PRINCETON, N.J. -- Donald Trump's net favorable rating among Republicans increased significantly over the past two weeks, putting him among the top six Republicans overall on this measure. Ted Cruz's image also improved, while Carly Fiorina's and Ben Carson's images remain significantly better than they were before the Aug. 6 debate. John Kasich, Jeb Bush and Scott Walker are among those whose images worsened.

These results are based on a comparison of Gallup Daily tracking across four two-week time periods, from mid-July to Sept. 1, with about 1,000 Republicans and Republican-leaning independents rating each candidate in each period. The complete data are presented at the end of this article.

The chart below displays how well-known (net familiarity, shown on the horizontal axis) and how well-liked (net favorability, shown on the vertical axis) each candidate is in the most recent two-week interviewing period.

Candidates in the upper-right section of the graph have above-average familiarity and above-average net favorable ratings, which is optimal from a candidate campaign perspective. Those in the lower-right section are better-known but less well-liked, signifying an inability to translate familiarity into positive affect. Those in the upper-left section are not as well-known but tend to be better-liked, making their major challenge one of becoming better known. And those in the lower left are behind on both dimensions, although some like Kasich and Santorum are just slightly below average on each dimension.

Here are some key insights based on how Republicans view the candidates today and how these views have changed over time:

Donald Trump: Trump's net favorability rating among Republicans climbed 16 points over the last two weeks. This marks a significant shift; Trump's image previous to the last two weeks had been relatively stable despite the extraordinary media attention his candidacy has engendered. He now joins Fiorina and Carson as having chalked up the largest gains on this dimension since mid-July. Trump had near-universal name identification when Gallup tracking began in July, and he retains the distinction of being the best known of the candidates. Still, even with his significant image gains, Trump remains sixth on the net favorability list, trailing Carson, Fiorina, Rubio, Cruz and Huckabee.

Ted Cruz: The Texas senator's net favorable rating ticked up seven points in the last two weeks, less than Trump's, but still a significant gain. Cruz now has the third-highest net favorable rating of any candidate, and his familiarity, at 69%, is above average.

Carly Fiorina: Although she was relegated to the earlier "Happy Hour" Fox News debate on Aug. 6, Fiorina received positive reviews for her performance, and the gains she saw after the debate have continued in the last two weeks. Her net favorable score is now 37, up five points from the Aug. 5-18 time period, and up 14 points since mid-July. Her familiarity is also up 14 points over the past eight weeks. CNN, the sponsor of the next Republican debate on Sept. 16, recently made the decision to change its inclusion criteria for the main debate in a way that almost certainly will allow Fiorina to participate. This may help the former Hewlett Packard CEO become even more familiar to Republicans -- important to her campaign given her still-below-average familiarity rating of 53%. Her current net favorable score puts her in the top five for all candidates.

Ben Carson: The former neurosurgeon has the distinction of holding the highest net favorable rating, 51, of any of the 17 GOP candidates. Carson, like Fiorina, saw a jump in his net favorability and familiarity after the debate, and he has held on to those gains. Carson's familiarity rating of 63%, however, is still only average.

Jeb Bush: Unlike Trump, Bush has not been able to translate his high name identification to his advantage. Bush is the second-best-known of the candidates, but the former Florida governor has had a bad summer in terms of his image -- with a six-point drop in his net favorable score in the last two weeks. Bush's slide puts him just below average on the image dimension, behind eight of his competitors.

Rick Perry, Lindsey Graham and Rand Paul: All of these candidates' net favorable scores have dropped over time. For Graham, this adds insult to injury. He is now the lowest rated candidate at -13, one of three candidates bottoming out in negative territory, along with George Pataki and Jim Gilmore. The path for Perry and Paul has been different. Both had much higher favorability scores in July. Despite Perry's image taking a big hit, it remains essentially tied with Bush's -- just below average. Paul's favorability, on the other hand, is now well below average at 11.

Marco Rubio and Mike Huckabee: Their net favorability and familiarity have not changed much, but both are still well-positioned image-wise, with above-average scores on both dimensions. They join Cruz and Trump as the four candidates in the positive, upper-right quadrant of the standings -- enjoying both above-average favorability and above-average familiarity.

Chris Christie: The New Jersey governor is notable for his high familiarity, and is third only to Trump and Bush in that regard. But his net favorable score has never been high, and is now at zero -- meaning that as many Republicans have an unfavorable opinion of the controversial governor as have a favorable opinion. At this point, Christie ranks among the least-liked candidates.

John Kasich: Although he didn't officially announce he was running for president until July 21, Kasich has made greater gains in familiarity than any other candidate, with his familiarity score shooting up from 34% in mid-July to 51% over the past two weeks. Unfortunately for the Ohio governor, his net favorability score -- after rising significantly in the period immediately after the debate -- has dropped again over the past two weeks, and he is now essentially back to where he started. Kasich's trajectory is clearly distinct from that of Carson and Fiorina, who also gained familiarity, but who, unlike Kasich, also gained significantly in net favorability.

Bottom Line

The last two months have seen widespread campaigning, media coverage, a highly watched debate and -- particularly in the case of Donald Trump -- continuing controversy. Tracking changes in each candidate's familiarity and favorability provides a valuable gauge of how all of this is playing out in the minds of the Republican audience.

Despite some political analysts' expectations that Trump's bombastic style and controversial statements could begin to weaken his standing among Republicans, the businessman and TV personality's net favorable score has actually jumped over the past two weeks, and he is now in a much stronger position image-wise than in mid-July. From a broad perspective, these data show no signs yet of an overall backlash among rank-and-file Republicans to his campaign, style or issue positions.

Jeb Bush has begun to criticize Trump directly in videos and speeches, reflecting his campaign's awareness of Trump's standing and Bush's own weakening position. Trump has fought back, and the two best-known candidates are now in a verbal shoving match of sorts. How effective Bush's ads, speeches and appearance in the Sept. 16 debate will be in slowing down Trump's momentum remains to be seen. At this point, the paths of the two best-known candidates have clearly diverged, with Trump going up and Bush going down.

Another group of candidates, including Rubio, Cruz, Huckabee and, to a lesser degree, Walker, started off with positive images but have yet to show signs of significant improvement like Fiorina, Carson or Trump.

The first Republican debate in early August enjoyed extremely high ratings and resulted in significant changes in how Republicans viewed a number of the candidates. The debate on Sept. 16 is the next major milestone in the long, expensive and arduous trek toward the first actual votes to be cast next February.

Survey Methods

Results for this Gallup poll are based on telephone interviews conducted July 8-Sept. 1, 2015, on the Gallup U.S. Daily survey, with a random sample of 13,996 Republicans and Republican-leaning independents, aged 18 and older, living in all 50 U.S. states and the District of Columbia. Each candidate was rated by a random subset of respondents during this period, with the sample sizes rating each candidate averaging about 1,000 Republicans and Republican-leaning independents within each two-week interviewing period.

For results based on the total sample of Republicans and Republican-leaning independents, aged 18 and older, rating each candidate at each time period, the margin of sampling error is ±4 percentage points at the 95% confidence level. All reported margins of sampling error include computed design effects for weighting.

Each sample of national adults includes a minimum quota of 50% cellphone respondents and 50% landline respondents, with additional minimum quotas by time zone within region. Landline and cellular telephone numbers are selected using random-digit-dial methods.