test analysis produced both the p-value and confidence interval. One can use either of these measures to determine whether the results are statistically significant. The results will correspond provided the same confidence level is applied to the tests. Note, however, if different test thresholds were used it is possible to obtain different results.

**Sig (2-tailed) -** The two-tailed significance value represents the p-value, or calculated probability, which is the probability of finding an absolute value equal to, or more extreme than, the observed value assuming the null hypothesis is true. The predefined significance level, \(\alpha\), is the probability of rejecting the null hypothesis when it is true. Traditionally, \(\alpha\) is either set to 0.05 or 0.01, although the choice of level is largely subjective. This is a two-tailed test, so the statistical significance is being tested in both directions. This means that the \(\alpha\) is used to test the significance in each direction. Using a 0.05 level, a p-value less than 0.05 is considered statistically significant and therefore the null hypothesis is rejected. A p-value larger than 0.05 is considered to not be statistically significant and it is argued the null hypothesis is not rejected. In the output, the p-value of ‘Age in years’ is 0. This is interpreted as saying there is a 0% probability of observing a mean of 53 for ‘Age in years’ assuming that the null hypothesis is true.

**Mean Difference - ** The ‘Mean Difference’ is the difference between the variables mean value and the test value. The calculated mean difference is -17.971.

**95% Confidence Interval of the Difference -** The confidence interval is a range of values that are calculated from a given dataset. The 95% confidence interval represents the range of values that has a 95% chance of containing the population ‘mean difference’. This is referred to as the 95% confidence interval. The lower bound of this confidence interal is -18.51 while the upper bound is reported to be -17.43.

In conclusion, since the confidence interval for ‘Age in years’ does not contain 0, the variable mean and test values differ significantly and so the null hypothesis cannot be accepted. Furthermore, since the p-value is less than 0.05 for ‘Age in years’ it is concluded with 95% confidence that the difference between the variable’s mean and 53 is statistically significant (because p-value < 0.05), and the null hypothesis is rejected.