Question

As you can see from this equation, the value of t becomes larger as the difference between the means becomes larger, or the standard error of the difference in the means becomes smaller For example, consider two groups of data with the following parameters Group Mean 20 10 Sample variance 10 10 Sample size In this case 20-10 10 10 10 2+2 The last thing we need to calculate is known as the degrees of freedom, which is defined as the sum of the two sample sizes minus 2. In this example, the degrees of freedom is 5 +5-2 8 With this value of t calculated, we can then determine if our value exceeds a critical level of t and therefore whether the means are significantly different. We can find the critical value of t from a statistical table. If you look at the t-table in the "Statistical Tables" section at the back of this book, you can find the column that uses an alpha value of 0.05 and then find the row that contains 8 degrees of freedom. The critical t-value is the number found in this row and column. In this case, the critical t-value is 2.3. Because our calculated t-value exceeds the critical t-value, we can conclude that the two means differ significantly. YOUR TURN For the following data, calculate the t-value Group Mean 10 5 Sample variance 4 4 Sample size Next calculate the degrees of freedom. Based on your calculated t-value and the critical t-value using a 0.05, determine if the two groups are significantly different.

Answer 1

By using the given formula for t

t = (10-5) / $\sqrt{}$ (4/8)+(4/8)

t= 5/1

t=5

calculated t-value =5

degrees of freedom = sum of two sample sizes -2

degrees of freedom = 8+8-2

degrees of freedom = 14

The critical t- value for degree of freedom 14 is 2.14

but our calculated t- value is 5 which exceeding the critical t- value. so we can conclude two means are different significantly